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

1. 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

2. 12.2 Percentage Returns (Figure 12.2) Total $42.18 Inflows Dividends $1.85 Endingmarket value $40.33 Time t t = 1 Outflows – $37

3. 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 + +

4. 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.

5. 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.

6. 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

7. 12.7 Variability of Returns • Variance and Standard Deviation • Variance = the average squared deviation between actual returns and their means:

8. 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

9. 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%

10. 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)

11. 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. 12.12. 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.

13. 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

14. 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%

15. 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%

16. 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

17. 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%

18. 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

19. 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 = _____%.