Chapter_01.ipynb

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    "# Chapter 1: What is Risk? #\n",
    "&copy; 2022 Kenneth Winston\n",
    "\n",
    "Risk is **`lack of information about the future.`** A situation is risky if it has widely varying possible outcomes and there's no way to determine with high confidence which outcome will occur. A riskless or risk-free situation is one whose future is known exactly.\n",
    "\n",
    "We humans yield to no species in our ability to worry, so there is a tendency to focus on whether or not negative outcomes might impend. Indeed, most definitions of the noun \"risk\" stress the downside: for example, _the possibility of loss, injury, or other adverse or unwelcome circumstance_ is the first of several definitions of risk in the [Oxford English Dictionary](https://www.oed.com/view/Entry/166306).[$^1$](#one_endnotes) This is a gloomy strain of the more general definition above: a magnitude 8 earthquake is not a risk because we lack information about whether or not it will be enjoyable. It is a risk because we lack information about whether or not this unequivocally unpleasant thing will happen.\n",
    "\n",
    "Expressing your love for the first time to another person involves _the possibility of loss, injury, or other adverse or unwelcome circumstance:_ [the other person may reject you](https://www.cnn.com/2020/01/07/us/mount-holyoke-professor-attack/index.html).[$^2$](#one_endnotes) So why do people override their pounding pulses and stammer out their feelings? It is because the unknown future also includes positive outcomes: [the other person may return your affection](http://shakespeare.mit.edu/cleopatra/full.html).[$^3$](#one_endnotes) Declaring your feelings is a risky situation, but you do so because you hope that a good outcome will occur.\n",
    "\n",
    "The Oxford English Dictionary encompasses positive outcomes in alternative definition of risk: _A person or thing regarded as likely to produce a good or bad outcome in a particular respect. Ex.: 'The key to their success is information:\n",
    "on-the-ground knowledge of who is a good credit risk.'_\n",
    "The phrase \"good credit risk\" in the\n",
    "example indicates that the good outcome (getting paid back after extending credit) \n",
    "was considered more likely due to on-the-ground knowledge.\n",
    "\n",
    "The philosopher Karl Popper noted that for scientific theories,\n",
    ">Confirmations should only count if they are the result of **`risky predictions`**; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory&mdash;an event which would have refuted the theory.[$^4$](#one_endnotes)\n",
    "\n",
    "Popper thus captures the essence of this type of risk: a momentous choice about the future has to be made. A scientist has to make a risky prediction (emphasis added above) that can be proved right or wrong; a lender has to decide whether or not making a loan will probably result in repayment; a lover has to choose speech or silence.\n",
    "\n",
    "So in practice there are two kinds of risks:<a name=\"peril_vs_venture\"></a>\n",
    "- **`perils`**, where there are no positive outcomes. There is only (a) nothing happens; or (b) bad things happen. Earthquakes, fires, floods, hurricanes and other natural disasters are risks in this sense.\n",
    "- **`ventures`**, where there are both positive and negative outcomes. Investments &mdash; such as making loans &mdash; are risks in this sense.\n",
    "\n",
    "**Perils** are managed by avoidance (stay out of earthquake zones); fortification (build strong structures); and backstops (have emergency services and a pool of money ready to deal with the inevitable damage).\n",
    "\n",
    "**Ventures** require a more subtle approach, because both positive and negative outcomes have to be weighed against each other. Should I make a [conjecture](https://dl.acm.org/doi/abs/10.1006/jcta.1999.3054);[$^5$](#one_endnotes) extend credit; or declare my love? These are tough questions."
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    "## 1.1 Frank Knight's Formulation ##\n",
    "<a name=\"frank_knight\"></a>\n",
    "\n",
    "In 1921, Frank Knight &mdash; then an Associate Professor of Economics at the University of Iowa; later the influential head of the University of Chicago's economics department &mdash; wrote [_Risk, Uncertainty, and Profit_](http://www.econlib.org/library/Knight/knRUP.html).[$^6$](#one_endnotes)\n",
    "\n",
    "Knight delved into the philosophical nature of knowledge itself, but eventually got down to a very pragmatic list of ways in which we can organize our knowledge (or lack thereof) about the future (pp. 224-225):\n",
    ">1. **A priori probability**. ...[O]n the same logical plane as the laws of mathematics.<a><a name=\"knight_a_priori\"></a>\n",
    "2. **Statistical probability**. Empirical evaluation of the frequency of association between predicates.<a><a name=\"knight_statistical_probability\"></a>\n",
    "3. **Estimates**. [T]here is _no valid basis of any kind_ for classifying instances.<a><a name=\"knight_estimates\"></a>\n",
    "\n",
    "An example of something with _a priori_ probability is the throw of a perfect die. As Knight says, \"the mathematician can easily calculate the probability that any proposed distribution of results will come out of any given number of throws.\" That doesn't help anyone know which face will come up on the next throw of the die; probability theory is silent on that subject. But a priori probability is vocal about the fact that betting even money on the same face coming up 50 times in a row is a bad idea when the die is fair.\n",
    "\n",
    "A little less information about the future attaches to Knight's second category, _statistical probability_. An example here might be the chance that a 40-year-old male dies in the next year. Life insurance companies have gathered extensive statistics about mortality rates among 40-year-old males. As long as they have a sufficiently large pool of insureds, they can make a reasonable guess as to what to charge for insuring a 40-year-old male life. But there is no _a priori_ mathematical model as there is with the throw of a die.\n",
    "\n",
    "The final category has the least information. Here intuition must be used. Will my beloved return my affection if I declare it? There is no mathematical model, so the first category doesn't apply. Very few people have had the opportunity to build large databases of outcomes of their previous declarations of love, so the second category doesn't apply either. The terrified lover is left only with hunches.\n",
    "\n",
    "Knight condenses his three categories into two with this more succinct statement (p. 233):\n",
    ">To preserve the distinction which has been drawn... between the measurable uncertainty and an unmeasurable one, we may use the term \"risk\" to designate the former and the term \"uncertainty\" for the latter.\n",
    "\n",
    "## 1.2 Finite Probability Spaces\n",
    "\n",
    "At about the same time as Frank Knight was developing his ideas, the foundations of modern probability theory were being constructed by people like &Eacute;mile Borel, Henri Lebesgue, and Andrey Kolmogorov. But Knight's formulation is amenable to a simple finite treatment.\n",
    "\n",
    "For his \"risk\" (measurable) category, he assumed a finite number of future outcomes $s_1,\\dots, s_n$ and a known set of associated probabilities $p_1, \\dots, p_n$ (where $\\sum_{i=1}^n p_i = 1$ and each $p_i\\geq 0$). In the more general language of probability theory, $\\{s_1, \\dots, s_n\\}$ is the **`sample space`**, often denoted $\\Omega$.\n",
    "    \n",
    "Some probabilists treat finite and discrete probability spaces as the poor cousins of continuous probability spaces. But as Carlo Rovelli[$^7$](#one_endnotes) notes,\n",
    ">Continuity is only a mathematical technique for approximating very finely grained things. The world is subtly discrete, not continuous.\n",
    "\n",
    "It may be mathematically convenient to smooth out the world so that, for example, derivatives can be taken. But in fact Knight's \"simple\" finite formulation is sufficient to describe all states of the world that could arise in finance, or more generally in human experience.    \n",
    "    \n",
    "<a><a name=\"knightian_risk\"></a>An American roulette wheel is subject to what is now called **`Knightian Risk`**. Such a wheel has 38 outcomes ($s_i$ = the ball falls in the slot numbered i for $i=1,\\dots,36$; $s_{37}$ = the ball falls in the slot labeled 0; and $s_{38}$ = the ball falls in the slot labeled $00$.) So the roulette sample space is\n",
    "\n",
    "$$\\Omega_{roulette} = \\{s_1, \\dots, s_{38}\\} = \\{1, \\dots, 36, 0, 00\\} \\label{eq:sampleroulette}\\tag{1.1}$$\n",
    "\n",
    "Every slot is equally likely, so $p_i=\\frac{1}{38}$ for $i=1,\\dots,38$.\n",
    "\n",
    "Casinos make money on their roulette wheels, just as they do at their dice tables. In both cases, bettors can wager on _events,_ which are combinations of outcomes. For example, in American roulette a bettor can place a bet on \"even,\" which pays off if the future outcome lies in the event\n",
    "$$E=\\{s_2,s_4,\\dots,s_{36}\\} \\label{eq:evenevent}\\tag{1.2}.$$\n",
    "Note that neither $s_{37}$ nor $s_{38}$ (neither 0 nor double-0) is contained in E. So the sum of the probabilities associated with the event E is only $\\frac{18}{38}\\approx47.4\\%$\n",
    "\n",
    "If you bet on even and it occurs, you get two dollars for every dollar you bet. If even doesn't occur you lose the money you bet and you get nothing. The expected value of a dollar bet is $\\frac{18}{38}*2+\\frac{20}{38}*0=18/19,$ meaning the casino expects to make 5.2 cents for every dollar bet on the even event. Put another way, the casino charges a 5.2% fee [per 4 minutes](https://www.roulettelife.com/index.php?topic=358.0)[$^8$](#one_endnotes) to provide the entertainment of betting on the even event.\n",
    "\n",
    "Knightian Risk is amenable to simple probabilistic calculations like this.\n",
    "\n",
    "<span style=\"color:red\">**Perhaps the most common mistake made in financial mathematics is to forget that modeling the world of finance with Knightian Risk is a tactic, not a law.**</span>"
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    "## 1.3 Knightian Uncertainty ##\n",
    "\n",
    "Within the broad umbrella of risk=lack of information about the future, Knight identified a more difficult type: what he called \"unmeasurable,\" and what economists now call Knightian Uncertainty.\n",
    "\n",
    "**`Knightian Uncertainty`** means either\n",
    "* The sample space $\\Omega=\\{s_1,\\dots,s_n\\}$ is known, but the associated probabilities $p_1,\\dots,p_n$ are not; or\n",
    "* The sample space $\\Omega$ is not known.\n",
    "\n",
    "Declaring love is a situation where the outcomes are (broadly) known: acceptance or rejection. But there is _no valid basis of any kind_ to arrive at accurate probabilities.\n",
    "\n",
    "[Keynes 1937](https://doi.org/10.2307/1882087) gave examples of Knightian Uncertainty:\n",
    ">By \"uncertain\" knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty... The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealth owners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatsoever.\n",
    "\n",
    "In Keynes's examples, the outcomes of whether or not there will be \"a European war\" are known: yes or no. But the \"prospect\" (probability) is not. Or more precisely, in 1937 the probability _was_ not; now we know there was a European (in fact, World) war. But in 1937 some future states of the world contained a European war and some didn't. Eventually ([by September 3, 1939 when France and Britain declared war on Germany](https://www.history.com/topics/world-war-ii/world-war-ii-history#section_2)[$^9$](#one_endnotes)) there were no longer any future states of the world that didn't have a European war in them.\n",
    "\n",
    "Even deeper uncertainty attached to his last example, \"the position of private wealth owners in the social system in 1970\" &mdash; a date 33 years in the future from the time of his writing. Neither all the outcomes nor all the probabilities were known. Keynes was concerned about whether socialism, capitalism, or communism would prevail, but those broad groupings didn't constitute a precise and exhaustive listing of the outcomes, let alone guide the choice of associated probabilities.\n",
    "\n",
    "We can be quite certain that if the upper-crust Keynes had tried to list the possible outcomes for \"the position of private wealth owners in the social system in 1970,\" he would not have included the eventual reality. By then, a kind of socialist-tinged capitalism would be in place and one of the larger private wealth owners would be a 30-year-old commoner from Liverpool &mdash; [John Lennon of the Beatles](https://www.biography.com/musician/john-lennon).[$^{10}$](#one_endnotes) Such open-ended outcomes defy the tidy enumeration required for Knightian Risk to obtain.\n",
    "\n",
    "<span style=\"color:red\">**The financial world is a world of Knightian Uncertainty, not of Knightian Risk.**</span>\n",
    "\n",
    "Despite the fuzziness of Knightian Uncertainty, decisions have to be made. Freezing and doing nothing is a choice. This is the idea behind [Pascal's Wager](\n",
    "https://plato.stanford.edu/entries/pascal-wager/):[$^{11}$](#one_endnotes) \"Il faut parier.\" You have to make a bet: even not deciding is deciding.\n",
    "\n",
    "In many cases quantitative finance makes a first approach to problems by assuming that they can be described by Knightian Risk. However we must never forget that this is an approximation; a guide; a forensic tool to help frame our thinking and intuition as we make decisions about an uncertain future."
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    "## 1.4 Making risky decisions ##\n",
    "\n",
    "All the focus on classifying what may happen in the future is done so that decisions can be made about what to do now: Set the payoffs on a roulette wheel; Price a life insurance policy; Determine an interest rate for a loan to a good credit risk; Declare love or pine away, mute.\n",
    "\n",
    "In this chapter we'll describe a framework for thinking about how risky decisions are made. The framework will reflect the intuitively obvious fact that there are very few purely right or wrong answers; in many situations, personal preferences for safety vs. risk play an important role.\n",
    "\n",
    "For now, consider the following questions about what you might do in the risky situations described below. There aren't any tricks of logic you need to worry about: just answer what seems right to you."
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    "### 1.4.1 Reader Poll 1 - St. Petersburg Paradox ###\n",
    "<a name=\"saint_petersburg\"></a>\n",
    "\n",
    "The **`St. Petersburg paradox`** was posed by Nicolas Bernoulli in 1713. One resolution of the paradox was proposed by his cousin Daniel Bernoulli, who worked on the problem while he was a mathematics professor in St. Petersburg. D. Bernoulli's solution was published in 1738, although he probably wrote it around 1728.\n",
    "\n",
    "N. Bernoulli asked how much someone should pay to enter a doubling lottery.\n",
    "In N. Bernoulli's lottery, a coin is tossed. If it comes up heads, the participant gets $\\$2$ and the lottery is over. If it comes up tails, it is tossed a second time. If it then comes up heads, the participant gets $\\$4$ and the lottery is over. Otherwise there's a third toss with an $\\$8$ payoff if heads, and so forth, doubling the payoff every time. The lottery continues until the first head comes up. If the head comes up on the $i^{th}$ toss, the payoff is $\\$2^i$.\n",
    "\n",
    "N. Bernoulli pointed out that the expected value is infinite, since the probability of the lottery ending on the $i^{th}$ toss is $2^{-i}$. One might (anachronistically, since Knight was two hundred years in the future) label this Knightian Risk or [_a priori_ probability](#knight_a_priori), and evaluate all the outcomes and all the probabilities to find that the expected value to the participant of entering the lottery is\n",
    "$$\\sum_{i=1}^\\infty 2^{-i} 2^i = \\sum_{i=1}^\\infty 1 = \\infty$$\n",
    "\n",
    "The lottery is risky &mdash; you don't know which toss of the coin will be the first head &mdash; but unequivocally positive: you will get at least $\\$2$ if you enter it. So it seems sensible that you would pay at least $\\$2$ to enter, since you'll get that half the time, and more than that the other half of the time. But it seems just as sensible that you would not pay infinity, or even a very large portion of your personal wealth, to enter this lottery.\n",
    "\n",
    "We'll analyze this in more detail, but for now answer intuitively:\n",
    "\n",
    "**<span style=\"font-size:24px;\">How much would you pay to enter this lottery?</span>**\n",
    "\n",
    "Make a note of your answer &mdash; call it $A_{pete}$. We'll come back to it later."
   ]
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"
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"
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    "### 1.4.2 Reader Poll 2 - The Generous Billionaires ###\n",
    "<a name=\"generous_billionaires\"></a>\n",
    "\n",
    "You are walking down the street when you run into John D. Rockefeller and Andrew Carnegie, both of whom have a net worth well over $\\$100$ billion.\n",
    "\n",
    "![rockefeller-gettyimages-3324020-612x612.jpg](attachment:503579b2-55e0-421d-bbba-a1330ff614f3.jpg)\n",
    "![carnegie-gettyimages-104563620-612x612.jpg](attachment:b4c3f413-7870-46e8-946b-7fbd218d6374.jpg)\n",
    "\n",
    "\"Hello,\" Rockefeller says, \"We've decided to be generous to the next person we see, and that's you! But we have a disagreement about how to dispense our generosity. So we need you to decide between the following two offers:\"\n",
    "\n",
    "Carnegie says: \"My offer is very simple. I'm just going to give you this check for \\$500,000,000.\"\n",
    "\n",
    "Rockefeller says, \"But my offer is more interesting. I'm going to toss a fair coin – 50% chance of either heads or tails. If it comes up heads, I'll give you \\$1,000,000,000. But if it comes up tails, I'll give you nothing.\"\n",
    "\n",
    "**<span style=\"font-size:24px;\">You must choose only one. Decide whether you want to take Carnegie's offer (sure thing) or Rockefeller's offer (coin toss).</span>**\n",
    "\n",
    "Make a note of your answer (Rockefeller or Carnegie) &mdash; call it $A_{generous}$. We'll come back to it later."
   ]
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     "slide_type": "slide"
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   "source": [
    "### Changing Generosity ###\n",
    "\n",
    "If you chose Carnegie's offer (the check for $\\$500,000,000$):\n",
    ">Assume that Rockefeller's offer ($\\$1,000,000,000$ or 0 depending on coin toss) remains unchanged, but that Carnegie is only offering a check for $\\$400,000,000$. Would you still take the check? What about a check for $\\$200,000,000$? What about $\\$100,000,000$? At some point you will switch: presumably if Carnegie's offer is only $\\$0.01$, you'll take Rockefeller's coin toss instead. So where's your switching point, i.e what amount of sure check from Carnegie will put you just on the edge between that check and Rockefeller's billion-or-zero coin toss? Make a note of this number &mdash; call it $A_{switch}$.\n",
    "\n",
    "If you chose Rockefeller's offer (billion-or-zero coin toss):\n",
    ">Assume that Rockefeller's offer remains unchanged, but that Carnegie offers a sure check for $\\$1,000,000,000$. At that point you are always better off with Carnegie, so presumably you would take Carnegie's offer over Rockefeller. So somewhere on the way up between a Carnegie offer of $\\$500,000,000$ and a Carnegie offer of $\\$1,000,000,000$ you switched from Rockefeller to Carnegie. What is your switching point? Make a note of this number &mdash; call it $A_{switch}$."
   ]
  },
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8HFsUUvomNmRsyZOQ5E7cD1Hr1zqDkSY98iYns0OI4nE4mh0qx6IbORyIsT7N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\nUfKobnbJAMrLCbmaBzmCAmGlOprjF1Fx07Ri6c6fnVxvLly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=\n"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4.3 Reader Poll 3 - The Probabilistic Thug ###\n",
    "<a name=\"probabilistic_thug\"></a>\n",
    "\n",
    "You are walking down a dark street when you run into a thug pointing a gun at you.\n",
    "\n",
    "![thug-gettyimages-dv766052-612x612.jpg](attachment:77996757-91ce-4c80-96c5-46f6d29d0013.jpg)\n",
    "\n",
    "\"Hello,\" the thug says, \"Because I am a thug, I am going to do something that one might characterize as unequivocally negative.\"\n",
    "\n",
    "\"I'm going to give you a choice. In Option A, I will break one of your fingers.\"\n",
    "\n",
    "\"Ouch,\" you say.\n",
    "\n",
    "\"But I'm going to give you another choice. In Option B, I will toss a fair coin. If it comes up heads, you can leave unharmed. But if it comes up tails, I will break two of your fingers on the same hand.\"\n",
    "\n",
    "**<span style=\"font-size:24px;\">Which would you choose?</span>**\n",
    "\n",
    "Make a note of this number &mdash; call it $A_{thug}$. We'll come back to it later."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.5 Basic Economics Terminology ##\n",
    "\n",
    "While many of the concepts in this book were formulated by people who won Nobel Prizes in economics,[$^{12}$](#one_endnotes) this isn't an economics book and an economics background isn't necessary. Here we'll give a brief background on some of the rudimentary economics terms that we'll use.\n",
    "\n",
    "Let's start with a definition: **`Economics is the study of how people allocate resources under uncertainty.`** Resources include human effort, the results of human effort, and natural resources like water. Uncertainty here encompasses both Knightian risk and Knightian uncertainty. \n",
    "\n",
    "The sample spaces we will study will generally encompass a range of allocations of effort and resources. We will be focused on characterizing and dealing with the uncertainty of which allocations will be desirable and which allocations will be undesirable. That is, we will be concerned with the risks of allocation.\n",
    "\n",
    "<a><a name=two_person_economy></a>\n",
    "The allocation problem studied in economics is essentially a problem of human cooperation. Suppose there were only two people in the world; one a farmer and the other a hunter. The farmer alone may fail to survive a year in which the crop is infested by insects; the hunter alone may fail to survive a year in which game migrates elsewhere. But by pooling their efforts, they might survive on apples in a year when the crop is good and the hunting is bad. Next year perhaps the apple crop will be bad, but since they cooperated, the hunter will still be alive to bring in enough wild boar meat so they can both survive. By cooperating and diversifying their efforts, they can better deal with the unknowns of the future food supply. \n",
    "\n",
    "Diversification is central to the risk and portfolio management techniques that will be discussed in this book. Indeed, diversification is central to all of economics and human organization: it does far less good to allocate redundant resources than to allocate non-overlapping resources. We saw this same idea in Joseph Tainter's observation about the Mayan food supply diversification techniques cited in the Introduction.\n",
    "\n",
    "Current world population is about [$8$ billion](https://www.census.gov/popclock/).[$^{13}$](#one_endnotes) Human efforts have branched out far beyond farming and hunting. How is it decided which things should get done and which things shouldn't, and who should do what? How are the efforts of $8$ billion people choreographed?\n",
    "\n",
    "While [conspiracy theorists](https://www.merriam-webster.com/dictionary/conspiracy%20theory)[$^{14}$](#one_endnotes) believe otherwise, in fact there is no choreographer. There is no global central decision-making authority that allocates the efforts of the $8$ billion people in the world. On the other hand, it is not the case that each person is entirely free to decide what to do. Certainly not in totalitarian countries where a central authority dictates behavior, but not even in countries that are nominally free. The world has a spectrum of systems to allocate human effort ranging from highly centrally planned to highly distributed.\n",
    "\n",
    "While allocation systems vary widely in different parts of the world, virtually every economic system uses money as some part of the allocation process. If I wanted to become a professional opera singer, in most parts of the world there would be nothing preventing me from giving a recital where I promise to hit [all nine high C's](https://www.nytimes.com/2019/02/08/arts/music/review-metropolitan-opera-donizetti-fille-camarena.html)[$^{15}$](#one_endnotes) in the aria _Pour mon &acirc;me_ from Donizetti's _La fille du r&eacute;giment_. But since I have a terrible singing voice and wouldn't be able to hit a single one of them, no one would pay to attend my recital. If I devoted my efforts to giving recitals to which no one came, I would not have enough money for food, shelter or clothing. Through (the lack of) money, I would receive the signal that I have to reallocate my efforts to something more useful and less painful to others.\n",
    "\n",
    "Money isn't the only factor in allocation. If someone offers you a large amount of money to commit a crime, it is to be hoped that primarily ethics and secondarily fear of arrest will cause you to decline. So personal preferences and a moral, legal, and regulatory framework usually also play a big role in the allocation of effort.\n",
    "\n",
    "To see how money directs effort and resources, consider the four functions through which it acts:\n",
    "\n",
    "Most simply, money is a **`medium of exchange`**. In the two-person economy we imagined the farmer and the hunter exchanging apples and boar meat. But suppose you are a farmer in a larger economy: exchange and barter are far less efficient than selling apples for cash to (say) a professional online gamer who stops by your orchard, and then using the cash to buy boar meat from a butcher who is miles away from your apples. Money streamlines the process of exchanging the results of peoples' productive efforts.\n",
    "\n",
    "The second use of money is as a **`store of value`**. If you happen to be a great farmer and singlehandedly grow enough apples to feed 100 people for a year, you can convert the apples into money by selling them to many people. You can then use the money at a later time. For example, when you are too old to operate a farm, you will still be able to pay younger farmers and hunters to supply you with apples and boar meat. You have converted your very productive 100-people-year effort into money and stored it for the future.\n",
    "\n",
    "This ability to translate productive effort across time represents a spectacular advance in human cooperation. You were very successful growing apples &mdash; but that was 40 years ago. Your apples are long gone. But you can still get a young person to go out and get meat for you. That's because the young person trusts the money &mdash; the hunter can use your money to get someone else to do something for her, like programming a boar-finding app. Money is intersubjective: as long as everyone believes they can use it to get other humans to give them valuable efforts and resources at different times and places, it works.\n",
    "\n",
    "A related use of money is as a **`unit of account`**, where money is used to keep track of economic activity and balances. When we said above that the farmer grew enough apples to feed 100 people for a year, we were trying to give a sense of the volume of his output. But that's not a very precise amount &mdash; was it enough to feed 100 very large sumo wrestlers, or 100 very small horse racing jockeys? It would have been less vague to describe the farmer's output as (say) $\\$300,000$ worth of apples.\n",
    "\n",
    "Economists from Adam Smith to Ludwig von Mises to F. A. Hayek have argued that the ability to communicate information through prices is what allows the human race to function at its high level of coordination. This lofty assessment was expressed eloquently in [Hayek 1945](https://www.jstor.org/stable/1809376), where Hayek explains\n",
    ">The economic problem of society is... a problem of the utilization of knowledge not given to anyone in its totality. ...this problem can be solved, and in fact is being solved, by the price system.\n",
    "\n",
    "By the \"price system,\" Hayek meant the fact that relative values of productive (or produced) items can be communicated by prices. Hayek points out that a manufacturer using tin as an input doesn't need to be an expert on how the tin is produced; the manufacturer only needs to know that tin is a lot cheaper to use than (say) aluminum. This is a bit overstated as a temporary price advantage (due, say, to an aluminum mine shutting down for brief repairs) is different from a permanent price advantage. While the user of tin may not need to be an expert metallurgist, some knowledge beyond price is desirable. Still, price communicates volumes.\n",
    "\n",
    "On the other hand, the value of money can change over time; we'll show various ways in which this can happen in the discussion around Figure 3.1 in Chapter 3. Purchasing power adjustments might need to be made. Still, the use of money as a unit of account brings clarity to the activities of individuals like the farmer; to the activities of companies; to cities; and to nations. Money's unit of account function also allows unlike assets to be aggregated into a balance sheet showing the overall value of an enterprise.\n",
    "\n",
    "This unit of account function of money also allows economists to make quantitative models of human economic activity, either in Knight's [a priori](#knight_a_priori) or his [statistical](#knight_statistical_probability) probability category. \n",
    "\n",
    "Utility functions, which we'll study [below](#utility_theory), are part of an [a priori probability](#knight_a_priori) model that gives specific formulas for human decision-making. For example, a casino's study of the amount of money lost by an average customer is a [statistical model](#knight_statistical_probability) that might help it decide whether or not to hire more croupiers."
   ]
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    "## 1.6 Basic Capital Markets Terminology ##\n",
    "\n",
    "The fourth function of money is as **`financial capital`**. Generally, **`capital`** is an item that increases the effectiveness of human effort or natural resources. It could be a tool, like a backhoe to help the apple farmer dig up his field. It could be a municipality's public transport system, built to facilitate the flow of people and goods. Capital can even be **`human capital`** &mdash; say a professional opera singer's talent and years of training that make him a better singer than, certainly, me.\n",
    "\n",
    "In modern economies, many people have gotten beyond hand-to-mouth existence. They have money beyond what is needed to satisfy their current &mdash; and maybe even their future &mdash; wants. They can begin to use the money to gain control of resources and to direct the productive efforts of other people. When money is used in this way - to facilitate the production of something, rather than for current or future consumption - it falls under our definition of capital.\n",
    "\n",
    "For example, we imagined a farmer who had done well enough growing apples to buy meat not only now, but in his retirement years in the future. But beyond this, the farmer might have an idea for a better way to get meat: create a cattle ranch rather than hunt for it. Ranching domesticated cattle is vastly more efficient than hunting for wild animals. If the farmer has enough money after satisfying his present and future wants, he might start a cattle ranch and pay some other people to run the ranch for him. He hasn't quit his day job growing apples; he has invested money but not his direct productive effort in the ranch.\n",
    "\n",
    "Economists have argued for centuries over what exactly constitutes capital and who should benefit from it. At one end of the spectrum, capital's \"economic value merely represents the power of one class to appropriate the earnings of another.\"[$^{16}$](#one_endnotes) This kind of thinking leads to the banning or heavy restriction of private ownership of capital.\n",
    "\n",
    "The other end of the spectrum is simply called **`capitalism`**. There, the ownership of capital by private individuals is thought to foster innovation and progress. For example, our farmer is highly incentivized to come up with his cattle ranch idea and make sure that it works, since his money is at stake. So according to a capitalist, rather than appropriating his ranch employees' earnings, the farmer is creating jobs for them and increasing food production efficiency. That benefits everyone, except maybe the farmer's boar-hunting friend, who is put out of business by the new ranch technology. One hopes she can get one of the many new jobs created at the ranch.\n",
    "\n",
    "Neither pure idea works in practice: both the banning of private ownership of capital, and laissez-faire (literally \"let them do\" [whatever they want to do]) capitalism have been tried. Ironically they both seem to lead to a similar result &mdash; the untenable concentration of power in the hands of a few. An old Soviet joke (sometimes attributed to the economist J. Kenneth Galbraith) says \"Under capitalism, man exploits man. Under communism, it's just the opposite.\"\n",
    "\n",
    "Most economic systems in the world today consist of some form of regulated capitalism, aiming to get the benefits that come with private ownership of capital (motivation, innovation, and efficiency), while avoiding the pitfalls (concentration of power in the hands of a few plutocrats).\n",
    "\n",
    "Returning to the ranch-owning farmer: he might be initially successful with his cattle ranch but he might decide that he could make an even bigger, even more efficient, ranch if he had more money than he personally can raise. He might estimate that the ranch is currently worth $\\$100,000$, all of which he owns. But if he could get another $\\$25,000$ to buy more grazing land and cattle sheds, he thinks the value of the ranch will be even more than $\\$125,000$. So &mdash; noticing that the online gamer who keeps buying his apples appears to be prosperous &mdash; he might ask her if she's interested in owning a $20\\%$ portion of the ranch company in exchange for her investing $\\$25,000$ of new capital. If all goes well, the new $\\$25,000$ does indeed make the ranch better and it becomes worth (say) $\\$200,000$ overall. The farmer's share is now worth $\\$160,000$; the gamer's, $\\$40,000$. The farmer and the gamer have converted their skills in producing apples and winning games &mdash; together with a good idea about meat production &mdash; into even more money.\n",
    "\n",
    "Just as money's medium of exchange function allowed more efficient allocation of human effort than barter or direct exchange, there are more efficient ways of allocating capital than a farmer having a one-on-one talk with a gamer. A **`security`** is a claim on ownership of something. In the case of the ranch, the farmer initially owned all the stock in the ranch company; **`stock`** is a security that is a claim on ownership of a company. A **`share`** is a unit of stock; the total number of shares representing all of the ownership of a company can vary. For example at this writing the ownership of the world's largest company by revenue, Walmart, is divided into [2.8 billion shares](https://www.nasdaq.com/symbol/wmt/stock-report).[$^{17}$](#one_endnotes)\n",
    "\n",
    "Security markets allow more efficient exchange of capital. Instead of having to find a specific investor and make a one-off exchange of shares for money, the cattle ranch entrepreneur could list shares of his ranch company on a **`stock exchange`** and potentially have millions of investors from all over the world evaluating his company's prospects and deciding whether or not to direct capital to it.\n",
    "\n",
    "Other securities include **`commodity contracts`**, which are claims on ownership of natural resources, and **`bonds`**, which are claims on specific monies that are expected to be generated by an activity in the future.\n",
    "\n",
    "An investor in a company's stock participates along with the other stockholders in the company's success or failure. An investor in a company's bonds receives specific amounts at specific dates if the company is able to pay them, but doesn't receive anything over the agreed-on amounts if the company does well.\n",
    "\n",
    "In securities markets, you can use your stored human effort to direct the efforts of others. If the collective decisions made by everyone buying and selling securities are wise, then the productive efforts of much of the human race will be directed efficiently and the world will prosper and progress. If not, there will be a situation like the Great Depression of the 1920s and 1930s or the Great Recession of 2008 and after. Former Federal Reserve Governor Frederick Mishkin summed this up by saying\n",
    ">the financial system [is] the brain of the economy... It acts as a coordinating mechanism that allocates capital, the lifeblood of economic activity, to its most productive uses by businesses and households. If capital goes to the wrong uses or does not flow at all, the economy will operate inefficiently, and ultimately economic growth will be low. No work ethic can compensate for a misallocation of capital and the resulting failure to invest in the most profitable ventures. Hard work will not be productive unless it is accompanied by the right amount and kinds of capital.[$^{18}$](#one_endnotes)\n",
    "\n",
    "This book focuses on quantitative models for the risks inherent in investing in securities, particularly portfolios of securities. But we should never forget that securities are just placeholders for human effort and natural resources. All the mathematical models we will discuss ultimately need to have a sensible effect on the allocation of human effort and natural resources."
   ]
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    "## 1.7 Basic Probability Terminology ##\n",
    "<a name=\"basic_probability_terminology\"></a>\n",
    "\n",
    "It's assumed that you are familiar with probability theory. (If you're not, [Durrett 2013](https://services.math.duke.edu/~rtd/PTE/PTE4\\_1.pdf) is a good probability textbook.) This section is not meant to be a course in probability, but rather is a clarification of the terminology that will be used in this book. At the end of this section we will have built up enough terminology so we can try to apply a standard concept in probability to your [Generous Billionaires](#generous_billionaires) choice.\n",
    "\n",
    "Probability theory starts with a **`sample space`** $\\Omega$ that is the set of all things that can happen; i.e. all outcomes. For example $\\Omega$ might be the set $\\Omega_{roulette}$ of 38 American roulette outcomes defined in \\eqref{eq:sampleroulette} above.\n",
    "\n",
    "An **`event`** is a subset of the sample space, such as $\\{2,4,\\dots,36\\}$ representing the \"even\" event as in \\eqref{eq:evenevent}. The sample space can be continuous. In order to make both countable and uncountable sample spaces work sensibly, probability theorists insist that the set of all events be a **`sigma-algebra`** (denoted $\\sigma$-algebra). A $\\sigma$-algebra on $\\Omega$ is a collection of subsets of $\\Omega$ that (a) includes the empty set; (b) is closed under complement; and (c) is closed under countable union and intersection. The pair $(\\Omega,S)$ is called a **`measurable space`** when $S$ is a $\\sigma$-algebra of $\\Omega$; $S$ contains the **`measurable subsets`** of $\\Omega$.\n",
    "\n",
    "A **`probability measure p`** on a measurable space $(\\Omega,S)$ maps $S$ into the unit interval $[0,1]$ and satisfies p($\\emptyset$)=0 ($\\emptyset$ means the null set), $p(\\Omega)=1$, and\n",
    "$$p\\bigl(\\bigcup_{i} E_i\\bigr) = \\sum_{i} p_i \\tag{1.3}$$\n",
    "where the $E_i$ are a countable collection of pairwise disjoint events in S. A **`probability space`** is the triple $(\\Omega,S,p)$ of sample space, associated $\\sigma$-algebra, and associated probability measure.\n",
    "The probability $p(E)$ of an event $E\\in S$ is the event's **`unconditional probability`**. The probability of event A given that another event B happened is called event A's **`conditional probability`**.\n",
    "\n",
    "For example, if you throw an unweighted six-sided die, you know before looking that the probability that the number two came up is $1/6$. But suppose you throw the die and I look at the result before you do. I might tell you that an even number came up and ask you for the probability that the number was two. You now know the probability is $1/3$, not $1/6$. \n",
    "\n",
    "Formally the **`conditional probability`** of event E, given that event F has occurred, is written $p(E\\mid F)$, and by definition equals\n",
    "$$p(E\\mid F)=\\frac{p(E\\cap F)}{p(F)}\\label{eq:condprob}\\tag{1.4}$$\n",
    "In the example above, $F$ was the event that an even number came up ($p(F)=1/2$) and event $E$ was the number two coming up. ($p(E)=p(E\\cap F)=1/6$). So $p(E\\mid F)=\\frac{1/6}{1/2}=\\frac{1}{3}$.\n",
    "\n",
    "If (a) the sample space $\\Omega$ is finite or countably infinite; and (b) the $\\sigma$-algebra is the power set of $\\Omega$, then the probability measure is a **`probability mass function p`** that assigns a value $p(\\omega)$ to each $\\omega\\in\\Omega$, where $\\sum_{\\omega\\in\\Omega}p(\\omega)=1$. If (a) is true but not (b), then there are one or more probability mass functions that are compatible with the probability measure.\n",
    "\n",
    "For example, suppose $\\Omega$ consists of the six outcomes of the throw of a single die, and $S=\\{\\emptyset,\\{1\\},\\{2,3,4,5,6\\},\\Omega\\}$. A probability measure that assigns $\\frac{1}{6}$ to the event $\\{1\\}$ and $\\frac{5}{6}$ to the event $\\{2,3,4,5,6\\}$ is compatible with the usual mass function that assigns $\\frac{1}{6}$ to each outcome. It is also compatible with a mass function that assigns $\\frac{1}{6}$ to each of $1,2,3,4;$ assigns $\\frac{1}{3}$ to $5$; and zero to $6$.\n",
    "\n",
    "However for most practical applications, when $\\Omega$ is countable then the $\\sigma$-algebra is simply the power set of $\\Omega$. When the sample space is not countable, the probability measure $p$ will be defined on elements of the $\\sigma$-algebra but not necessarily on individual outcomes.\n",
    "\n",
    "For our purposes a **`random variable`** $X$ is a function that maps $\\Omega$ into the real numbers $\\mathbb{R}$, where $\\Omega$ is the sample space of a probability space $(\\Omega,S,p)$. The intuition is easiest for a **`discrete random variable`** where $\\Omega$ is countable and $S$ is the power set of $\\Omega$; in that case we can look at the values of the random variable on each outcome.\n",
    "\n",
    "For example $\\Omega$ might be a set of people taking a Mathematical Finance $300$ class; $S$ the power set of $\\Omega$; and the probability mass function $p(\\omega)=1/n$ where $n$ is the number of people in $\\Omega$. The random variable $X(\\omega)$ might be the score of person $\\omega$ on $\\omega$'s Math Finance $300$ final exam. We could then write an expression like $Pr(X>90)$ to mean $p(\\{\\omega\\mid X(\\omega)>90\\})=\\sum_{X(\\omega)>90}p(\\omega)$. $Pr(X>90)$ tells us the probability that a person taking Math Finance $300$ scored over $90$ on the final exam.\n",
    "\n",
    "A random variable is an example of a **`measurable function`**. That means the function's domain is the sample space $\\Omega$ of a probability space $(\\Omega,S,p)$, and its range is the sample space $A$ of a measurable space $(A,B)$. Further, if $s=\\{\\omega \\mid X(\\omega)\\in b\\}$, then $s\\in S$ whenever $b\\in B$; i.e. if the range is measurable, so is the domain. Note that \"measurable\" has different meanings for domain and range.\n",
    "\n",
    "For our purposes the range sample space $A$ will either be finite, countable, the real numbers $\\mathbb{R}$, or an interval on the real line. Usually $B$ is either the power set of $A$, or the **`Borel algebra`** of $A$ (the smallest $\\sigma$-algebra containing all of its open sets).\n",
    "\n",
    "The **`probability distribution`** associated with a random variable $X$ ($Pr_X$ or just $Pr$ when the association is clear) is defined as the function\n",
    "$$Pr(X\\in b)=p(\\{\\omega \\mid X(\\omega)\\in b\\})\\text{ when } b\\in B$$\n",
    "\n",
    "For example $X(\\omega)$ might be the logarithm of the price of an asset in economic scenario $\\omega$, and the $b$ we're interested in might be the interval $(-\\infty,5]$ indicating we want to know the probability that the log-price is less than or equal to 5. In that case we might use a notation like $Pr(X\\leq5)$.\n",
    "\n",
    "$Pr(X\\leq x)$ is called a **`cumulative distribution function (cdf)`** for the random variable $X$, and is often also denoted $F(x)$ (or $F_X(x)$ if we want to be explicit about the underlying random variable). Because of the properties of probability measures, $F(x)$ is a nondecreasing function ranging from 0 to 1 over its domain, which is the real numbers or some subset of the real numbers.\n",
    "\n",
    "If $F(x)$ is differentiable, then its derivative $\\text{pdf}(x)=F^\\prime(x)$ is called the **`probability density function (pdf)`** of the random variable $X$. (Notation like $\\text{pdf}_X(x)$ can be used if it isn't clear what random variable $X$ underlies the distribution.) When $X$ takes on only a countable number of values then as noted above $\\text{pdf}(x)$ is a probability mass function giving the probability that the discrete value $x$ will be observed.\n",
    "\n",
    "<a name=\"characteristic_function\"></a>A **`characteristic function`** is another way to express a probability distribution. If $X$ is a random variable, then its characteristic function $\\varphi_X(t)$ is\n",
    "$$\\varphi_X(t)=\\int e^{itx}dF_X(x)=\\int e^{itx}f_X(x)dx$$\n",
    "where $F_X(x)$ and $f_X(x)$ are respectively the cdf and pdf of the probability distribution and $i$ is the imaginary unit. Thus the characteristic function is the Fourier transform of the pdf. If the pdf is symmetric about zero then the characteristic function is real-valued; otherwise it can be complex. The pdf can be recovered from the inverse Fourier transform:\n",
    "$$f_X(t)=\\frac{1}{2\\pi}\\int e^{-itx}\\varphi_X(x)dx$$\n",
    "\n",
    "The most widely used probability distributions include the uniform distribution $F(x)=x$ where $0\\leq x\\leq1$; and the normal distribution $\\text{pdf}(x)=\\frac{1}{\\sqrt{2\\pi}}\\exp(-x^2/2)$.\n",
    "\n",
    "The **`expectation operator`** $\\mathbb{E}[]$ gives the average value of a function of a random variable over the random variable's probability distribution. More formally,\n",
    "\n",
    "$$\\mathbb{E}[f(X)]=\\int{f(x)\\text{pdf}(x)dx}=\\int{f(x)dF(x)}\\tag{1.5}$$\n",
    "\n",
    "Note the distribution over which the expectation is taken is often not explicitly stated in the $\\mathbb{E}[]$ notation. If it's not clear by context which pdf(x) or F(x) is being used, a superscript or a subscript is attached to $\\mathbb{E}$.\n",
    "\n",
    "The **`average or mean value`** $\\mathbb{E}[X]=\\int{x\\cdot \\text{pdf}(x)dx}=\\int{xdF(x)}$ is also called the **`first moment`** of the distribution and is often denoted as $\\overline{X}$. Often the Greek letter $\\mu$ is used for the mean, i.e. $\\mu_X=\\overline{X}$, or just $\\mu=\\overline{X}$ when the context is clear.\n",
    "\n",
    "Another metric that captures a central value of a distribution is its **`median`**, often denoted by the Greek letter $\\nu$ (\"nu\"):\n",
    "$$\\nu_X=m \\text{ such that} \\int_{-\\infty}^m \\text{pdf}_{X}(x)dx=\\int_m^{\\infty} \\text{pdf}_X(x)dx=\\frac{1}{2}\\label{eq:probability_median}\\tag{1.6}$$\n",
    "That is, the median is the point where it's equally likely that a point of the distribution will be to its left or to its right on the real line. \\eqref{eq:probability_median} works for continuous distributions; for discrete distributions some interpolation may be needed.\n",
    "\n",
    "<a name=\"central_moments\"></a>The $i^{th}$ **`(central) moment`** of the distribution is\n",
    "$$m_i=\\mathbb{E}[(X-\\mu)^i]=\\int{(x-\\mu)^i \\text{pdf}(x)dx} \\tag{1.7}$$\n",
    "where $\\mu=\\overline{X}$ is the mean of the distribution.\n",
    "\n",
    "The second moment, called **`variance`**,[$^{19}$](#one_endnotes) is sometimes written $Var(X)$. Here $Var(X)=m_2=\\mathbb{E}[(X-\\mu)^2]=\\int{(x-\\mu)^2 \\text{pdf}(x)dx}$. The square root of variance is called **`standard deviation`**; usually when people refer to the **`volatility`** of a distribution, they mean its standard deviation. Often the Greek letter $\\sigma$ is used for standard deviation, i.e. $Var(X)=\\sigma^2$ or $\\sigma^2(X)$.\n",
    "\n",
    "**`Skewness or skew`** is the scaled third central moment, $s=m_3/\\sigma^3$. If the distribution is symmetric about its mean, then its skewness is zero. There is some ambiguity about the definition of skewness, with some authors looking at the difference between a distribution's mean and its median, all divided by standard deviation. This is (a) not the definition we will use; and (b) not equivalent to our (third-moment-based) definition. The general concept is similar &mdash; zero skew means some kind of symmetry; positive skew means a distribution that tends to stretch out more to the right than to the left. But the two definitions can differ on specific distributions.\n",
    "\n",
    "<a name=\"kurtosis\"></a>While any number of moments of a distribution can be computed, most distributions that are of practical use can be specified by their first four moments. The scaled fourth moment ($m_4/\\sigma^{4}$) is called **`kurtosis`**. Kurtosis is a unitless quantity that is often compared to the kurtosis of a normal distribution for context. The term **`excess kurtosis`** is often used, meaning kurtosis minus three, since three is the kurtosis of a normal distribution. In fact kurtosis is so often reported relative to a normal distribution that sometimes writers say \"kurtosis\" when they mean \"excess kurtosis,\" which of course can be rather confusing. We will try to set context when we use this term. A distribution with positive excess kurtosis is called **`leptokurtic`** or **`fat-tailed`**, meaning it has more probability attached to unusual observations than a normal distribution. A distribution with zero excess kurtosis is **`mesokurtic`**, and a **`thin-tailed`** distribution with negative excess kurtosis is called **`platykurtic`**.\n",
    "\n",
    "<a name=\"stochastic_dominance\"></a>A random variable $X$ **`first order stochastically dominates`** another random variable $Y$ if $F_Y(x)\\geq F_X(x)$ for all scalars $x$. (There are other kinds of stochastic dominance, but if we say just \"stochastic dominance,\" we will mean first order.) A standard result is: $X$ stochastically dominates $Y$ if and only if $\\mathbb{E}[f(X)]\\geq \\mathbb{E}[f(Y)]$ for all nondecreasing functions $f$ where the expectation is defined. In particular stochastic dominance of $X$ over $Y$ implies $\\mathbb{E}[X]\\geq \\mathbb{E}[Y]$, although this implication does not work in the other direction.\n",
    "\n",
    "An even more overwhelming form of dominance is called **`statewise dominance`**, where $X(\\omega)\\ge Y(\\omega)$ for all $\\omega\\in\\Omega$, $\\Omega$ the sample space. **`Strict statewise dominance`** occurs when there is statewise dominance and at least one $\\omega$ where $X(\\omega)>Y(\\omega)$. If $X$ and $Y$ represent financial variables like rates of return, strict statewise dominance is unlikely to occur because an arbitrageur would simultaneously buy $X$ and sell $Y$. That would cost nothing but would be at least break-even, and possibly profitable, in all future states of the world. We'll discuss arbitrage more fully in Chapter 2.\n",
    "\n",
    "Intuitively, $X$ stochastically dominates $Y$ when $Y$ has more probability associated with low outcomes than $X$ does. Eventually both cumulative distribution functions must get to their highest values &mdash; the value 1. But $Y$ is always in more of a hurry to get to 1 than $X$, meaning $Y$ is always more likely to have a low (disappointing) result than $X$.\n",
    "\n",
    "Does that help us make the [Generous Billionaires](#generous_billionaires) choice? If $X$ was the sure check for $\\$500,000,000$ and $Y$ was the coin toss for $\\$1,000,000,000$ or zero, then neither was stochastically dominant. $X$'s cumulative distribution function looks like $F_X(x)=0$ for $x<500,000,000$ and $F_X(x)=1$ otherwise; $Y's$ cdf looks like $F_Y(x)=0$ for $x<0$; $F_Y(x)=\\frac{1}{2}$ for $0\\leq x < 1,000,000,000$; and $F_Y(x)=1$ for $x \\geq 1,000,000,000$. So $F_Y(x)>F_X(x)$ between $0$ and $500,000,000$, but then the inequality goes the other way between $500,000,000$ and $1,000,000,000$.\n",
    "\n",
    "If the sure check was for $\\$1,000,000,000$ ($Z$), then $Z$ would stochastically dominate the coin toss $Y$. In fact this $Z$ _statewise dominates_ $Y$, which is an even stronger condition; $Z$ is better than (or equal to) $Y$ in every future state of the world. Certainly any sentient decision maker would prefer a statewise dominant random variable.\n",
    "\n",
    "Suppose the [Generous Billionaires](#generous_billionaires) have only one coin between them and they both make offers referencing a toss of that coin. Andrew Carnegie offers to give you $\\$100,000,000$ if the coin comes up tails, and nothing if it comes up heads (random variable $W$). John D. Rockefeller makes his same offer &mdash; nothing if the coin comes up tails, $\\$1,000,000,000$ if heads (random variable $Y$). $Y$ stochastically dominates $W$, but it doesn't statewise dominate. Still, no matter what attitude you have toward risk and reward, you should prefer the stochastically dominant offer - since the future states are arbitrary, the stochastically dominant offer will be statewise dominant in a re-ordering of states.\n",
    "\n",
    "So unfortunately these observations don't help with the original [Generous Billionaires](#generous_billionaires) choice, since the original offers were designed so that there wasn't stochastic dominance. To frame choices where there isn't clear dominance, an additional mechanism is needed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "UtilityTheory"
    ]
   },
   "source": [
    "## 1.8 Utility Theory ##\n",
    "<a name=\"utility_theory\"></a>\n",
    "\n",
    "**`Utility theory`** is a disciplined way to assess tradeoffs between risk and reward. This will be our first exploration of a mathematical framework that attempts to describe and predict human financial behavior.\n",
    "\n",
    "The concept appears to have been invented by [Gabriel Cramer](https://plato.stanford.edu/entries/paradox-stpetersburg/#HistStPetePara)[$^{20}$](#one_endnotes) &mdash; who is most well known for Cramer's Rule for solving systems of linear equations &mdash; in 1728. Writing to N. Bernoulli, he summed it up as follows:\n",
    ">the mathematicians estimate money in proportion to its quantity, and men of good sense in proportion to the usage that they may make of it.\n",
    "\n",
    "Cramer favored a square root function for utility. In other words $\\$25$ is not $25$ times as useful as $\\$1$; it is only $5$ times as useful.\n",
    "\n",
    "Applying Cramer's square root utility function to the [St. Petersburg](#saint_petersburg) lottery shows its expected (Cramer) utility rather than its expected value. A win of $\\$2^i$ only has \"usage\" or utility of $\\$2^{i/2}$, so summing probabilities times utilities gives\n",
    "$$\\sum_{i=1}^\\infty 2^{-i} (2^i)^{\\frac{1}{2}} = \\sum_{i=1}^\\infty 2^{-i/2}=\n",
    "\\frac{2^{-1/2}}{1-2^{-1/2}}= \\sqrt{2}+1 \\approx 2.41$$\n",
    "Thus entering the St. Petersburg lottery has the same usefulness as you would get from $(\\sqrt{2}+1)^2=5.83$ sure dollars. So (assuming usefulness is assessed with a square root utility function) the St. Petersburg lottery is worth the same as $\\$5.83$, not infinity. If your $A_{pete}$ from the reader poll above was close to $\\$5.83$, then you may have been (probably not consciously) using a square root utility function.\n",
    "\n",
    "Daniel [Bernoulli 1738](https://dx.doi.org/10.2307/1909829) pursued the idea further, stating\n",
    ">The determination of the value of an item must not be based on the price, but rather on the utility it yields... There is no doubt that a gain of one thousand ducats[$^{21}$](#one_endnotes) is more significant to the pauper than to a rich man though both gain the same amount.\n",
    "\n",
    "Daniel Bernoulli expressed two fundamental ideas in the quote above. His first idea echoes Cramer's observation of ten years earlier.  In the same paper, Bernoulli suggested a logarithmic utility function which is still widely used; this seems to capture preferences more realistically than Cramer's square root function, which is more aggressive.\n",
    "\n",
    "With a logarithmic utility function, the usefulness of $\\$2^i$ is $i$. Without loss of generality base-2 logarithms can be used here; any other base just applies a constant scale factor which cancels out when comparing utilities to make decisions. So the expected logarithmic utility is\n",
    "$$\\sum_{i=1}^\\infty 2^{-i} i = 2$$\n",
    "The sure amount that has a log-2-utility of 2 is $2^2=\\$4$. This amount tends to be the most popular with bidders for the [St. Petersburg](#saint_petersburg) lottery; if your $A_{pete}$ from Section 1.4.2 above was $\\$4$, then you then you may have been (probably not consciously) using a logarithmic utility function.\n",
    "\n",
    "So both Cramer and Bernoulli \"solved\" the St. Petersburg Paradox by explaining through a utility function why people would not bid infinity to enter it.\n",
    "\n",
    "But Bernoulli's second sentence quoted above introduces a new idea: that the game would likely not be seen in isolation &mdash; it would have to be evaluated in the context of the gambler's entire wealth, so the true answer is more complicated. Suppose the [Generous Billionaires](#generous_billionaires) hadn't been so generous and had only offered a choice between (a) a sure check for $\\$0.50$ and (b) a coin toss for $\\$1.00$ or zero. Probably neither amount of the diminished choice is significant compared to your usual spending patterns, so you might take the coin toss just because $\\$1.00$ is a little more noticeable than $\\$0.50$. So, as Bernoulli noted, context matters.\n",
    "\n",
    "While Cramer and Daniel Bernoulli were convincing when they explained why no one bids infinity for the St. Petersburg Paradox, they omitted a simpler and more practical consideration that was eventually pointed out by Cramer in a 1728 personal communication to N. Bernoulli. According to the bank [Credit Suisse](https://www.credit-suisse.com/media/assets/corporate/docs/about-us/research/publications/global-wealth-report-2022-en.pdf),[$^{22}$](#one_endnotes) at the end of 2021 the recognizable wealth of all the people in the world was $\\$464$ trillion. That's about two to the $49^{th}$ power. \n",
    "\n",
    "So even if the world agreed to pool its wealth to pay you (if necessary) in the St. Petersburg lottery, the payoff would be capped at about $2^{49}$, meaning that the terms after $i=49$ have a finite sum. In reality the economic agent offering you the St. Petersburg lottery is not the entire world, so the cap starts quite a bit earlier than $i=49$. Thus the supposed infinite expected value of the St. Petersburg Paradox does not arise from any lottery that could be played in practice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.8.1 Von Neumann Morgenstern Utility Theory ###\n",
    "\n",
    "In 1944, utility theory was formalized into a mathematical discipline by John von Neumann and Oskar Morgenstern (\"VNM\"). VNM established a full axiomatic system around the general intuition of utility theory in [Theory of Games and Economic Behavior](https://archive.org/details/in.ernet.dli.2015.215284/page/n5).[$^{23}$](#one_endnotes)\n",
    "\n",
    "As we saw above, a utility function can describe some behaviors reasonably. But it's implausible to think that economic agents are continually computing utility functions as they make choices. (An economic agent takes economic actions and is generally a person, a group of people, a company or other organization, a government, or an algorithm.) But it's certainly true that economic agents have preferences: they might prefer billionaire offer 1 to billionaire offer 2. So it's not implausible to assume that economic agents can express a preference between pairs of probability distributions assigning probabilities to different levels of wealth. More generally, agents can express preferences between probability distributions that include non-monetary outcomes (\"I declare my love and things go well;\" \"I prove [P=NP](https://www.claymath.org/millennium-problems/p-vs-np-problem);\"[$^{24}$](#one_endnotes) etc.).\n",
    "\n",
    "[VNM 1953](https://archive.org/details/in.ernet.dli.2015.215284/page/n5) analyzed preferences by starting with a finite, discrete formulation &mdash; essentially the same as the formulation of Knightian Risk. They assumed:\n",
    "\n",
    "1. There is a situation we wish to evaluate with $n$ mutually exclusive outcomes of interest, which we can denote by $s_1, s_2, \\dots, s_n$.\n",
    "\n",
    "    (a). A very simple setup might be the toss of a coin, with two possible outcomes &mdash; heads ($s_1$) or tails ($s_2$). When the outcomes map to monetary amounts, VNM called them \"prizes.\"\n",
    "\n",
    "    (b). Going to the other extreme, a maximally complex setup would be to enumerate all the future states of the universe. Note there are only a finite number of configurations that can be taken on in a finite amount of space over a finite amount of time; physical reality is discrete in that sense.[$^{25}$](#one_endnotes) Thus the sample space of economic outcomes on the planet Earth (and say a billion light-years' vicinity) for the next billion or so years is finite. As we noted when discussing Knightian Risk, modeling economics and finance with continuous mathematics is a convenience &mdash; for example, it is helpful to be able to take derivatives of functions &mdash; but it is not reality, which is finite. Thus there is nothing intrinsically continuous about economic reality and the discrete VNM framework is sufficient.\n",
    "\n",
    "2. There is a set of probabilities associated with future outcomes: that is, a vector of nonnegative real numbers $p_1, p_2, \\dots, p_n$ that sum to one where $p_i$ is the probability of outcome $s_i$ occurring. VNM used the term _lottery_ to denote a set of probabilities.\n",
    "\n",
    "    (a). This is a discrete probability measure.\n",
    "\n",
    "3. An economic agent makes choices between lotteries (probability vectors) with a preference relation.\n",
    "\n",
    "For example, there might be three outcomes: $s_1$=you receive $\\$0$; $s_2$=you receive $\\$500,000,000$; and $s_3$=you receive $\\$1,000,000,000$. You may be asked to decide between two probability vectors, $p_1=(0,1,0)$ and $p_2=(.5,0,.5)$.\n",
    "\n",
    "$p_1$ means you definitely receive $\\$500,000,000$, while $p_2$ means you have a 50-50 chance of getting either $\\$1,000,000,000$ or nothing.\n",
    "This is a reframing of your [Generous Billionaires](#generous_billionaires) choice.\n",
    "\n",
    "More generally, let $s$ be the $n$-vector whose entries contain all possible future outcomes. Define $\\Delta(s)$ as the set of all lotteries on $s$; that is, the set of all probability $n$-vectors $p$ where $p^{\\intercal}u=1$ and all elements of $p$ are non-negative. In this book when $u$ is vector, it is a vector of all ones with dimension determined by context. $\\intercal$ denotes transpose. So $p^{\\intercal}u$ is the dot product of $p$ and $u$.\n",
    "\n",
    "Clearly $\\Delta(s)$ is convex &mdash; if $p_1, p_2\\in\\Delta(s)$, then for any $0\\leq\\alpha\\leq1$, $\\alpha p_1+(1-\\alpha)p_2\\in\\Delta(s)$ must hold.\n",
    "Note that $s$ hasn't actually been used in the definition of $\\Delta(s)$, so any vector of $n$ outcomes has the same set of lotteries, namely the segment of the hyperplane $p^{\\intercal}u=1$, each $p_i\\geq0$, in $n$-space $\\mathbb{R}^n$. It will however be convenient to keep in mind a set of outcomes $s$ when looking at $\\Delta(s)$.\n",
    "\n",
    "A ranking between lotteries in $\\Delta(s)$ is a binary relation $\\succeq$ where $\\succeq\\subseteq\\Delta(s)\\times\\Delta(s)$. For two lotteries $p,q\\in\\Delta(s)$ we write $p\\succeq q$ if $p$ is preferred to or equivalent to $q$. (Equivalence is denoted by $\\equiv$ and means both $p\\succeq q$ and $q\\succeq p$). $p\\succ q$ means that $p\\succeq q$ but it is not true that $q\\succeq p$.\n",
    "\n",
    "The agent's decision process is encoded in the $\\succeq$ function. Therefore we need to determine the properties of such preference functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.8.2 VNM Axioms and Theorem ###\n",
    "\n",
    "VNM[$^{26}$](#one_endnotes) required that certain axioms apply to preference functions, arguing that these axioms were simply expressions of rationality. The first set of requirements (translated into modern terminology) indicated that preference functions are now what are called _total preorders_,[$^{27}$](#one_endnotes) satisfying these axioms: \n",
    "\n",
    "1. _Transitivity._ For $p,q,r\\in\\Delta(s)$, $p\\succeq q$ and $q\\succeq r$ means $p\\succeq r$.\n",
    "2. _Connex._ For $p,q\\in\\Delta(s)$, either $p\\succeq q$ or $q\\succeq p$ or both; if both are true then we say $p\\equiv q$.\n",
    "\n",
    "A third property, _reflexivity_ ($p\\succeq p$ so $p\\equiv p$) follows from these two.\n",
    "\n",
    "These axioms indicate that an economic agent has one of three mutually exclusive opinions about every pair $p$ and $q$ of lotteries; either $p$ is strictly preferred to $q$; or $q$ is strictly preferred to $p$; or $p$ and $q$ are equivalent. A lottery is equivalent to itself, but there can be other lotteries that are not the same but are equivalent. The existence of unequal equivalence is the difference between a total preorder and a total order. Transitivity means there are no circular preferences; if I like chocolate better than vanilla and vanilla better than strawberry, then I like chocolate better than strawberry.\n",
    "\n",
    "While humans aren't always rational, it can generally be assumed that departures from these axioms will be quickly corrected. VNM adopted two other axioms that are sensible but not as basic as the first three. We've updated the language and format from their original presentation:\n",
    "\n",
    "<span>3.</span> _Independence_. If $p, q, r\\in\\Delta(s)$ with $p\\succ q$ and $\\alpha\\in(0, 1)$, then $\\alpha p+(1-\\alpha)r\\succ \\alpha q+(1-\\alpha)r$.\n",
    "\n",
    "Intuition: if $p$ is preferred to $q$, that preference remains unchanged when we mix in a piece of a third lottery $r$. If I like chocolate better than strawberry, then &mdash; no matter how I feel about vanilla &mdash; I like (a mixture of chocolate and vanilla) better than (the same mixture of strawberry and vanilla).\n",
    "\n",
    "While this is not horribly implausible, it is also not as basic a guide to rational behavior as the previous axioms. It is certainly possible that there could be interactions between items that would alter the results. To get powerful results, VNM had to make powerful assumptions: in this case, they assumed that lotteries are independent of each other and there are no such interactions.\n",
    "\n",
    "The last VNM axiom is even stronger:\n",
    "\n",
    "<span>4.</span> _Continuity_. If $p, q, r \\in\\Delta(s)$ with $p\\succ q\\succ r$, then there is a scalar $\\alpha\\in(0,1)$ such that $\\alpha p+(1-\\alpha)r\\equiv q$.\n",
    "\n",
    "Intuition: If we have three ordered lotteries, we can create a linear mixture of the worst one ($r$) and the best one ($p$) that is equivalent to the one in the middle ($q$). So if I prefer chocolate to vanilla, and I prefer vanilla to strawberry, then there is some mixture of chocolate and strawberry that I like the same as vanilla.\n",
    "\n",
    "This property requires that preferences don't just jump from one level to another, but vary smoothly between (for example) strawberry and chocolate without skipping over the vanilla satisfaction level. Like the independence axiom, this is not implausible but is also not entirely fundamental. I might hate the taste of mixtures and dislike even the smallest adulteration of my beloved chocolate, so there is no combination that gets me to the same satisfaction level as vanilla.\n",
    "\n",
    "The two strong VNM axioms are not implausible: they basically enforce a kind of linearity of preference when combining lotteries. Eventually the strength of these axioms gets the theory into trouble: we'll show later that at some point going down this path departs from reasonably describing choices that most people make. But for now and to a first order, these axioms seem to give a sensible description of how people make economic choices. A preference function seems much more intuitive than a utility function. But VNM[$^{28}$](#one_endnotes) proved that utility functions and preference functions lead to the same results.\n",
    "\n",
    ">**VNM Theorem.** An economic agent has a preference function $\\succeq$ satisfying the four VNM axioms if and only if the agent has a associated utility function $U:\\Delta(s)\\rightarrow\\mathbb{R}$ where for any $p,q\\in\\Delta(s)$, $p\\succeq q \\text{ if and only if } U(p)\\geq U(q)$.\n",
    "\n",
    "More precisely, let $\\Delta(s)$ be a convex subset of ${\\rm I\\!R^n}$. Let $\\succeq$ be a binary relation on $\\Delta(s)$. Then $\\succeq$ satisfies the four axioms above if and only if there is a function $U:\\Delta(s)\\rightarrow\\mathbb{R}$ such that:\n",
    "<br>&#9658;(a)  U represents $\\succeq$ (i.e. $\\forall p, q\\in\\Delta(s)$, $p\\succeq q \\iff U(p)\\geq U(q)$)\n",
    "<br>&#9658;(b)  U is affine (i.e. $\\forall p,q\\in\\Delta(s), \\alpha\\in[0, 1]$, $U(\\alpha p + (1- \\alpha)q) = \\alpha U(p) + (1- \\alpha)U(q)$)\n",
    "\n",
    "Further, U is unique up to a positive linear transformation: If $V:\\Delta(s)\\rightarrow\\mathbb{R}$ also satisfies (a) and (b), then there are $b,c\\in\\mathbb{R}$ (where $b > 0$) such that $V = bU + c$.\n",
    "\n",
    "The proof of the VNM theorem is quite long although not particularly hard. We'll give a flavor of the proof but not the whole thing. The first thing VNM note is\n",
    ">**Lemma** If $p,q\\in\\Delta(s)$ with $p\\succ q$, and $\\alpha>\\beta\\in [0,1]$, then $\\alpha p + (1-\\alpha)q \\succ \\beta p + (1-\\beta)q$.\n",
    "\n",
    "**Proof of lemma** Define $\\gamma=\\frac{\\beta}{\\alpha}$; $\\gamma$ is in the unit interval. Since $p\\succ q$, the independence axiom says $\\alpha p+(1-\\alpha) q \\succ \\alpha q+(1-\\alpha) q = q$. Let $r=\\alpha p+(1-\\alpha) q$; we can apply the independence axiom to $r\\succ q$ by adding some (more) $r$ to both sides: $(1-\\gamma)r + \\gamma r\\succeq (1-\\gamma)q+\\gamma r$. Collecting terms, the RHS is $\\beta p + (1-\\beta)q$ and the LHS is $r=\\alpha p + (1-\\alpha)q$, proving the lemma.\n",
    "\n",
    "Continuing along these lines, they prove that the map from the unit interval to linear combinations $\\alpha p + (1-\\alpha)q$ is one-to-one, monotone, and onto $\\{r \\mid p\\succeq r\\succeq q\\}$. They then break down lotteries into combinations of 100% lotteries, i.e. they let $x_i$ be the lottery that gives outcome $s_i$ with 100% probability. Without loss of generality, we can assume the lotteries are ordered so that $x_n\\succeq x_{n-1}\\succeq \\dots \\succeq x_1$. Start construction of the utility function $U$ by defining $U(x_1)=0$ and $U(x_n)=1$, unless $x_n\\equiv x_1$ in which case the trivial utility function $U(x)=0$ for all lotteries $x$ works.\n",
    "\n",
    "From the continuity axiom we know that there is an $\\alpha_i$ so that $\\alpha_i x_n + (1-\\alpha_i)x_1\\equiv x_i$ for any $1\\leq i \\leq n$. They set $U(x_i)=\\alpha_i$. The 100% lotteries then become the basis for all the other lotteries, since a general lottery $x$ is an n-vector of probabilities $x=(p_1,\\dots,p_n)$; we define $U(x)=\\sum{p_i \\alpha_i}$. The axioms and observations like the Lemma allow them to prove that this utility function encodes preference order.\n",
    "\n",
    "So in fact VNM not only proved that there is a utility function $U$ that operates on lotteries and encodes preference order: they also proved (as the construction of $U$ shows) that we can just have utility functions that operate on outcomes (which are probably monetary amounts). So if $p=(p_1,...,p_n)$ is a lottery in $\\Delta(s)$, a VNM preference function can be encoded as $\\sum_{i=1}^n p_i u(s_i)$. We use the small-u notation to indicate a function that operates on outcomes, while the big-U notation indicated a function that operates on lotteries."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.8.3 Risk Preferences ###\n",
    "\n",
    "A special kind of outcome set is monetary, where each outcome state $s_i$ maps to an amount of money. We noted above in that case, VNM called the outcomes **`prizes`**. A utility function on prizes maps real numbers to real numbers.\n",
    "\n",
    "So in utility terms, your original meeting with the billionaires had three possible prizes: $s_1$=you receive $\\$0$; $s_2$=you receive $\\$500$Mn; and $s_3$=you receive $\\$1Bn$.\n",
    "\n",
    "We asked about the preference between two lotteries $p_1=(0,1,0)$ and $p_2=(.5,0,.5)$. $p_1$ is a sure thing: you definitely receive $\\$500Mn$. Risk is lack of knowledge about future outcomes of an action, but you know exactly what will happen with $p_1$. So there is no risk in $p_1$.\n",
    "\n",
    "$p_2$ on the other hand is a risky lottery. The poll above asked whether or not $p_1\\succ p_2$. We now know (assuming the VNM Theorem holds) that can be answered by looking at whether or not\n",
    "$$\\sum_{i=1}^3 p_1(i) u(s_i) > \\sum_{i=1}^3 p_2(i) u(s_i)$$\n",
    "This is equivalent to asking if $u(500Mn)>\\frac{1}{2}u(0)+\\frac{1}{2}u(1Bn)$.\n",
    "\n",
    "Given the VNM equivalence, a more universal notation can be used when outcomes are prizes. Write $\\mathbb{E}_p[X]$, where $p$ is a lottery, to mean the expected value of the random variable $X$ that maps the sample space $\\Omega=\\{1,2,\\dots,n\\}$ to amounts $\\{s_1,\\dots,s_n\\}$ under the probability measure (mass function) $p$:\n",
    "$$\\mathbb{E}_p[X]=\\sum p_i X(i)=\\sum p_i s_i\\label{eq:risk_aversion_expected}\\tag{1.10}$$\n",
    "For the [St. Petersburg](#saint_petersburg) lottery, this quantity was infinite. For the risky billionaire coin toss, this quantity was $\\$500$Mn.\n",
    "\n",
    "\\eqref{eq:risk_aversion_expected} is a scalar monetary amount, so if there is a utility function that operates on monetary amounts, it can be applied to \\eqref{eq:risk_aversion_expected}: $u(\\mathbb{E}_p [X])$ is the utility of definitely receiving the expected value of the lottery $p$.\n",
    "\n",
    "On the other hand, the utility of the risky lottery can be evaluated with the expression\n",
    "$$\\mathbb{E}_p[u(X)]=\\sum p_i u(X(i))=\\sum p_i u(s_i) \\tag{1.11}$$\n",
    "\n",
    "The difference is the order in which we apply probabilities and utilities &mdash; if expected value is taken first, then a sure thing is created after which its utility is evaluated. If utility is applied first, then there are a variety of outcomes with different utilities whose probability-weighted expectation is taken.\n",
    "\n",
    "We can characterize attitudes towards risk as follows. For nonsure p's:\n",
    "\n",
    "- **`Risk aversion`**: $u(\\mathbb{E}_p[X])>\\mathbb{E}_p[u(X)]$\n",
    "\n",
    "- **`Risk indifference or neutrality`**: $u(\\mathbb{E}_p[X])=\\mathbb{E}_p[u(X)]$\n",
    "\n",
    "- **`Risk seeking`**: $u(\\mathbb{E}_p[X])<\\mathbb{E}_p[u(X)]$\n",
    "\n",
    "In your [Generous Billionaires](#generous_billionaires) meeting, $\\mathbb{E}_{p_2}[X]=\\$500$Mn, so we asked about the relationship between $u(500Mn)=u(\\mathbb{E}_{p_2}[X])$ and $\\mathbb{E}_{p_2}[u(X)]$ (the utility of taking the risk of the coin toss); in other words we asked whether you were risk averse, neutral, or risk seeking.\n",
    "\n",
    "If your $A_{generous}$ choice was for the sure check, then you are risk-averse. Most people in fact are risk-averse. This seems to be a deep evolutionary tendency; in fact even other species demonstrate risk aversion. [Chen, Lakshminarayanan, and Santos 2006](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=911244) set up a token-based economy for capuchin monkeys, and found that &mdash; once they understood the idea of token-based money &mdash; monkeys preferred to spend on definite rewards (one apple slice, say) than random rewards (a variable number of apple slices).\n",
    "\n",
    "More accurately, most people (and primates) demonstrate _upside risk aversion_. Your [Probabilistic Thug](#probabilistic_thug) choice $A_{thug}$ was probably for the coin toss, figuring that you had a 50% chance of escaping unharmed. While having two broken fingers is worse than having one broken finger, it probably isn't twice as bad. In other words, the negative utility grows more slowly than risk neutral/linear, just like positive utility. This probably made you **`downside risk-seeking`**. Since the utility of any number of broken fingers is negative, and assuming the utility of nothing happening (no broken fingers) is zero, your decision probably looked like $-.5|u_2|>-|u_1|$, or $|u_2|<2|u_1|$ (with obvious, if morbid, notation).\n",
    "\n",
    "Recall that a function $f$ is **`concave`** if $f(ax + (1-a)y) \\geq af(x) + (1-a)f(y)$ for all $a$ in $[0,1]$ (mnemonic: \"inside the cave is better,\" where the cave is the set of parentheses that surround the argument of the function). If the inequality goes the other way, the function is **`convex`**; if both sides are equal the function is **`affine`**. When a function $f$ is twice differentiable, it is concave, affine, or convex according to whether the second derivative $f^{\\prime\\prime}$ is negative, zero, or positive.\n",
    "\n",
    "It is not hard to see the following\n",
    ">**Proposition**: A utility function u on prizes is risk averse on all lotteries if and only if it is strictly concave; is risk indifferent iff affine; and risk seeking on all lotteries iff strictly convex.\n",
    "\n",
    "This indicates that utility functions might reverse shape on the downside, since as we've seen, behavior might be downside risk-seeking.\n",
    "\n",
    "Figure 1.1 shows a concave (logarithmic) utility function in blue. If it starts raining from the top of the graph down to the bottom of the graph, a concave utility function will shed water. The figure shows utility in the range of the [Generous Billionaires](#generous_billionaires) amounts for someone with starting wealth $\\$100,000$. The utility of $\\$1$Bn is only about $3.5\\%$ higher than the utility of $\\$500$Mn. This small increase makes the agent risk averse; the utility at $\\$1$Bn would have to be twice the utility at $\\$500$Mn minus the utility of zero (shown at the top of the orange line) to make up for the $50\\%$ chance of getting nothing.\n",
    "\n",
    "Similarly, Figure 1.2 shows a convex (negative logarithmic) utility function in blue based on number of fingers broken by the [Probabilistic Thug](#probabilistic_thug). The upside-down logarithm is now convex (holds water), reflecting the idea that two broken fingers is not twice as bad as one broken finger."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1920x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParaLms['figure.dpi']= 300\n",
    "\n",
    "starting_wealth=10**5\n",
    "def util_fn(x):\n",
    "    #log utility function with starting wealth\n",
    "    return(np.log(x+starting_wealth))\n",
    "\n",
    "x=np.arange(-starting_wealth+.01,10**9,10**6)\n",
    "y=util_fn(x)\n",
    "plt.title(\"Figure 1.1: Concave Upside Utility\")\n",
    "plt.xlabel(\"Added Wealth\")\n",
    "plt.ylabel(\"Utility\")\n",
    "plt.grid()\n",
    "plt.annotate('500Mn', xy=(5*10**8, util_fn(5*10**8)), xytext=(5*10**8, 10),\n",
    "            arrowprops=dict(arrowstyle='->',facecolor='black'))\n",
    "plt.annotate('1Bn', xy=(10**9, util_fn(10**9)), xytext=(.9*10**9, 11),\n",
    "            arrowprops=dict(arrowstyle='->',facecolor='black'))\n",
    "plt.plot(x,y)\n",
    "#Show linear increase from utility of $500Mn\n",
    "y2=x*(util_fn(5*10**8)-util_fn(0))/(5*10**8)+util_fn(0)\n",
    "plt.annotate('2*u(500Mn)-u(0)', xy=(10**9, 2*util_fn(5*10**8)-util_fn(0)), \\\n",
    "             xytext=(.5*10**9, 26), arrowprops=dict(arrowstyle='->',facecolor='black'))\n",
    "\n",
    "plt.plot(x,y2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1920x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def thug_fn(x):\n",
    "    #log utility function for number of broken fingers\n",
    "    return(-np.log(x+1))\n",
    "\n",
    "x=np.arange(0,10,1)\n",
    "y=thug_fn(x)\n",
    "plt.title(\"Figure 1.2: Convex Downside Utility\")\n",
    "plt.xlabel(\"Fingers Broken\")\n",
    "plt.ylabel(\"Utility\")\n",
    "plt.grid()\n",
    "plt.annotate('1 Finger', xy=(1, thug_fn(1)), xytext=(1, -3),\n",
    "            arrowprops=dict(arrowstyle='->',facecolor='black'))\n",
    "plt.annotate('2 Fingers', xy=(2, thug_fn(2)), xytext=(5, -.25),\n",
    "            arrowprops=dict(arrowstyle='->',facecolor='black'))\n",
    "plt.plot(x,y)\n",
    "#Show linear decrease from utility of 1 broken finger\n",
    "y2=x*thug_fn(1)\n",
    "plt.annotate('2*u(1 Finger)', xy=(2, 2*thug_fn(1)), xytext=(3, -4),\n",
    "            arrowprops=dict(arrowstyle='->',facecolor='black'))\n",
    "\n",
    "plt.plot(x,y2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\Omega$ be a finite sample space and let $X$ be a random variable that gives a monetary amount $X(\\omega)$ when the state of the world is $\\omega\\in\\Omega$. Let $p$ be a lottery, i.e. a set of probabilities $p(\\omega)>0$ with $\\sum_{\\omega\\in\\Omega}p(\\omega)=1$. Let $u$ be a utility function that operates on monetary amounts (prizes). Then the **`certainty equivalent`** of prizes $X$ under lottery $p$ is the number $m$ such that\n",
    "$$u(m) = \\mathbb{E}_p[u(X)]\\label{eq:certainty_equivalent}\\tag{1.12}$$\n",
    "$m$ is the sure prize that the utility function values equally with the risky set of outcomes $X$ with probabilities $p$. The amount $A_{switch}$ you recorded in the billionaire choice problem was your certainty equivalent of the billion dollar coin toss.\n",
    "\n",
    "For most sensible purely financial situations, a fifth axiom of utility functions on prizes holds: people never prefer less money to more. The fact that people are sometimes philanthropic is not a counterexample, since the outcome set that takes philanthropy into account includes non-monetary outcomes comprising different levels of social satisfaction.  If the only outcomes are monetary, it is reasonably safe to assume more is preferred to less, and therefore utility functions on prizes are nondecreasing. For a scalar utility function $u$, this means $u$'s first derivative is non-negative: $u^{\\prime}(x)\\geq 0$.\n",
    "\n",
    "This leads to another\n",
    ">**Proposition:** Suppose the outcome set consists of an interval of the real line and $u$ is a continuous utility function on this interval. Then every lottery $p$ has at least one certainty equivalent. If $u$ is strictly increasing, then $p$ has at most one certainty equivalent.\n",
    "\n",
    "For well-behaved utility functions, the degree of risk aversion can be captured with [Pratt 1964](https://doi.org/10.2307/1913738)'s **`coefficient of absolute risk aversion`**, which is minus the second derivative divided by the first derivative of a (twice continuously differentiable strictly increasing) utility function:\n",
    "$$\\text{Coeff}_{abs}(u,x)=-\\frac{u^{\\prime\\prime}(x)}{u^{\\prime}(x)}\\label{eq:coeff_abs_risk_aversion}\\tag{1.13}$$\n",
    "\n",
    "One way to understand the coefficient of absolute risk aversion is in a certainty-equivalent context as in \\eqref{eq:certainty_equivalent}. Let $x$ be an agent's current wealth and let $z$ be a zero-mean lottery. Then \\eqref{eq:certainty_equivalent} can be rewritten as\n",
    "$$u(x-c)=\\mathbb{E}_p[u(x+z)]$$\n",
    "Here $c$ is the amount that needs to be deducted from current wealth to induce the risk-averse agent to take risk. ($c$ will be negative if the agent is risk-seeking.) The LHS can be approximated by a Taylor series for $u$ about $x$: $u(x-c)\\approx u(x)-c\\cdot u^\\prime(x)$. Another Taylor series for $u$ about $x$ on the RHS gives $\\mathbb{E}_p[u(x+z)]\\approx u(x)+\\mathbb{E}_p[z]u^\\prime(x)+\\frac{1}{2}\\mathbb{E}_p[z^2]u^{\\prime\\prime}(x)=u(x)+\\frac{1}{2}\\sigma_z^2 u^{\\prime\\prime}(x)$ where $\\sigma_z^2$ is the variance of $z$. Equating the two Taylor approximations gives\n",
    "$$c\\approx\\frac{1}{2}\\sigma_z^2\\text{Coeff}_{abs}(u,x)$$\n",
    "The risk aversion deduction $c$ is the product of a term that describes the riskiness of the gamble ($\\sigma_z^2$) times the agent's risk aversion at the current level of wealth $\\text{Coeff}_{abs}(u,x)$.\n",
    "\n",
    "Similarly, the **`coefficient of relative risk aversion`** is $\\text{Coeff}_{rel}(u,x)=\\text{Coeff}_{abs}(u,x)\\cdot x$. Relative risk aversion is expressed as a percentage of wealth, rather than as absolute monetary amounts.\n",
    "\n",
    "For example, Gabriel Cramer's utility function was $u(x)=\\sqrt{x}$. So $u^{\\prime}(x)=\\frac{1}{2\\sqrt{x}}$, and $u^{\\prime\\prime}(x)=-\\frac{1}{4x^{3/2}}$, giving an absolute risk aversion of $\\frac{1}{2x}$. For positive arguments x, this indicates the square root's absolute risk aversion is positive &mdash; that is, the square root is risk-averse.\n",
    "\n",
    "The square root's relative risk aversion is &frac12;, a constant. This means that the square root function belongs to the CRRA (Constant Relative Risk Aversion) class of utility functions. CARA (Constant Absolute Risk Aversion) is another important class.\n",
    "\n",
    "Intuitively, a more risk averse agent should be reluctant to take some risks that a less risk averse agent would plunge into. This leads to the\n",
    ">**Definition**. Given two utility functions $u$ and $v$ and a random variable $X$ mapping state indices to prizes, _$u$ **`is more risk averse than`** $v$_ if, for every lottery $p$ and sure amount $m$ where $\\mathbb{E}_p[u(X)]\\geq u(m)$, then $\\mathbb{E}_p[v(X)]\\geq v(m)$, while there exists a lottery $q$ and a sure amount $k$ such that $\\mathbb{E}_q[v(X)]\\geq v(k)$ but $\\mathbb{E}_q[u(X)]<u(k)$.\n",
    "\n",
    "This definition says if $u$ is \"willing\" to take the risk on $p$, then $v$ is too, but there is some $q$ where $v$ is \"willing\" to take the risk but $u$ isn't. This intuitive concept of degree of willingness to take gambles ties in to the numerical coefficient $\\eqref{eq:coeff_abs_risk_aversion}$ in the way one would hope:\n",
    ">Theorem (Pratt): $u$ is more risk averse than $v$ if and only if $u$'s coefficient of absolute risk aversion is higher than $v$'s.\n",
    "\n",
    "Suppose there is a binary lottery: it takes 0 with 50% probability, takes $\\$10$ with $50\\%$ probability. This is a losing lottery, so participants will demand compensation to enter it. If a participant has a utility function $u$ and starting wealth is $w$, then the indifference point $c$ &mdash; the minimum amount that participant will demand to be paid to enter this losing lottery &mdash; is:\n",
    "$$u(w)=.5*u(w+c)+.5*u(w+c-10)$$\n",
    "\n",
    "- If the indifference point $c$ is the same for all wealth levels $w$, then $u$ is **`CARA (Constant Absolute Risk Aversion)`**.\n",
    "- If $c$ is increasing in $w$, then u is **`IARA (Increasing Absolute Risk Aversion)`**.\n",
    "- If $c$ is decreasing in $w$, then u is **`DARA (Decreasing Absolute Risk Aversion)`**.\n",
    "Most people act as if their utility function is DARA, which was Daniel Bernoulli's insight back in 1738. \n",
    "\n",
    "Imagine another binary lottery: it takes $0$ with $50\\%$ probability, and takes $10\\%$ of the participant's wealth with $50\\%$ probability. Let $f$ be the fraction of a participant's existing wealth $w$ that the participant will demand to be paid in order to be indifferent to entering this lottery. Then the indifference fraction $f$ is where:\n",
    "$$u(w)=.5u(w(1+f))+.5u(w(1+f-.1))$$\n",
    "\n",
    "- If $f$ is the same for all wealth levels $w$, then $u$ is **`CRRA (Constant Relative Risk Aversion)`**.\n",
    "- If $f$ is increasing in $w$, then $u$ is **`IRRA (Increasing Relative Risk Aversion)`**.\n",
    "- If $f$ is decreasing in $w$, then $u$ is **`DRRA (Decreasing Relative Risk Aversion)`**.\n",
    "Most people act as if their utility function is CRRA.\n",
    "\n",
    "In fact many economists assume that utility functions are CRRA, which (after solving the differential equation $-\\frac{u^{\\prime\\prime}(x)}{u^{\\prime}(x)}\\cdot x=k$) gives a utility function of the form $u(x)=ax^{1-k}+b$, usually standardized to $u(x)=\\frac{x^{1-k}-1}{1-k}$, where $k$ is the degree of relative risk aversion. Many economists have attempted to infer a societal $k$, i.e. an average degree of relative risk aversion across a population such as participants in the US stock market. [T&ouml;dter 2008](https://doi.org/10.1080/17446540701335474) used $77$ years of US stock market data from $1926-2002$, solving\n",
    "$$\\sum_{t=1}^{77}\\pi_t(1+rf_t)^{1-k}=\\sum_{t=1}^{77}\\pi_t(1+rm_t)^{1-k}$$\n",
    "for $k$, where $rf_t$ is the riskfree rate in year $t$; $rm_t$ is the return on the US stock market in year $t$, and a uniform distribution $\\pi_t=\\frac{1}{77}$ $\\forall t$ is assumed. T&ouml;dter finds an average $k=3.5$, but with a wide $[1.4,7.1]$ $95\\%$ confidence interval.\n",
    "\n",
    "Generally economists find that most plausible utility functions fall in the **`HARA`** class **`(Hyperbolic Absolute Risk Aversion)`**. A utility function $u$ is HARA if its <a name='coeff_abs_risk_tolerance'></a> **`coefficient of absolute risk tolerance`** $-\\frac{u^{\\prime}(x)}{u^{\\prime\\prime}(x)}$ is a linear function of the form $ax+b$. Note the coefficient of absolute risk tolerance is the reciprocal of the coefficient of absolute risk aversion.\n",
    "\n",
    "Note if $a=0$ we have CARA and if $b=0$ we have CRRA. If $a\\neq 0$ and $a\\neq 1$, then $u(x)=(a-1)^{-1}(ax+b)^{(a-1)/a}$ up to an affine transformation."
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    "### 1.8.4 Drawbacks of Utility Theory ###\n",
    "<a name='utility_drawbacks'></a>\n",
    "\n",
    "The mathematical scaffolding built on utility theory is powerful; surely all this cleverness must be a great guide to how people make economic decisions. If we knew each person's utility function, couldn't we set about maximizing utility globally and move toward economic optimality for the human race?\n",
    "\n",
    "Unfortunately not. Almost as soon as utility theory was proposed, inconsistencies between utility theory and common sense started becoming apparent. Utility remains a powerful concept and a good first-order guide to economic decision-making. But it buckles under even mild pressure, departing from what people actually do. One point of departure is the overstrong set of assumptions about what constitutes rational decision making: while necessary to reason mathematically, some of these assumptions are debatable. Another point of departure comes from humans' stubborn insistence on being irrational.\n",
    "\n",
    "There is an entire industry based in significant part on the failure of utility theory to capture individual preferences: it's called **`wealth management`**. Wealth managers advise individuals on how to achieve their financial goals. A related field is **`robo-investing`** where an individual's data and preferences are collected by an automated process. Decisions in the robo-investing process are then made algorithmically.\n",
    "\n",
    "Neither human nor robot advisers typically assume that their advisees' preferences can be described by a utility function. [Pan and Statman 2012](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2144481#) described some typical drawbacks:\n",
    "- \"Each investor has a multitude of risk tolerances... For example, an investor might have low risk tolerance in a retirement mental account, populating it with bonds or Treasury bills, while at the same time have high risk tolerance in a 'get rich' mental account, populating it with aggressive growth funds or even lottery tickets.\"\n",
    "- \"Investors' risk tolerance varies by circumstances and associated emotions.\" Investors are subject to mood swings, displaying exuberance and higher risk tolerance in overheated markets and fear and lower risk tolerance in crashing markets.\n",
    "- \"Foresight is different from hindsight, and the risk tolerance of investors, assessed in foresight, is likely different than the risk tolerance of investors assessed in hindsight.\" Some investors will tend to look backward and will want to change their investments radically based on perceived missed opportunities or just bad results in the past, while others will maintain forward-looking preferences.\n",
    "\n",
    "The interplay of emotions, changing life circumstances, recent events, and rational investing goals is impossible to capture in a single static utility function. But the explosion of hard-to-calibrate parameters that would come with multiple time-varying utility functions robs the utility function framework of predictive power. If I say $y=x^k$ but I have to keep adjusting $k$ because actually $y=e^x$, I haven't said anything.\n",
    "\n",
    "There are internal inconsistencies even within the utility function framework. Consider Daniel Bernoulli's framework: logarithmic utility dependent on current wealth $w$. If an economic actor's current $w$ is low enough, utility theory predicts that the actor will not take __**any**__ gamble beyond that wealth level.\n",
    "\n",
    "For example, if someone's current wealth is $w=\\$100$, and she is offered a coin toss where tails means she loses $\\$101$ and heads means she wins $\\$1,000,000,000,000$, logarithmic utility says she will decline the gamble since\n",
    "$$\\frac{1}{2}ln(100-101)+\\frac{1}{2}ln(100+10^{12})=-\\infty<ln(100)$$\n",
    "In fact there is no finite amount of money on the \"win\" side of the coin toss that will induce such an economic actor to take the gamble. But that's absurd: of course anyone who is close to destitute would not mind being totally destitute, or even owing a little, in order to have a chance at a trillion dollars.\n",
    "\n",
    "This particular example can be patched up by flooring the argument to the logarithm. But Rabin's Paradox (due to Matthew [Rabin 2000](https://www.jstor.org/stable/2999450)) indicates this isn't just a technical problem with the logarithm: there's a fundamental problem that is difficult to fix. Rabin proves a theorem that states that\n",
    ">within the expected-utility model, anything but virtual risk-neutrality over modest stakes implies manifestly unrealistic risk aversion over large stakes. This theorem is entirely \"nonparametric,\" assuming nothing about the utility function except concavity.\n",
    "\n",
    "Rabin shows inconsistencies like this:\n",
    ">Suppose that, from any initial wealth level, a person turns down gambles where she loses $\\$100$ or gains $\\$110$, each with $50\\%$ probability. Then she will turn down $50-50$ bets of losing $\\$1,000$ or gaining _any_ sum of money.\n",
    "\n",
    "This is similar to the observation about a person with low wealth and a logarithmic utility function, but it applies to any concave (risk-averse) utility function. The conclusion from Rabin's theorem is that it's difficult to calibrate a utility function to make reasonable decisions over both modest amounts and large amounts.\n",
    "\n",
    "There is also the possibility of **`background noise`**. It is rare that economic agents are presented in isolation with a decision like the [St. Petersburg](#saint_petersburg) Paradox, or the [Generous Billionaires](#generous_billionaires), or the [Probabilistic Thug](#probabilistic_thug). In business or life decisions, risks of changes in the general economic or personal environment may be as large or larger than the risk of success or failure of a particular venture. In fact, [Pomatto, Strack and Tamuz 2020](https://doi.org/10.1086/705555) have shown that if there are two random variables $X$ and $Y$ with $\\mathbb{E}[X]>\\mathbb{E}[Y],$ then there must exist a zero-mean background noise random variable $Z$ independent of $X$ and $Y$ so that $X+Z$ stochastically dominates $Y+Z$. Thus the right kind of background noise can obliterate any risk considerations that might go into a decision between $X$ and $Y$.\n",
    "\n",
    "For example suppose $X$ is the [Generous Billionaires](#generous_billionaires) coin toss ($\\$1$Bn on heads and zero on tails), and $Y$ is a sure check for $\\$400$Mn. Then $\\mathbb{E}[X]>\\mathbb{E}[Y],$ but as we've seen risk aversion will cause many people to choose $Y$ anyway. However let $Z$ <u>cost</u> $\\$250$Mn on heads and pay $\\$250$Mn on tails. Then $X+Z$ pays $\\$750$Mn and $\\$250$Mn on heads and tails, respectively. This stochastically dominates $Y+Z$ which pays $\\$150$Mn and $\\$650$Mn on heads and tails, respectively. Thus any minimally rational economic agent will prefer $X+Z$ to $Y+Z$, so the presence of the background noise $Z$ has befuddled any risk preference the agent had.[$^{29}$](#one_endnotes)\n",
    "\n",
    "Another inconsistency is called the **`Allais problem`**, described in [Allais 1953](https://www.jstor.org/stable/1907921). Maurice Allais would win the [Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel in 1988](https://www.nobelprize.org/prizes/economic-sciences/1988/allais/facts/).[$^{30}$](#one_endnotes) As slightly modified and simplified by [fellow (2002) Nobel Prizewinner Daniel Kahneman](https://www.nobelprize.org/prizes/economic-sciences/2002/kahneman/facts/),[$^{31}$](#one_endnotes) the Allais problem envisions two choices:\n",
    ">Choice 1: (a) $61\\%$ chance to win $\\$520,000$ or (b) $63\\%$ chance to win $\\$500,000$.\n",
    "\n",
    ">Choice 2: (a) $98\\%$ chance to win $\\$520,000$ or (b) $100\\%$ chance to win $\\$500,000$.\n",
    "\n",
    "Most people choose 1a and 2b. But if 1a is preferred to 1b, we must have\n",
    "$$.61u(520)+.39u(0)>.63u(500)+.37u(0)$$\n",
    "where u(x) means the utility of gaining x thousand dollars. Thus\n",
    "$$.61(u(520)-u(500))>.02(u(500)-u(0))$$\n",
    "Assuming only that the utility function $u$ is sensible (more is preferred to less, $u^{\\prime}>0$), both sides of this last inequality are positive.\n",
    "\n",
    "Preferring the certain 2b to the highly probable 2a means\n",
    "$$u(500)>.98u(520)+.02u(0)>0$$\n",
    "which gives\n",
    "$$.02(u(500)-u(0))>.98(u(520)-u(500))$$\n",
    "Thus for any sensible utility function, $1a\\succ 1b$ and $2b\\succ 2a$ are incompatible.\n",
    "\n",
    "One way to address the Allais problem is to assume that people are systematically irrational in the way they perceive probabilities. This is a key tenet of the  **`Prospect Theory`** put forward by [Kahneman and Amos Tverskey 1979](https://www.jstor.org/stable/1914185). Prospect Theory is in turn part of the field of **`behavioral economics`**, which uses both psychological theory and empirical observations to back the idea that humans are not only irrational, but are reliably irrational when making economic decisions.\n",
    "\n",
    "More precisely, let $d(p)$ be a monotone increasing distortion function applied to probabilities (the unit interval $[0,1]$), where $d(0)=0$ and $d(1)=1$ but $d$ is nonlinear in between. If people are acting on $d(probability)$ rather than on the stated probability, it can explain why someone would choose 1a and 2b in the Allais problem. [Kahneman 2011](https://us.macmillan.com/books/9780374533557/thinkingfastandslow) gives some experimentally determined estimates of $d(p)$ for gains, and notes that the estimates for losses are very similar.[$^{32}$](#one_endnotes) These are shown expressed in percentage units in Figure 1.3:"
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AAAAAAAAAANyAoA4AAAAAAAAAAABwA4I6AAAAAAAAAAAAwA0I6gAAAAAAAAAAAAA3IKgDAAAAAAAAAAAA3ICgDgAAAAAAAAAAAHADgjoAAAAAAAAAAADADQjqAAAAAAAAAAAAADcgqAMAAAAAAAAAAADcgKAOAAAAAAAAAAAAcAOCOgAAAAAAAAAAAMANCOoAAAAAAAAAAAAANyCoAwAAAAAAAAAAANyAoA4AAAAAAAAAAABwA4I6AAAAAAAAAAAAwA0I6gAAAAAAAAAAAAA3IKgDAAAAAAAAAAAA3ICgDgAAAAAAAAAAAHADgjoAAAAAAAAAAADADQjqAAAAAAAAAAAAADcgqAMAAAAAAAAAAADcgKAOAAAAAAAAAAAAcAOCOgAAAAAAAAAAAMANCOoAAAAAAAAAAAAANyCoAwAAAAAAAAAAANyAoA4AAAAAAAAAAABwg/8H5oOw4ep9TtkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1920x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Kahneman's decision weights function\n",
    "\n",
    "x=[0,1,2,5,10,20,50,80,90,95,98,99,100]\n",
    "y=[0,5.5,8.1,13.2,18.6,26.1,42.1,60.1,71.2,79.3,87.1,91.2,100]\n",
    "plt.title(\"Figure 1.3: Kahneman's Empirical Decision Weights d(p)\")\n",
    "plt.xlabel(\"Probability\")\n",
    "plt.ylabel(\"Decision Weight\")\n",
    "plt.grid()\n",
    "plt.plot(x,x,label=\"linear\")\n",
    "plt.plot(x,y,label=\"d(p)\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note $d$ increases rapidly just above 0 showing the **`possibility effect`** (people overvalue small possibilities of events happening), and increases rapidly again between 90 and 100 percent, showing the **`certainty effect`** (people overvalue guarantees versus mere high likelihood). Both effects can be gamed by dispassionate adversaries, even without knowledge of an economic actor's utility function.\n",
    "\n",
    "These drawbacks tell us not to rely too heavily on utility theory alone. In general financial and economic modeling cannot replace human intuition, but it can inform it and be informed by it. When taken together with common sense, utility theory can be a powerful tool to help understand decision making in the presence of risk."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**<span style=\"font-size:24px;\">Chapter 1 Endnotes</span>**\n",
    "<a name=\"one_endnotes\"></a>\n",
    "\n",
    "$^1$ Oed.com, September 2022. \"risk, n.\". Oxford English Dictionary. https://www.oed.com/view/Entry/166306.\n",
    "<br><br>\n",
    "$^2$ Madeline Holcombe and Giulia McDonnell, \"A confession of love ended in a professor attacking her friend with a fire poker, police say.\" CNN, January 7, 2020. https://www.cnn.com/2020/01/07/us/mount-holyoke-professor-attack/index.html.\n",
    "<br><br>\n",
    "$^3$ William Shakespeare, _Romeo and Juliet_, Act II, Scene II.\n",
    "http://shakespeare.mit.edu/romeo_juliet/full.html.\n",
    "<br><br>\n",
    "$^4$ [Popper 1962](https://www.google.com/books/edition/Conjectures_and_Refutations/zXh9AwAAQBAJ?hl=en&gbpv=0).\n",
    "<br><br>\n",
    "$^5$ [Kim and Pittel 2000](https://doi.org/10.1006/jcta.1999.3054).\n",
    "<br><br>\n",
    "$^6$ [Knight 1921](http://www.econlib.org/library/Knight/knRUP.html).\n",
    "<br><br>\n",
    "$^7$ [Rovelli 2018](https://www.penguinrandomhouse.com/books/551483/the-order-of-time-by-carlo-rovelli/). Chapter 5.\n",
    "<br><br>\n",
    "$^8$ Roulette Life, 'How long does it take to spin 100 times in to a BM casino (average)?,' post dated June 15, 2015 by user kav. https://www.roulettelife.com/index.php?topic=358.0.\n",
    "<br><br>\n",
    "$^9$ History.com editors, 2009. 'World War II,' Section 2, Outbreak of World War II (1939). Online article. https://www.history.com/topics/world-war-ii/world-war-ii-history#section_2.\n",
    "<br><br>\n",
    "$^{10}$ Biography.com editors, Original Published Date April 2, 2014; Last Updated April 14, 2021. 'John Lennon: Biography.' Online article. https://www.biography.com/musician/john-lennon.\n",
    "<br><br>\n",
    "$^{11}$ H&aacute;jek, Alan, \"Pascal’s Wager,\" The Stanford Encyclopedia of Philosophy (Fall 2022 Edition), Edward N. Zalta (ed.), <https://plato.stanford.edu/archives/fall2022/entries/pascal-wager/>. \n",
    "<br><br>\n",
    "$^{12}$ Alfred Nobel, who died in 1896, didn't include economics in his list of prizeworthy fields. \"In 1968, Sveriges Riksbank (Sweden’s central bank) established The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.\"\n",
    "(https://www.nobelprize.org/prizes/facts/nobel-prize-facts/) All the Nobel Prizes cited in this book are of this type.\n",
    "<br><br>\n",
    "$^{13}$ U.S. and World Population Clock, September 30, 2022. https://www.census.gov/popclock/.\n",
    "<br><br>\n",
    "$^{14}$ Conspiracy Theory: \"a belief that some covert but influential agency (typically political in motivation and oppressive in intent) is responsible for an unexplained event.\" Under \"conspiracy, n.\". OED Online. September 2022. Oxford University Press. https://www.oed.com/view/Entry/39766.\n",
    "<br><br>\n",
    "$^{15}$ Anthony Tommasini, \"Review: A Tenor Reaches 18 High C's at the Metropolitan Opera,\" _The New York Times,_ February 8, 2019. https://www.nytimes.com/2019/02/08/arts/music/review-metropolitan-opera-donizetti-fille-camarena.html.\n",
    "<br><br>\n",
    "$^{16}$ [George 1879](http://www.henrygeorge.org/pchp2.htm), Chapter 2.\n",
    "<br><br>\n",
    "$^{17}$ Walmart, Inc, Common Stock. September 30, 2022. https://www.nasdaq.com/symbol/wmt/stock-report.\n",
    "<br><br>\n",
    "$^{18}$ [Mishkin 2006](https://fraser.stlouisfed.org/title/statements-speeches-frederic-s-mishkin-919/globalization-a-force-good-35638).\n",
    "<br><br>\n",
    "$^{19}$ The word \"variance\" is used by accountants to mean \"difference;\" for example if the corporate budget was $\\$100$Mn and the company spent $\\$110$Mn, the accounting variance is $-\\$10$Mn. In financial contexts with non-quantitative audiences it's best to be clear whether accounting variance or statistical variance is being used.\n",
    "<br><br>\n",
    "$^{20}$ [Cramer 1728](https://plato.stanford.edu/entries/paradox-stpetersburg/#HistStPetePara).\n",
    "<br><br>\n",
    "$^{21}$ The Austrian Mint (https://www.muenzeoesterreich.at/eng/Produkte/1-Ducat) makes modern restrikes of gold ducats. Based on gold content (which hasn't changed much since Bernoulli's time), we can guess that Bernoulli's \"one thousand ducats\" is the equivalent of around $\\$200,000$ today.\n",
    "<br><br>\n",
    "$^{22}$ Credit Suisse Research Institute, 'Global Wealth Report 2022.' https://www.credit-suisse.com/media/assets/corporate/docs/about-us/research/publications/global-wealth-report-2022-en.pdf. p. 5.\n",
    "<br><br>\n",
    "$^{23}$ [VNM 1953](https://archive.org/details/in.ernet.dli.2015.215284/page/n5).\n",
    "<br><br>\n",
    "$^{24}$ Stephen Cook, 'The P vs. NP Problem,' Clay Mathematics Institute. https://www.claymath.org/millennium-problems/p-vs-np-problem.\n",
    "<br><br>\n",
    "$^{25}$ It has been estimated that a cubic meter of space can take on at most 10 to the 10 to the 70 configurations ([Cain 2015](https://phys.org/news/2015-03-universe-finite-infinite.html)). It may never be known whether or not the universe is finite, but that is not relevant for the economic reality of the human race on the planet Earth over a finite time period. This is the gist of [Rovelli 2018](https://www.penguinrandomhouse.com/books/551483/the-order-of-time-by-carlo-rovelli/)'s previously cited comment that the world is \"subtly discrete.\"\n",
    "<br><br>\n",
    "$^{26}$ [VNM 1953](https://archive.org/details/in.ernet.dli.2015.215284/page/n5), p. 26.\n",
    "<br><br>\n",
    "$^{27}$ [Stanley 1997](https://www.cambridge.org/us/academic/subjects/mathematics/discrete-mathematics-information-theory-and-coding/enumerative-combinatorics-volume-2?format=PB), p. 297.\n",
    "<br><br>\n",
    "$^{28}$ [VNM 1953](https://archive.org/details/in.ernet.dli.2015.215284/page/n5), Appendix A.1 p. 617ff.\n",
    "<br><br>\n",
    "$^{29}$ For this simple example the background noise $Z$ is not independent, but the general result ensures that independent background noise $Z$ can be found. In the general result, risk preference is not being altered through diversification of the original choices $X$ and $Y$.\n",
    "<br><br>\n",
    "$^{30}$ Nobelprize.org. Maurice Allais: Facts. Website. https://www.nobelprize.org/prizes/economic-sciences/1988/allais/facts/.\n",
    "<br><br>\n",
    "$^{31}$ Nobelprize.org. Daniel Kahneman: Facts. Website. https://www.nobelprize.org/prizes/economic-sciences/2002/kahneman/facts/.\n",
    "<br><br>\n",
    "$^{32}$ [Kahneman 2011](https://us.macmillan.com/books/9780374533557/thinkingfastandslow), Chapter 29, Table 4."
   ]
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