Suppose Frances is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds. Fraction of Portfolio Average Standard Deviation of
in Diversified Stocks Annual Return Portfolio Return (Risk)
Combination (Percent) (Percent) (Percent)
A 0 2.00 0
B 25 4.50 5
C 50 7.00 10
D 75 9.50 15
E 100 12.00 20
If Frances reduces her portfolio's exposure to risk by opting for a smaller share of stocks, he must also accept a average annual return.
Suppose Frances currently allocates 25% of her portfolio to a diversified group of stocks and 75% of her portfolio to risk-free bonds; that is, she chooses combination B. She wants to increase the average annual return on her portfolio from 4.5% to 9.5%. In order to do so, she must do which of the following?
a. Sell some of her stocks and place the proceeds in a savings account
b. Sell some of her bonds and use the proceeds to purchase stocks
c. Sell some of her stocks and use the proceeds to purchase bonds
Accept more risk
The table uses the standard deviation of the portfolio's return as a measure of risk. A normal random variable, such as a portfolio's return, stays within two standard deviations of its average approximately 95% of the time.
Suppose Dina modifies her portfolio to contain 75% diversified stocks and 25% risk-free government bonds; that is, she chooses combination D. The average annual return for this type of portfolio is 4.5%, but given the standard deviation of 15%, the returns will typically (about 95% of the time) vary from a gain of34.5% to a loss of___.