Suppose Caroline 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 in Diversified Stocks
Average Annual Return
Standard Deviation of Portfolio Return (Risk)
A 0 1.50 0
B 25 3.00 5
C 50 4.50 10
D 75 6.00 15
E 100 7.50 20
There is a relationship between the risk of Caroline’s portfolio and its average annual return.
Suppose Caroline currently allocates 75% of her portfolio to a diversified group of stocks and 25% of her portfolio to risk-free bonds; that is, she chooses combination D. She wants to reduce the level of risk associated with her portfolio from a standard deviation of 15 to a standard deviation of 5. In order to do so, she must do which of the following? Check all that apply.
Sell some of her stocks and use the proceeds to purchase bonds
Sell some of her bonds and use the proceeds to purchase stocks
Place the entirety of her portfolio in bonds
Accept a lower average annual rate of return
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 Caroline modifies her portfolio to contain 25% diversified stocks and 75% risk-free government bonds; that is, she chooses combination B. The average annual return for this type of portfolio is 3%, but given the standard deviation of 5%, the returns will typically (about 95% of the time) vary from a gain of13% to a loss of .
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