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**Chapter 10 Notes & Questions**

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**Return on Investment In nominal terms:**

Total dollar return = Dividend income + Capital gain (or loss) Total cash if stock is sold = Initial investment + Total return

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**Return on Investment In percentage terms: Dividend yield = Dt+1 / Pt**

Capital gains yield = (Pt+1 – Pt) / Pt

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Risk Premium The excess return required from an investment in a risky asset over that required from a risk-free investment (usually the return on T-bills).

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Average Return Arithmetic average = “the return in an average year over a particular period”. That is, add up the annual returns, then divide by the number of periods.

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Average Return Geometric average = “what is the average compound return per year over a particular period?” That is, multiply (1+Rt) for all t up to final period T, take the 1/T root, then subtract 1.

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**Variance and Standard Deviation**

Variance = the average squared difference between the actual return and the annual return. Standard deviation = the (positive) square root of the variance.

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**Which average calculation method to use?**

The arithmetic average is probably too high for longer periods (longer than ~ 10 years); for several decade projections, split the difference; for very long forecasts, use geometric mean.

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Efficient Markets In an efficient capital market, current market prices fully reflect available information. The efficient markets hypothesis (EMH) posits that actual capital markets, such as the NYSE, are efficient.

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Three Forms of EMH Strong form of EMH: all information of every kind is reflected in stock prices; i.e., there is no such thing as inside information. Semistrong form efficient: all public information is reflected in the stock price Weak form efficient: at a minimum, the current price of a stock reflects its own past prices (i.e., technical analysis is futile).

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Question 21 Arithmetic and Geometric Returns. A stock has had the following year-end prices and dividends: What are the arithmetic and geometric returns for the stock? Year Price Dividend 1 $99.15 -- 2 107.11 $1.60 3 91.65 2.00 4 127.16 2.20 5 162.15 2.60 6 192.60 3.00

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Question 22 Calculating Returns. Refer to Table 10.1 in the text and look at the period from 1973 through 1980. Calculate the average return for Treasury bills and the average annual inflation rate (consumer price index) for this period. Calculate the standard deviation of T-bill returns and inflation over this time period. Calculate the real return for each year. What is the average real return for T-bills? Many people consider T-bills to be risk-free. What does this tell you about the potential risks of T-bills?

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**Q22 (Cont.) Year T-bill return Inflation Real return 1973 .0729 .0871**

1974 .0799 .1234 1975 .0587 .0694 1976 .0507 .0486 1977 .0545 .0670 1978 .0764 .0902 1979 .1056 .1329 1980 .1210 .1252 .6197 .7438

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Question 23 Calculating Investment Returns. You bought one of Rocky Mountain Manufacturing Co.’s 8 percent coupon bonds one year ago for $1, These bonds make annual payments and mature nine years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 7.2 percent. If the inflation rate was 3.5 percent over the past year, what would be your total real return on investment?

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Question 24 Using Return Distributions. Suppose the returns on long-term government bonds are normally distributed. Based on the historical record, what is the approximate probability that your return on these bonds will be less than -3.7% in a given year? What range of returns would you expect to see 95% percent of the time? What range would you expect to see 99% of the time?

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Question 28 Using Probability Distributions. Suppose the returns on long-term corporate bonds and T-bills are normally distributed. Based on the historical record, use the NORMDIST function in Excel to answer the following questions: What is the probability that in any given year, the return on long-term corporate bonds will be greater than 10 percent? Less than 0 percent? What is the probability that in any given year, the return on T-bills will be greater than 10 percent? Less than 0 percent? In 1979, the return on long-term corporate bonds was percent. How likely is it that such a low return will recur at some point in the future? T-bills had a return on percent in this same year. How likely is it that such a high return on T-bills will recur at some point in the future?

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Chapter McGraw-Hill/IrwinCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. A Brief History of Risk and Return 1.

Chapter McGraw-Hill/IrwinCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. A Brief History of Risk and Return 1.

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