Chapter 16: The Stock Market Overview He that could know what would be dear need be a merchant but one year. Proverb [1] Your stock market score could well determine the quality of your retirement. This chapter does not attempt to provide an overview of the stock market, but rather it covers some topics in finance that have game-theory-like qualities. [1] Browning (1989), 378. Stock Market Commentators How seriously should we take commentators who predict future stock price movements? To figure this out, we first have to examine why anyone would widely disseminate his stock picks. Pretend a pirate claims to know the location of a buried treasure. You figure there’s a 1 percent chance that he is both sane and honest. The pirate then gives you a usable map that seems to show the exact location of the treasure. Do you still believe the pirate? Since it’s unlikely that a sane pirate will reveal the location of treasure, the fact that the pirate freely tells you where his treasure is buried reduces the chance that he actually has any useful information. Now imagine that instead of a pirate revealing the whereabouts of a treasure, a financial analyst reveals the name of a stock she claims will rapidly increase in value. The analyst’s willingness to part freely with this information should itself eviscerate the credibility of that information. Knowledge about what stock will increase is valuable. If the analyst were someone whom many people believed and trusted. then the analyst would never just give away this information; she would sell it. Might not the analyst, however, both sell this information and freely reveal it? No. Those who paid would be upset that they had to pay for something others got for free. Consequently, the fact that the analyst willingly disseminates this knowledge shows that either the analyst does not believe her own predictions or lacks the credibility to actually get paid for this information. What if the analyst works for a business publication, writing articles concerning which stocks will increase? If the owners of the magazine really believed in the analysis, they would not disclose the predictions but would trade on them themselves. No sane magazine owners would publish a map to a buried treasure if they believed the map to be accurate and the treasure to be precious. Similarly, sane magazine owners would sell the predictions for the price of their magazine only if they didn’t believe that the predictions were valuable. It’s possible that the analyst is reliable, but no one believes her, and so the analyst can’t sell this valuable information. If you do choose to follow this analyst’s advice, however, you should at least acknowledge that the market doesn’t value her opinion. People in the financial industry don’t think this information has much value, or the analyst wouldn’t freely part with her predictions. Not all financial advice should be suspect. You shouldn’t trust a pirate who gives you his map, because the pirate himself would be hurt by your taking his treasure. There are some types of financial “treasure,” however, that everyone can enjoy. Consider two pieces of information: 1. Acme stock is undervalued. 2. Investors should diversify their portfolios. Since only a few people can benefit from purchasing an “undervalued” stock, telling many people about (1) decreases the value of this information. In contrast, the idea that investors should diversify doesn’t decrease the value of anything when many people act on it. You should consequently trust financial advice when the advisor wouldn’t personally benefit from hoarding this information. The Future Is Now As the following game illustrates, stock prices respond very quickly to new information. Pretend you have an asset that is useless to anyone but me. Next week I will be willing to pay $60 for this asset. How much is this asset worth today? Obviously, it’s worth $60, yet many investors seem not to understand this game. Imagine investors believe that the Federal Reserve Board will cut interest rates next week. For reasons I won’t detail, interest rate cuts help stocks. Does this mean that next week stock prices will rise when interest rates fall? Of course not. Say a stock is worth $58 if interest rates are not cut and $60 if they are. If it is known that interest rates will be cut next week, then the value of the stock will increase to $60 today; the market won’t wait for next week. Next week, when interest rates do change, they will not influence stock prices. Interest rate cuts increase stock prices only when first anticipated. Just as expected interest rate cuts don’t move the stock market, anticipated corporate developments don’t change stock prices. Consider, for example, when the expiration of a patent will hurt a pharmaceutical company’s stock price. When a drug company discovers some useful new compound, they obtain a patent on it. The patent gives the pharmaceutical company the sole right to sell the discovered drug for some limited period of time. After the patent expires, anyone can make and sell the drug. The pharmaceutical company obviously loses lots of money when a patent expires, because it loses its right to be the exclusive provider of the drug. If a pharmaceutical company’s patent will expire next week, will its stock price fall next week? No, since everybody knows that the patent will expire next week. It can’t be that this week the stock is trading at $50, but everyone knows that next week the stock will trade at only $40. If this were the case, everyone would sell the stock this week, causing its price to fall immediately. If everyone knows the patent will expire next week, then next week’s expiration will have no effect on the stock price. Recall, it’s the announcement of the rate cut that affects the stock market, not the actual rate cut. Similarly, the expiration will affect the stock market when people first learn that a patent will expire. The time at which a patent will expire is known when the government initially issues the patent, so the expiration of the patent affects the stock price when the patent is first given. For example, imagine that a pharmaceutical company’s stock sold for $50 yesterday, but today the company unexpectedly discovers a wonder drug. Assume that if the company were given an infinite patent on this drug, then the company’s stock would jump to $60. If, however, the company is granted only a 14-year patent, then the discovery will cause the company’s stock price to jump to only $58. Today the stock will trade for $58 since the effect of the patent’s expiration is factored into the stock price when the patent is first issued, not when the patent actually expires. Short-Run Holders Should Care About the Long Term Too [2] A firm announces its one-year plan, but you don’t care because you’re planning on selling the stock in one day. Actually, because anticipated future events affect today’s stock price, even short-term day traders should worry about their investments’ long-run prospects. You consider buying a stock on Monday and selling it Tuesday. Should you be concerned about what could happen to the stock on Friday? Yes, because it will affect the price received on Tuesday. If the person you sell the stock to is one of those boring buy-and-hold people, then obviously he will care about what happens on Friday. What he is willing to pay on Tuesday will be influenced by what he suspects will occur on Friday. But let’s say that you sell the stock to another short-term trader who plans to sell it on Wednesday. Even if this buyer intends to sell to another person with a short time horizon, either that next buyer will care about Friday, or she will sell to someone who does. What she is willing to pay will be affected by what is supposed to happen on Friday. When a trader sells a stock, the price he gets is determined by what the next buyer will pay, which is affected by what the next buyer will pay, and so on. Consequently, not wanting to hold your stock for the long run does not mean that the long run doesn’t have a hold on you. Short-term traders should care about the future exactly as much as long-run investors do. If this were not true, short- and long-term traders would place different values on the same stock. If the short-run people valued the stock less, they would never buy the stock, and the market would rightly ignore their preferences. Market prices would then reflect long-run evaluations. If short-term traders valued it more, then they would be in trouble because if the short-term investors paid more than the long-run investors thought the stock was worth, then the short-term investors would be able to profitably sell the stock only to other short-run investors. But since short terms become long runs, these traders would eventually have to sell for a loss. What if, however, it’s known that a stock’s price will go up to $90 today and go back to $80 tomorrow? If this kind of situation arose, then short- and long-run investors would indeed have different perspectives. This situation, however, should never manifest itself. A stock’s value is determined by what someone would pay for it. Why would anyone pay $90 today for something that is going to be worth only $80 tomorrow? Perhaps because they will sell it to someone before the price goes down. But then why would this second buyer pay more than $80? [2] CNBC.com (April 25, 2000). Risk Versus Return The basic lesson of the stock market is that investors get greater average returns for taking on higher risk. What would you rather have: 1. $100,000 or 2. a 50 percent chance of getting $200,000 and a 50 percent chance of getting nothing? Both choices give you on average $100,000. The majority of investors, however, would prefer the first choice: the sure thing. Most people dislike risk, which is why so many of us buy insurance. True, many people also enjoy gambling, but for most gambling is a form of entertainment, not an investment strategy. When most people invest, they want to avoid risk. People’s desire to avoid risk ensures that stocks pay higher returns because they are risky. Investors can either put their money in U.S. government bonds where they are guaranteed a certain rate of return, or they can buy stocks. Stocks are much riskier than government bonds. Would it make sense to live in a world where on average stocks and government bonds gave the same return? If they did offer the same return, everyone would buy the government bonds. The only reason anyone willingly takes a chance on stocks is because on average they yield a higher return. For our economy to survive, people need to buy both stocks and government bonds. Market forces ensure that the prices of stocks adjust until investors are willing to buy both stocks and government bonds. The market induces investors to buy both financial products by giving stock investors on average higher returns. The Return on Art Should you invest in art? Only if you’re willing to sacrifice profits for artistic pleasure. On average, art appreciates less than stocks. To see this, imagine living in a world where on average a piece of artwork goes up as much as stocks do. If this were the case, most everyone would rather have a nice painting than a stock certificate. Consequently, if on average stocks and art performed equally well, no one would buy stocks. Since capitalism requires that people invest in stocks, the market automatically adjusts the return on stocks so that they do financially better on average than art does. Stocks’ superior performance doesn’t mean you should never invest in art; rather, you should accept that on average your artistic investments will earn a lower return than your stock market investments. Survivorship Bias in Mutual Fund Reports Mutual funds remain one of the most important investment vehicles for the middle class. Mutual funds compete intensely for investors. They often tout superior past performance as proof that they will continue to yield a good return. How reliable, however, are reports of past performance? The SEC closely regulates how mutual funds' managers calculate and describe past returns, so these reports are factually accurate; but performance reports can, however, be both accurate and misleading. Mutual fund performance reports can be skewed by survivorship bias. To understand survivorship bias, consider the following fraudulent scheme used to cheat sports bettors: First, find the mailing addresses of 1,600 people who place heavy bets on sports. Write to each of them and say that you will predict the outcome of three football games. Then, for $100, you will sell them your prediction for who will win the Super Bowl. If your prediction on the Super Bowl proves incorrect, you will refund their money. For the first game, you should send to 800 people a letter predicting that one team will win, and to the other 800, a letter predicting that the other team will be victorious. Next, forget about the people to whom you made the false prediction. For the 800 people for whom you correctly picked the outcome, send half of them a letter claiming that one team will win the next game, and send the other half a letter claiming the opposite team will win. After the second game you will now have 400 people to whom you have correctly predicted the outcome of two games. You repeat the same process for these 400 people. At the end of the third game you now have 200 people to whom you have correctly predicted the outcome of three football games. You mail each of these 200 people a letter saying that you will correctly predict the outcome of the Super Bowl for $100. You also promise to return their money if you incorrectly predict the outcome. For the people who send you the $100, you tell half of them that one team will win and the second half that the other team will be victorious. You then return the money to the people for whom you incorrectly predicted the Super Bowl outcome. Assuming that all 200 people paid you for your super bowl prediction you have now made a profit of $10,000 minus postal costs. Furthermore, all the people whose money you have kept are satisfied since they got what they paid for. Now, imagine that instead of playing this game with sports bettors, you play it with investors. You start with a large number of mutual funds. They all make different investments. You close down the ones that do badly and keep the ones that do well. You only advertise the funds that do well, saying they have a successful track record and thus you must be good at investing. The managers of mutual funds don't exactly play this game. Poorly performing mutual funds, however, are often closed down, making the ones that are kept operating seem better than they really are. For example, imagine that this year 100 new mutual funds are started. Further imagine that each fund manager makes his investment decisions by throwing darts at a newspaper listing of stocks. After a year the funds that do poorly are closed down. On average, the surviving funds' performances will be well above average. This doesn't mean that these funds' managers have any skill at picking investments, but rather that survivorship bias makes past performance misleadingly attractive. Conclusion For reasons that this book hasn’t gone into, economists believe that stock price movements are mostly random, so attempts at market predictions are folly. The wisest investment strategy you can follow is to buy a diversified portfolio (or invest in an index fund), continually add to the portfolio over your working life, and sell only when you need the funds for retirement. Lessons Learned  If someone freely gives you stock advice, ask why she can’t get anyone to pay them for the information.  Events affect stock prices when they are anticipated, not when they actually occur.  Even short-term traders need to be concerned with the long-term prospects of stocks.  To compensate investors for taking on risk, market forces cause stocks on average to pay higher returns than safe government bonds.  Survivorship bias makes mutual funds’ past performances seem misleadingly impressive. Chapter 17: Further Readings and References I hope that after reading Game Theory at Work you are motivated to learn more about game theory and economics. I have not been paid, unfortunately, for recommending any of the following books. Further Readings in Game Theory Games of Strategy by Avinash K. Dixit and Susan Skeath is an excellent undergraduate textbook. The book requires no knowledge of economics but does require some understanding of calculus. It would make an excellent second book for a reader who has completed Game Theory at Work and wants to undertake a rigorous study of game theory. Co-opetition by Adam M. Brandenburger and Barry J. Nalebuff is a nontechnical business book on how to negotiate, cooperate, and compete. Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff is a nontechnical game theory book for a general audience, although it is less focused on business. Games, Strategies, and Managers by John McMillan provides a very nontechnical introduction to game theory. The Evolution of Cooperation by Robert Axelrod is a nontechnical explanation of cooperation in repeated prisoners’ dilemma games. Prisoner’s Dilemma by William Poundstone is a nontechnical book devoted to the history, philosophy, and application of prisoner’s dilemma. A Beautiful Mind by Sylvia Nasar is a biography of John Nash. Game Theory for Applied Economists by Robert Gibbons is a more advanced game theory book than Games of Strategy. As the title implies, it assumes that the reader has some knowledge of economics. Strategy: An Introduction to Game Theory by Joel Watson is an advanced game theory textbook for undergraduates that incorporates contract theory. http://www.gametheory.net is an excellent web resource for game theory. [...]... probability of the prize being in box A Before the host opened one of the two other boxes, there was a 1/3 chance of the prize being in box A, and after he opened one of the other boxes, there is still a 1/3 chance of the prize being in box A Let’s say that the host opened box B and showed you that it was empty Now, since there is a 1/3 chance that box A has the prize, and a zero chance that box B has the prize,... that it is equally likely that the car is of high quality or it's junk The seller knows the car's quality The following gives the value of the car to both you and the seller Car's Quality Value To You Value to Seller High $10,000 $6,000 Junk $0 In the game you make an offer to buy the car If the offer is rejected, the game ends Even though there is a 50 percent chance that the car is of high quality,... game In Figure 52 the macho strategies are A for Player One and X for Player Two If one player chooses the macho strategy, and the other, the wimpy strategy, the player who takes the macho course will do much better than his opponent Figure 53 is a coordination game because the parties want to work with each other to get either A,X or B,Y The players should be open with each other about their moves If... to how economists think the stock market works Most of what is written about the stock market for general audiences has the validity and intellectual rigor of astrology, so many investors would benefit from this book References Akerlof, G., 'The Market for Lemons: Quality Uncertainty and the Market Mechanism,' Quarterly Journal of Economics, 89: 488-500, 1970 Axelrod, Robert, The Evolution of Cooperation,... are empty, but the third contains an expensive prize You don’t know which box has the prize, but the host does You are first told to choose one of the boxes Next, the game show host will pick an empty box that you didn’t choose and open it, showing that it’s empty Finally, the host gives you the option to change boxes You can switch from the box you picked to the other unopened box Is there any advantage... label the three boxes as A, B, and C and assume that you picked box A Obviously there is a 1/3 probability that the prize is in box A and a 2/3 probability that the prize is in either box B or C Either or both boxes B or C are empty Thus, after you pick box A, it will always be possible for the host to open either box B and C to reveal an empty box Consequently, the host’s actions do not affect the probability... equilibrium where either firm charges more than $13 If this occurred, each firm would want to slightly undercut the other and take all the customers There can't be a Nash equilibrium where a firm charges an amount below its cost and loses money, because such a firm would rather charge a very high amount and get no customers There are, however, many other Nash equilibria besides the one where both firms... about the movie, if it was worth $8 yesterday to attend it should still be worth $8 today Chapter 3 The Dangers of Price Competition 5 Answers 5 Assume that three people secretly write down a dollar amount on a piece of paper They must pick a whole dollar amount between $0 and $100 The person who writes down the lowest number wins the amount she wrote down If there is a tie, the winners split the total... $5, Debbie would take the $5 if the envelope was empty and reject the money if it had $100 Thus, Jim is better off offering $0 than $5 17 If you offer to buy the car for less than $6,000 the seller will always reject your offer if the car is of high quality So, for example, if you offer to buy the car for $200, 50 percent of the time your offer will be rejected, and 50 percent of the time it will be... no one is going to pick $99 or $100, the only chance to win with $98 is if both of the others also choose $98 In this case, however, you would have been better off writing down $97 Thus, $98 is out This process continues all the way down to $1 You don’t want to pick $0 because then you would always get nothing You would rather split $1 than get zero Therefore, the only reasonable outcome in this game . the same stock. If the short-run people valued the stock less, they would never buy the stock, and the market would rightly ignore their preferences. Market. effect on the stock price. Recall, it’s the announcement of the rate cut that affects the stock market, not the actual rate cut. Similarly, the expiration