8. Risk and return

Suppose Becky 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	3.50	0
B	25	7.50	5
C	50	11.50	10
D	75	15.50	15
E	100	19.50	20

There is a relationship between the risk of Becky's portfolio and its average annual return.

Suppose Becky 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 7.5% to 15.5%. 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 stocks and place the proceeds in a savings account

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

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 Becky 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 15.5%, but given the standard deviation of 15%, the returns will typically (about 95% of the time) vary from a gain of to a loss of .