Chapter 6: The Meaning and Measurement of Risk and Return

Question 1

Define and measure the expected rate of return of an individual investment.

Answer 1

When we speak of “returns” on an investment, either we are talking about historical return, what we earned on an investment in the past, or expected returns, where we are attempting to determine the return we can “expect” to receive in the future. In a world of uncertainty, we cannot make forecasts with certitude. Thus, we must speak in terms of expected events. The expected return on an investment may therefore be stated as a weighted average of all possible returns, weighted by the probability that each will occur.

Question 2

Holding-Period Return (Historical or Realized Rate of Return)

Answer 2

The rate of return earned on an investment, which equals the dollar gain divided by the amount invested.

Question 3

Expected Rate of Return

Answer 3

The arithmetic mean or average of all possible outcomes where those outcomes are weighted by the probability that each will occur.

Question 4

Holding-Period Dollar Gain (DG) Equation

Answer 4

Price at end of period + Cash distribution (ie. dividend) - Price at beginning of period.

Question 5

Holding-Period Rate of Return (r) Equation

Answer 5

Dollar Gain/Price at the beginning of period = (Price at end of period + Dividend - Price at beginning of period)/Price at beginning of period

Question 6

Expected Cash Flow (CF-bar)

Answer 6

(Cash flow in state 1 (i.e. CF1) x Probability of state 1 (i.e. Pb1)) + (Cash flow in state 2 (i.e. CF2) x Probability of state 2 (i.e. Pb2)) + . . . + (Cash flow in state n (i.e. CFn) x Probability of state n (i.e. Pbn))

Question 7

Expected Rate of Return (r-bar)

Answer 7

(Rate of return for state 1 (i.e. r1) x Probability of state 1 (i.e. Pb1)) + (Rate of return for state 2 (i.e. r2) x Probability of state 2 (i.e. Pb2)) + . . . + (Rate of return for state n (i.e. rn) x Probability of state n (i.e. Pbn))

Question 8

Define and measure the riskiness of an individual investment.

Answer 8

Risk associated with a single investment is the variability of cash flows or returns and can be measured by the standard deviation.

Question 9

Risk

Answer 9

Potential variability in future cash flows.

Question 10

Standard Deviation

Answer 10

A statistical measure of the spread of a probability distribution calculated by squaring the difference between each outcome and its expected value, weighting each value by its probability, summing over all possible outcomes, and taking the square root of this sum.

Question 11

Variance in Rates of Return (σ2)

Answer 11

[(Rate of return for state 1 (i.e. r1) - Expected rate of return (i.e. r-bar))^2 x Probability of state 1 (pb1)] + [(Rate of return for state 2 (i.e. r2) - Expected rate of return (i.e. r-bar))^2 x Probability of state 2 (pb2)] + . . . + [(Rate of return for state n (i.e. rn) - Expected rate of return (i.e. r-bar))^2 x Probability of state n (pbn)]

Question 12

Compare the historical relationship between risk and rates of return in the capital markets.

Answer 12

Ibbotson Associates have provided us with annual rates of return earned on different types of security investments as far back as 1926. They summarize among other things, the annual returns for six portfolios of securities made up of :
1. Common stock of large companies
2. Common stock of small firms
3. Long-term corporate bonds
4. Long-term U.S. government bonds
5. Intermediate-term U.S. government bonds
6. U.S. Treasury bills
A comparison of the annual rates of return for these respective portfolios for the years 1926 to 2011 shows a positive relationship between risk and return, with Treasury bills being least risky and common stocks of small firms being most risky. From the data, we are able to see the benefit of diversification in terms of improving the return-risk relationship. Also, the data clearly demonstrate that only common stock has in the long run served as an inflation hedge, and that the risk associated with common stock can be reduced if investors are patient in receiving their returns.

Question 13

Explain how diversifying investments affects the riskiness and expected rate of return of a portfolio or combination of assets.

Answer 13

We made an important distinction between nondiversifiable risk and diversifiable risk. We concluded that the only relevant risk, given the opportunity to diversify out portfolio, is a security’s nondiversifiable risk, which we called by two other names: systematic risk and market-related risk.

Question 14

Systematic Risk (Market Risk or Nondiversifiable Risk)

Answer 14

1. The risk related to an investment return that cannot be related to an investment return that cannot be eliminated through diversification. Systematic risk results from factors that affect all stocks. Also called market risk or nondiversifiable risk.
2. The risk of a project from the viewpoint of a well-diversified shareholder. This measure takes into account that some of the project’s risk will be diversified away as the project is combined with the firm’s other projects, and, in addition, some of the remaining risk will be diversified away by shareholders as they combine this stock with other stocks in their portfolios.

Question 15

Unsystematic Risk (Company Unique Risk or Diversifiable Risk)

Answer 15

The risk related to an investment return that can be eliminated through diversification. Unsystematic risk is the result of factors that are unique to the particular firm. Also called company-unique risk or diversifiable risk.

Question 16

Characteristic Line

Answer 16

The line of “best fit” through a series of returns for a firm’s stock relative to the market’s returns. The slope of the line, frequently called beta, represents the average movement of the firm’s stock returns in response to a movement in the market’s returns.

Question 17

Beta

Answer 17

The relationship between an investment’s returns and the market’s returns. This is a measure of the investment’s nondiversifiable risk.

Question 18

Portfolio Beta

Answer 18

The relationship between a portfolio’s returns and the market returns. It is a measure of the portfolio’s nondiversifiable risk.

Question 19

Asset Allocation

Answer 19

Identifying and selecting the asset classes appropriate for a specific investment portfolio and determining the proportions of those assets within the portfolio.

Question 20

Monthly Holding Return Equation

Answer 20

(Price at end of the month - Price at beginning of the month)/Price at beginning of month = (Price at end of the month/Price at beginning of the month) - 1.

Question 21

Average Holding-Period Return Equation

Answer 21

(Return in month 1 + Return in month 2 + . . . + Return in last month)/Number of monthly returns

Question 22

Standard Deviation Equation

Answer 22

{[(Return in month 1 - Average return)^2 + (Return in month 2 - Average return)^2 + . . . + (Return in last month - Average return)^2]/(Number of monthly returns - 1)}^(1/2)

Question 23

Portfolio Beta Equation

Answer 23

(Percentage of portfolio invested in asset 1 x Beta for asset 1 (i.e. β1)) + (Percentage of portfolio invested in asset 2 x Beta for asset 2 (i.e. β2)) + . . . + (Percentage of portfolio invested in asset n x Beta for asset n (i.e. βn))

Question 24

Explain the relationship between an investor’s required rate of return on an investment and the riskiness of the investment.

Answer 24

The capital asset pricing model provides an intuitive framework for understanding the risk-return relationship. The CAPM suggests that investors determine an appropriate required rate of return, depending upon the amount of systematic risk inherent in a security. This minimum acceptable rate of return is equal to the risk-free rate plus a risk premium for assuming risk.

Question 25

Required Rate of Return

Answer 25

Minimum rate of return necessary to attract an investor to purchase or hold a security.

Question 26

Risk-Free Rate of Return

Answer 26

The rate of return on risk-free investments. The interest rates on short-term U.S. government securities are commonly used to measure this rate.

Question 27

Risk Premium

Answer 27

The additional return expected for assuming risk.

Question 28

Capital Asset Pricing Model (CAPM)

Answer 28

An equation stating that the expected rate of return on an investment (in this case a stock) is a function of

1. The risk-free rate
2. The investment’s systematic risk, and
3. The expected risk premium for the market portfolio of all risky securities.

Question 29

Security Market Line

Answer 29

The return line that reflects the attitudes of investors regarding the minimum acceptable return for a given level of systematic risk associated with security.

Question 30

Investor’s Required Rate of Return Equation

Answer 30

Risk-free rate of return + Risk premium

Question 31

Risk Premium Equation

Answer 31

Investor’s required rate of return (i.e. r) - risk-free rate of return (i.e. rf)

Question 32

Required Return on Security (r) Equation

Answer 32

Risk free rate of return (i.e. rf) + Beta for security (i.e. β) x (Required return on the market portfolio (i.e. rm) - Risk-free rate of return (i.e. r1))

Question 33

Investor’s Required Rate of Return Use

Answer 33

measures an investor’s required rate of return based on a risk-free rate plus a return premium for assuming risk.

Question 34

Risk Premium Use

Answer 34

Indicates the additional return an investor should require to assume additional risk.

Question 35

Investor’s Required Rate of Return Use

Answer 35

Calculates the rate of return an investor should require based on the capital asset pricing model, which only considers systematic risk to determine the appropriate risk premium.

Question 36

Holding-Period Dollar Gain Use

Answer 36

Measures the dollar gain on an investment for a period of time.

Question 37

Holding-Period Rate of Return Use

Answer 37

Calculates the percentage rate of return for a security held for a period of time.

Question 38

Expected Cash Flow Use

Answer 38

Estimates the cash flows that can be expected from an investment, recognizing that there are multiple possible outcomes from the investment.

Question 39

Expected Rate of Return Use

Answer 39

An estimate of the expected rate of return on an investment, recognizing that there are multiple possible outcomes from the investment.

Question 40

Standard Deviation in Rates of Return (Variance)^(1/2) Use

Answer 40

A measure of risk, as determined by the square root of the variance of cash flows or rates of returns, which measures the volatility of cash flows or returns.

Question 41

Monthly Holding-Period Return Use

Answer 41

Calculates the percentage rate of return for a security held for a single month.

Question 42

Average Monthly Holding-Period Rate of Return Use

Answer 42

Finds the average monthly holding-period return for a number of monthly returns.

Question 43

Standard Deviation of Monthly Holding-Period Returns Use

Answer 43

Measure of the volatility of monthly holding-period returns over a series of months.

Question 44

Portfolio Beta Use

Answer 44

Finds the beta for an entire portfolio of stocks.