Stock Returns, Risk, and Portfolio Management
Stock Returns and Risk Premium
1. Calculating Percentage Return on a Stock
What is the percentage return on a stock that was purchased for $50.00, paid a $3.00 dividend after one year, and was then sold for $49.00?
Formula: % Return = (Capital Gain + Dividend) / Initial Share Price
= ($49.00 – $50.00) + $3.00 / $50.00
= 4.00%
2. Calculating Inflation Rate
If a share of stock provided a 14.0% nominal rate of return over the previous year while the real rate of return was 6.0%, then the inflation rate was:
Formula: 1 + Real Rate of Return = (1 + Nominal Rate of Return) / (1 + Inflation Rate)
1 + 0.06 = 1.06
1.06 = 1.14 / (1 + x) (x = inflation rate)
3. Risk Premium for Common Stocks
In a year in which common stocks offered an average return of 18%, Treasury bonds offered 10%, and Treasury bills offered 7%, the risk premium for common stocks was:
18% – 7% = 11%
Note: The risk premium is calculated as the difference between the return on common stocks and the return on Treasury bills.
Standard Deviation and Portfolio Diversification
4. Standard Deviation: Individual Stock vs. Portfolio
What is the typical relationship between the standard deviation of an individual common stock and the standard deviation of a diversified portfolio of common stocks?
Answer: An individual stock’s standard deviation will be higher.
5. Volatility and Returns: Treasury Bills vs. Stocks
The fact that historical returns on Treasury bills are less volatile than common stock returns indicates that:
Answer: Common stocks should offer a higher return than Treasury bills.
Risk Types and Diversification
6. Diversifiable Risk
Risk factors that are expected to affect only a specific firm are referred to as:
Answer: Diversifiable risk
7. Diversifying Portfolio Risk
Which of the following risk types can be diversified by adding stocks to a portfolio?
Answer: Unique risk
8. Unique Risk Example
Which of the following risks would be classified as a unique risk for an auto manufacturer?
Answer: Steel prices
9. Example of Diversifiable Risk
Which one of the following is the best example of a diversifiable risk?
Answer: A firm’s sales decrease
10. Purpose of Portfolio Diversification
The primary purpose of portfolio diversification is to:
Answer: Eliminate firm-specific risk.
11. Reducing Unsystematic Risk
Which one of the following is least apt to reduce the unsystematic risk of a portfolio?
Answer: Reducing the number of stocks held in the portfolio
12. Systematic Risk Example
Which one of the following is an example of systematic risk?
Answer: Investors panic, causing security prices around the globe to fall precipitously.
Systematic Risk, Beta, and Cost of Capital
1. Measuring Systematic Risk
Systematic risk is measured by:
Answer: Beta
2. Evaluating Proposed Assets
Proposed assets can be evaluated using the company cost of capital, providing that the:
Answer: New assets have the same risk as existing assets.
3. Stock’s Beta
The sensitivity of a stock’s returns to the returns on a market portfolio is referred to as the:
Answer: Stock’s beta.
4. Acceptable Investment Return
A proposed investment must earn at least as much as the ______ if it is to be deemed acceptable.
Answer: Project cost of capital
5. Market Portfolio Yield
If Treasury bills are yielding 10% at a time when the market risk premium is 6%, then the:
Answer: Market portfolio should yield 16% (10% + 6%).
6. Calculating Portfolio Beta
What is the beta of a three-stock portfolio including 25% of Stock A with a beta of 0.90, 40% of Stock B with a beta of 1.05, and 35% of Stock C with a beta of 1.73?
Formula: Portfolio Beta = (0.25 x 0.9) + (0.4 x 1.05) + (0.35 x 1.73)
= 0.225 + 0.42 + 0.606
= 1.25
7. Expected Return with Beta
If Treasury bills yield 6.0% and the market risk premium is 9.0%, then a portfolio with a beta of 1.5 would be expected to yield:
Formula: Expected Return = 6.0% + 1.5(9.0%)
= 19.5%
8. Expected Return for a Stock
What rate of return should an investor expect for a stock that has a beta of 0.8 when the market is expected to yield 14% and Treasury bills offer 6%?
Formula: r = rf + B(rm – rf)
= 6% + 0.8(14% – 6%)
= 6% + 6.4%
= 12.4%
Note: 0.8(14% – 6%) = 0.064, which translates to 6.4%.
9. Unique Risks and Expected Returns
Why do stock market investors appear not to be concerned with unique risks when calculating expected rates of return?
Answer: Unique risks are assumed to be diversified away.
10. Security Market Line and Return
If a security plots below the security market line, it is:
Answer: Offering too little return to justify its risk.
11. Stock’s Beta and Regression Line
The slope of the regression line that exhibits the past relationship between a stock’s return and the market’s return is the:
Answer: Stock’s beta.
12. Comparing Expected Returns
Which of the following statements is more likely to be correct concerning the statement, “Stock A has a higher expected return than Stock B”?
Answer: Stock A has a higher beta.
13. Inappropriate Discount Rate
The company cost of capital may be an inappropriate discount rate for a capital budgeting proposal if:
Answer: The proposal has a different degree of risk.