In this model, the value of the stock today is the present value of the expected cash flows (equal to one dividend payment plus a final sales price).

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1 Money & Banking Notes Chapter 7 Stock Mkt., Rational Expectations, and Efficient Mkt. Hypothesis Computing the price of common stock: (i) Stockholders (those who hold or own stocks in a corporation) are residual claimants (of all funds flowing into the firm): meaning that the stockholders receive whatever remains after all other claims against the firm s assets have been satisfied. (ii) Dividends are payments made periodically (sometimes quarterly or annually) to stockholders. (iii) A basic principle of finance: the value of any investment is found by computing the present value of all cash flows the investment will generate over its life. The One-Period Valuation Model In this model, the value of the stock today is the present value of the expected cash flows (equal to one dividend payment plus a final sales price). the current (today s) price of the stock the dividend paid at the end of year 1 P 0 = Div 1 (1 + k e ) + P 1 (1 + k e ) the (selling) price of the stock at the end of the first period the required return on investments in equity (the discount factor)

2 or fairly valued Example: Suppose you want to buy a share of stock (say, IBM) which currently sells for $50 (P 0 ) per share and pays a dividend of $0.16 (Div 1 ) per year. An analyst predicts that it will sell for $60 per share next year (P 1 ). Would you buy this stock today? Alternatively, you can also ask: Does the current price of the stock of $50 reflect the analyst s forecast? Is the stock undervalued (current selling price of $50 < estimated P 0 ), overvalued (current selling price of $50 > estimated P 0 ) or correctly valued (current selling price of $50 = estimated P 0 )? Suppose you decide that you would want a return on investment (k e ) of 12 % from buying this stock then holding it for a year. Using the one-period valuation model above, you can now calculate what you think the value is of this stock today (P 0 ). P 0 = 0.16 (1+0.12) + 60 (1+0.12) = $53.71 estimated P0 or the value you place on the stock check for yourself Your own calculations show that the IBM stock is worth more (at $53.71) to you than what it is currently selling for (at $50), so the stock is undervalued (at $50, it is undervalued or a bargain by your estimate.) You would want to buy this stock because it can rise in value. the value you place on the stock The Generalized Dividend Valuation Model The value of stock today is the present value of all future cash flows P D D D P... (1 ) (1 ) (1 ) (1 ) 1 2 n n n ke ke ke ke If P n is far in the future, it will not affect P P 0 t 1 Dt (1 k ) The price of the stock is determined only by the present value of the future dividend stream e t 0 n Equation (2) Equation (1)

3 In the generalized dividend valuation model, written in full above (equation 1), the value of the stock today is the present value of all expected cash flows (equal to all future dividend payments plus a final sales price (P n ) when the stock is finally sold in period n). But if P n is far into the future, it is so small or negligible that it does not affect P 0. Thus, the generalized valuation model can be rewritten as equation (2) above. What if stocks don t pay dividends? Many companies don t pay dividends. The important thing to remember is that buyers of the stock expect that the firm will pay dividends. Note that calculating an infinite stream (flow) of dividends can be quite difficult. Thus, a need for simplification. The Gordon Growth Model (GGM) important assumptions

4 How the (Stock) Market Sets Prices The price is set by the buyer willing to pay the highest price. (Although the price may not be the highest that the asset can fetch, it would be incrementally higher than what any other buyer is willing to pay.) The market price will be set by the buyer who can take best advantage of the asset. (A buyer who can put the asset into its most productive use would offer to pay a higher price than another buyer and the asset will be sold to him/her.) Superior information about an asset can increase its value by reducing its perceived risk. Example: Suppose you d like to buy a stock that s expected to pay a $2 dividend next year (= D 1 in the GGM equation). Market analysts expect the firm to grow at 3 % indefinitely (forever), which translates to a growth in dividends of g = 0.03 in the GGM equation. After plugging these numbers into the GGM equation, we have P 0 = Div 1 (k e g) = $2 (k e 0.03) Thus, we can then make an estimate of the present value of the stock if we make a further assumption about our required rate of return (k e ) for buying this stock.

5 Suppose further that also interested in this stock are two other trader/investor friends of yours: Michalea V and AiAi, and just the three of you constitute the entire market for this stock. Let s assume that each of you have a different perceived risk about this stock which translates into your respective discount rates. You feel very uncertain (high risk) about the future dividends of this company and their constant growth so you require a return of, say, 15 %. Your friend Michalea V has friends who work inside the industry and so she knows more about the company, its inner workings and prospects. She is more confident (less uncertain) about it (i.e., her perceived risk is lower than yours) so her required return is 12 %. Your friend AiAi dates the CEO of the company and so she knows more about the company than the two of you, is more confidents about its prospects, and assigns a required return of only 10 %. These numbers are shown in Table 1 below along with the corresponding estimates of P 0 using the GGM equation. Table 1 Investor Discount Rate (k e ) Est. Stock Price You 15 % $16.67 Michaela V 12 % $22.22 AiAi 10 % $28.57 P 0 = $2 ( ) double check these numbers

6 Table 1 shows that you are willing to pay $16.67 for the stock. Michaela V would pay $22.22 and AiAi would pay $ Why is AiAi willing to pay the most (more than everyone else)? It s because she is the investor with the lowest perceived risk (her lowest perceived risk comes from her superior information about the company). If there were no other traders for this stock (only the three of you), the market price for the stock would range between $22.22 and $ So the players in the mkt., bidding against each other, establish the market price. Thus, information is important in valuing assets. When new information is released about the firm, market participants (investors ) expectations (about future dividends or the risk of those dividends) change (or are revised) and, thus, stock prices change. Is it any wonder then that stock prices are constantly changing as well? Monetary Policy and Stock Prices How does monetary policy affect stock prices? Two ways, according to the GGM equation: When the U.S. Federal Reserve lowers interest rates, the return on bonds (an alternative asset to stocks) declines, and investors are likely to accept a lower required rate of return on an investment in equity (k e ). (i) the decline in k e would lower the denominator in the GGM equation, leading to a higher value for P 0, raising stock prices.

7 P 0 = Div 1 ( k e g) A lower k e lowers the whole denominator and raises P 0 (ii) the lowering of interest rates by the Fed would stimulate the economy, and raise the growth rate in dividends, g, which in turn would lower the denominator in the GGM equation, leading again to a higher value for P 0, raising stock prices. P 0 = Div 1 (k e g ) A higher g lowers the whole denominator and raises P 0 The Theory of Rational Expectations Adaptive expectations = the view that changes in expectations will occur slowly over time as past data changes (e.g., expectations of inflation are viewed as being an average of past inflation rates; if inlfation rates averaged 5 % in the past, future or expected inflation rates would slowly rise to 5 % also; and if past inflation rates were a steady 10 %, expected inflation would be 10 %, but slowly, say, 6 % in the first year, 7 % in the second year, and so on). A problem with adaptive expectations is that people use more information than just past data to form their expectations. E.g., inflation expectations can be affected by people s predictions of future monetary policy as welll as current and past monetary policy. Also, people can change their expectations quickly in light of new information.

8 The theory of rational expectations says that expectations will be identical to optimal forecasts (the best guess or best possible guess of the future) using all avalilable information. Suppose that under normal circumstances (a sunny day, no unusual events like street rallies), it takes you about 10 minutes to walk from your apt. to the bus stop every day when you go to school (sometimes it s 8 min., sometimes it s 12 min., but on average it s 10 min.). But when it rains (which can cause a little flooding), it takes you a little longer, say, an additional 5 min. (so, total walking time = 15 min.). If today it rains, the optimal forecast for your walk to the bus stop is 15 minutes the best guess using all available information (your average walking time of 10 min. plus the fact that it is raining, which adds an additional 5 min.). Then, according to the theory of rational expectations, your expectations would also be the same, 15 min. An expectation (of your walking time) of min. 10 on a rainy day would not be rational because it is not the best guess using all available informtion. You re ignoring the additional 5 min. that a rainy day adds to the forecast or guess. Suppose on some days your walk to the bus stop takes you 13 min. and on other days it takes you 17 min. Does this mean that you 15-min. expectation is no longer rational? No, 15 min. is still rational.

9 The forecast does not have to be perfectly accurate to be rational. The forecast only need to be the best possible given the available information, meaning, it has to be correct on average. There is bound to be variations (some randomness), thus, an optimal forecast will never be completely accurate. Thus, even though a rational expectation equals the optimal forecast using all available information, a prediction based on it may not always be perfectly accurate. An expectation may fail to be rational because: (i) people may be aware of all available information but takes too much effort to make the expectation the best guess possible (ii) people may be unaware of some relevant available information, so their best guess will not necessarily be accurate Formal Statement of the Theory X e = X of The expectation of X equals the optimal forecast of X using all available information. Rationale Behind the Theory Statement of the Theory Why would people want to make their expectations match the best possible guess of the future, using all available information? It is costly for people not to do so.

10 If you often underpredict your walking time to the bus stop, you could be late for class and there is a risk you could fail a class for being late often. If you overpredict, you could get to class early but you could be giving up sleep or leisure time unnecessarily. Thus, accurate expectations are desirable. There are strong incentives for people to make expectations equal to optimal forecasts by using all available information. In financial markets, people with better forecasts of the future get rich. The application of the theory of rational expectations to financial markets (where it is called the efficient market hypothesis or the theory of efficient capital markets) is thus particularly useful. The Efficienct Market Hypothesis Current prices in a financial market will be set so that the optimal forecast of a security s return using all available information equals the security s equilibrium return. Stated differently, in an efficient market, a security s price fully reflects all available information. Arbitrage = the process of of buying a good in one market at a low price and selling it in another market at a higher price to profit from the price difference. In financial markets, arbitrage happens when market participants eliminate (take advantage of) unexploited profit opportunities (i.e., returns on a security that are larger than what is justified by the charactritics of that security). Pure arbitrage is when the elimination of unexploited profit opportunities involves no risk.

11 In short, arbitrage leads to the efficient market hypothesis. Stated differently, in an efficient market, all unexplained profit opportunities will be eliminated. the optimal forecast of a security s return R of = R * the security s equilibrium return When the optimal forecast of the return of a security (R of ) is greater than its equilibrium (normal) return (R * ), an unexploited profit opportunity exists. People (not everyone, but even just a few smart money people) would start buying this security, driving up its current price relative to its expected future price and lowering its R of until such time that R of = R * (i.e., until the efficient mkt. condition is satisfied and the buying stops; or, until stocks are correctly/fairly valued). Argue the opposite case to show that the eficient mkt. condition is also achieved while starting with the optimal forecast of the return of a security (R of ) being less than its equilibrium (normal) return (R * ). stocks are undervalued at this point stocks are overvalued at this point point where stocks are fairly/correctly valued

12 How Valuable are Published Reports by Investment Advisors? Information in newspapers and in the published reports of investment advisers is readily available to many market participants and is already reflected in market prices. So acting on this information will not yield abnormally high returns (returns greater than the equilibrium return), on average. The empirical evidence for the most part confirms that recommendations from investment advisers cannot help us consistently outperform (or beat) the general market. A person who has done well in the past cannot guarantee that he/she will do well in the future. Should You Be Skeptical of Hot Tips? A hot tip is probably information already contained in the price of the stock. Stock prices respond to announcements only when the information is new and unexpected. A buy and hold strategy is the most sensible strategy for the small investor (i.e., buy the stocks and hold them for a long period of time). Or, instead of individual stocks, buy into a no-load mutual fund. Stock prices will respond to announcements (will be affected) only when the informtion being announced is new and unexpected. If the news about the firm is expected, no stock price response will occur. Stock prices do reflect publicly available information.

13 Why the Efficient Market Hypothesis Does Not Imply that Financial Markets are Efficient Market fundamentals = items that have a direct impact on the future income streams of the security (e.g., the demand for the company s product, how much competition it faces, how much capital it has, how loyal are its customers, how large the size is of its market, etc.). Fundamental analysis refers to the detailed analysis of a company (and its financial statements) to estimate its value. Some financial economists believe all prices are always correct (or expectations are rational) and reflect the true market fundamentals (intrinsic) values of the securities and so financial markets are efficient in a stronger sense. However, prices in markets like the stock market are unpredictable (just look at the existence of market crashes and bubbles). This casts serious doubt on the stronger view that financial markets are efficient. Market bubbles = when the prices of assets rise above their fundamental values. Behavioral Finance Behavioral finance = a field of study that applies concepts from other social sciences like anthropology, sociology and psychology to understand the behavior of securities prices.

14 Short sales = when investors borrow stocks from brokers in the belief that stock prices are high now with the goal of profitting by buying them back later ( covering the short ) when stock prices drop or expected to drop. Loss aversion = when people are more unhappy when they suffer losses than they are happy when they achieve gains. The efficient mkt. hypothesis suggests that smart money participants will sell their stock holding when a stock price goes up irrationally (i.e., not supported by fundamentals; or, when R of < R * or, when stocks are overvalued). For this to happen, smart money participants have to engage in short sales so that the stock price falls to a level justified by fundamentals (or, when R of = R * ). Work by psychologists, however, suggests that people are subject to loss aversion (losses from short sales can turn out to be excessive or huge if prices went up instead of down). Hence, they might avoid short sales of the stock (in which case the stock might continue to stay high or overvalued). Thus, the lack of enough actual short selling in the market (causing stoks to be sometimes over-priced or overvalued) may be explained by loss aversion.

15 Overconfidence (the belief of investors that they are smarter than other investors and so they trade on those beliefs while ignoring the pure facts) and social contagion (fads) provide an explanation for speculative stock market bubbles (which crashes when prices finally get too far out of line with fundamentals). The large trading volume in securities markets may be explained by investor overconfidence.