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Chapter 12 Some Lessons from Capital Market History. 12.1 Returns 12.2 The Historical Record 12.3 Average Returns: The First Lesson 12.4 The Variability of Returns: The Second Lesson 12.5 Capital Market Efficiency 12.6 Summary and Conclusions.

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## 12.1 Returns 12.2 The Historical Record 12.3 Average Returns: The First Lesson

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**Chapter 12Some Lessons from Capital Market History**• 12.1 Returns • 12.2 The Historical Record • 12.3 Average Returns: The First Lesson • 12.4 The Variability of Returns: The Second Lesson • 12.5 Capital Market Efficiency • 12.6 Summary and Conclusions Vigdis Boasson Mgf 301 School of Management, SUNY at Buffalo**12.2 Percentage Returns (Figure 12.2)**Total $42.18 Inflows Dividends $1.85 Endingmarket value $40.33 Time t t = 1 Outflows – $37**12.3 Percentage Returns (Figure 12.2) (concluded)**Dividends paid at Change in market end of period value over periodPercentage return = Beginning market value Dividends paid at Market value end of period at end of period1 + Percentage return = Beginning market value + +**12.4 Percentage Returns (Figure 12.2) (concluded)**1.85 + (40.33 - 37) Percentage return = 37 = 14% Total dollar return = dividend income + capital gain (Loss). Percentage return = Dividend yield + Capital gains yield.**12.5 Average Returns**• Average Returns = Sum of the T observed returns divided by T. • Risk Premium = The difference between a risky investment return and the risk-free rate. • Take the T-bill rate as the risk-free rate and common stocks as an average risk. The excess return is the difference between an average risk return and returns on T-bills.**12.6 Average Annual Returns and Risk Premiums: 1926-1996**(Table 12.3) Investment Average Return Risk Premium Large company stocks 12.7% 8.9% Small company stocks 17.7 13.9 Long-term corporate bonds 6.0 2.2 Long-term government bonds 5.4 1.6 U.S. Treasury bills 3.8 0.0**12.7 Variability of Returns**• Variance and Standard Deviation • Variance = the average squared deviation between actual returns and their means:**12.8 Historical Returns, Standard Deviations, and Frequency**Distributions: 1926-1996 (Figure 12.10) Average Standard Series Annual Return Deviation Large Company Stocks 12.7% 20.3% Small Company Stocks 17.7 34.1 Long-Term Corporate Bonds 6.0 8.7 Long-Term Government Bonds 5.4 9.2 U.S. Treasury Bills 3.8 3.3 Inflation 3.2 4.5**12.9 The Normal Distribution (Figure 12.11)**Probability 68% 95% Return onlarge companystocks > 99% + 3 73.6% – 3 – 48.2% – 2 – 27.9% – 1 – 7.6% 012.7% + 1 33.0% + 2 53.3%**12.10 Market Efficiency**Efficient capital market: market in which current market prices fully reflect available information. In such a market, it is not possible to devise trading rules that consistently “beat the market” after taking risk into account. Efficient markets hypothesis (EMH) : asserts that modern US stock markets are efficient. EMH implies that securities represent zero NPV investments - meaning that they are expected to return exactly their risk-adjusted rate. “In an efficient market, prices ‘fully reflect’ available information.” Professor Eugene Fama, financial economist (1976)**12.11 Reaction of Stock Price to New Information in**Efficient and Inefficient Markets (Figure 12.12) Efficient market reaction: The price instantaneously adjusts to and fully reflects new information; there is no tendency for subsequent increases and decreases.Delayed reaction:The price partially adjusts to the new information; 8 days elapse before the price completely reflects the new informationOverreaction:The price overadjusts to the new information; it “overshoots” the new price and subsequently corrects. Price ($) Overreaction andcorrection 220 180 140 100 Delayed reaction Efficient market reaction Days relativeto announcement day +4 +6 –4 –2 0 +2 +7 –8 –6**12.12. Forms of market Efficiency**• Three forms of market efficiency: • 1. Weak form efficiency = A form of the theory that suggests you can’t beat the market by knowing past prices. • 2. Semi-strong form efficiency = Perhaps the most controversial form of the theory, it suggests you can’t consistently beat the market using publicly available information. • 3. Strong form efficiency = The form of the theory that states no information of any kind can be used to beat the market. Evidence shows this form does not hold.**12.12 Example: Average returns**How are average annual returns measured? Mean value Assume your portfolio has had returns of 10%, -7%, 28%, and -11% over the last four years. What is the average annual return? Your average annual return is simply: [.10 + (-.07) + .28 + (-.11)]/4 = ________% per year**12.13 Example: Return volatility**Return Volatility: The usual measure of volatility is the standard deviation, which is the square root of the variance: Year Actual Average Return Squared return return deviation deviation 1 .10 .05 .05 .0025 2 -.07 .05 -.12 .0144 3 .28 .05 .23 .0529 4 -0.11 .05 -.16 .0256 Total .20 .00 .0954 The variance, Var(R) = .0954/( 4 -1 ) = .0318 The standard deviation, or SD(R) = = .1783 or 17.83%**12.14 Historical average returns, risk premiums and**volatility • Risk premiums: The risk premium is the difference between a risky investment’s return and a riskless return. Based on historical data: Investment Average Standard Risk return deviation premium Common 12.7% 20.3% 8.9%stocks Small 17.7% 34.1% 13.9%stocks LT Corporates 6.0% 8.7% 2.2% Long-term 5.4% 9.2% 1.6%Treasury bonds Treasury bills 3.8% 3.3% 0.0%**12.15 Example: calculating returns**• Suppose a stock had an initial price of $54 per share, paid a dividend of $1.75 per share during the year, and had an ending price of $65. Calculate: a. percentage total return b. dividend yield c. capital gains yield**12.16 Solution:**a. percentage total return : R = [$1.75 + ($65 - 54)]/$54 = 23.61% b. dividend yield = $1.75/$54 = .0324 = 3.24% c. capital gains yield = ($65 - 54)/$54 = .2037 = 20.37%**12.17 ExampleCalculating average returns and volatility:**• Using the following returns, calculate the average returns, the variances, and the standard deviations for stocks X and Y. Returns Year X Y 1 14% 22% 2 3 -5 3 -6 -15 4 11 28 5 9 17**12.22 Solution to Problem 12.7 (concluded)**Mean return on X = (.14 + .03 - .06 + .11 + .09)/5 = .062. Mean return on Y = (.22 - .05 - .15 + .28 + .17)/5 = _____. Variance of X = [(.14-.062)2 + (.03-.062)2 - (0.06-.062)2 + (.11-.062)2 + (.09-.062)2]/(5 - 1) = .0025. Variance of Y = [(.22-.094)2 + (-.05-.094)2 - (-.15-.094)2 + (.28-.094)2 + (.17-.094)2]/(5 - 1) = .03413. Standard deviation of X = (.0025)1/2 = 5%. Standard deviation of Y = (.03413)1/2 = _____%.

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