Question

Suppose Simone 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.

Combination	Fraction of Portfolio in Diversified Stocks	Average Annual Return	Standard Deviation of Portfolio Return (Risk)
	(Percent)	(Percent)	(Percent)
A	0	1.00	0
B	25	3.00	5
C	50	5.00	10
D	75	7.00	15
E	100	9.00	20

If Simone reduces her portfolio's exposure to risk by opting for a smaller share of stocks, he must also accept a ( higher, lower) average annual return.

Suppose Simone 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.

Accept a lower average annual rate of return

Place the entirety of her portfolio in bonds

Sell some of her bonds and use the proceeds to purchase stocks

Sell some of her stocks and use the proceeds to purchase bonds

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 Simone modifies her portfolio to contain 50% diversified stocks and 50% risk-free government bonds; that is, she chooses combination C. The average annual return for this type of portfolio is 5%, but given the standard deviation of 10%, the returns will typically (about 95% of the time) vary from a gain of    to a loss of .

Answer 1

If Simone reduces her portfolio's exposure to risk by opting for a smaller share of stocks, she must also accept a lower average annual return.

Suppose Simone 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?

Correct options:

- Accept a lower average annual rate of return

- Sell some of her stocks and use the proceeds to purchase bonds

Suppose Simone modifies her portfolio to contain 50% diversified stocks and 50% risk-free government bonds; that is, she chooses combination C. The average annual return for this type of portfolio is 5%, but given the standard deviation of 10%, the returns will typically (about 95% of the time) vary from a gain of 25% (= 5% + 2 x 10%) to a loss of 15%    .(= 5% - 2 x 10%)