Suppose the quantity demanded for a security is
BD = 100 0.1b,
and the quantity supplied of the security is
BS = 50 + 0.1b,
where b is the price of the security in dollars.
a. Calculate the equilibrium price and quantity of the security.
b. Suppose demand increases by 50, so that BD = 150 0.1b. Now, calculate the new equilibrium price and quantity of the security.
Consider three alternative bonds that you might invest in, each of which matures in one year. The following table shows the probability that you will receive each possible return. For example, if you buy bond A, the probability is 90 percent that your return will be 20 percent and the probability is 10 percent that your return will be 100 percent (in other words, you lose the entire amount invested).
Bond Probability Return
Bond A 90% 20%
10% 100%
Bond B 75% 40%
25% 40%
Bond C 60% 10%
40% 10%
a. Calculate the expected return for all three bonds in percentage terms.
b. The standard deviations of the returns on these bonds are: Bond A, 36.0 percent; Bond B, 34.6 percent; Bond C, 9.8 percent. If you are extremely risk averse, which of the three bonds would you buy? Why?
c. Would a risk-averse investor ever buy Bond A instead of one of the other bonds? Why or why not?
Suppose that the price of a stock is $50 at the beginning of a year and $53 at the end of the year, and it pays a dividend of $2 during the year.
a. What is the stock’s current yield?
b. What is the stock’s capital-gains yield?
c. What is the stock’s return?
Suppose an investor purchased 100 shares of JDSU stock at a price of $50 per share on December 31, 2011. On December 31, 2012, JDSU paid dividends of $1.50 per share, and the investor received the dividends, then sold the stock at a price of $65 per share.
a. If there were no taxes or inflation, what was the total return?
b. If there were no taxes, but inflation was 3.5 percent, what was the real return?
c. If the tax rate was 15 percent on dividends and capital gains, what was the after-tax real return?
Write the equation for the capital-asset pricing model.
Describe, in words, what the CAPM is trying to explain, and describe each element of the equation in part a.
Use the capital-asset pricing model to predict the returns next year of the following stocks, if you expect the return to holding stocks to be 12 percent on average, and the interest rate on three-month T-bills will be 2 percent. Show your calculations.
A stock with a beta of 0.3
A stock with a beta of 0.7
A stock with a beta of 1.6
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