Chapter outline

CHAPTER 6

Risk and

Rates of Return

CHAPTER ORIENTATION

This chapter introduces the concepts that underlie the valuation of securities and their rates of return. We are specifically concerned with common stock, preferred stock, and bonds. We also look at the concept of the investor's expected rate of return on an investment.

CHAPTER OUTLINE

I. The relationship between risk and rates of return

A. Data have been compiled by Ibbotson and Sinquefield on the actual returns for various portfolios of securities from 1926-2002.

B. The following portfolios were studied.

1. Common stocks of small firms

2. Common stocks of large companies

3. Long-term corporate bonds

4. Long-term U.S. government bonds

5. U.S. Treasury bills

C. Investors historically have received greater returns for greater risk-taking with the exception of the U.S. government bonds.

D. The only portfolio with returns consistently exceeding the inflation rate has been common stocks.

II. Effects of Inflation on Rates of Return

A. When a rate of interest is quoted, it is generally the nominal or, observed rate. The real rate of interest represents the rate of increase in actual purchasing power, after adjusting for inflation.

B. Consequently, the nominal rate of interest is equal to the sum of the real rate of interest, the inflation rate, and the product of the real rate and the inflation rate.

III. Term Structure of Interest Rates

The relationship between a debt security’s rate of return and the length of time until the debt matures is known as the term structure of interest rates or the yield to maturity.

IV. Expected Return

A. The expected benefits or returns to be received from an investment come in the form of the cash flows the investment generates.

B. Conventionally, we measure the expected cash flow, , as follows:

= X i P(X i)

where N = the number of possible states of the economy.

X i = the cash flow in the i th state of the economy.

P(X i) = the probability of the i th cash flow.

V. Riskiness of the cash flows

A. Risk can be defined as the possible variation in cash flow about an expected cash flow.

B. Statistically, risk may be measured by the standard deviation about the expected cash flow.

C. Risk and diversification

1. Total variability can be divided into:

a. The variability of returns unique to the security (diversifiable or unsystematic risk)

b. The risk related to market movements (nondiversifiable or systematic risk)

2. By diversifying, the investor can eliminate the "unique" security risk. The systematic risk, however, cannot be diversified away.

3. The market rewards diversification. We can lower risk without sacrificing expected return, and/or we can increase expected return without having to assume more risk.

4. Diversifying among different kinds of assets is called asset allocation. Compared to diversification within the different asset classes, the benefits received are far greater through effective asset allocation.

5. Risk and being patient

a. An investor in common stocks must often wait longer to earn the higher returns than those provided by bonds.

b. The capital markets reward us not just for diversifying, but also for being patient. The returns tend to converge toward the average as we lengthen our holding period.

6. The characteristic line tells us the average movement in a firm's stock price in response to a movement in the general market, such as the stock market. The slope of the characteristic line, which has come to be called beta, is a measure of a stock's systematic or market risk. The slope of the line is merely the ratio of the "rise" of the line relative to the "run" of the line.

7. If a security's beta equals one, a 10 percent increase (decrease) in market returns will produce on average a 10 percent increase (decrease) in security returns.

8. A security having a higher beta is more volatile and thus more risky than a security having a lower beta value.

9. A portfolio's beta is equal to the average of the betas of the stocks in the portfolio.

VI. Required rate of return

A. The required rate of return is the minimum rate necessary to compensate an investor for accepting the risk he or she associates with the purchase and ownership of an asset.

B. Two factors determine the required rate of return for the investor:

1. The risk-free rate of interest which recognizes the time value of money.

2. The risk premium which considers the riskiness (variability of returns) of the asset and the investor's attitude toward risk.

C. Capital asset pricing model-CAPM

1. The required rate of return for a given security can be expressed as

= + beta x

or

kj = krf + βj (km- krf)

2. Security market line

a. Graphically illustrates the CAPM.

b. Designates the risk-return trade-off existing in the market, where risk is defined in terms of beta according to the CAPM equation.

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