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	1.50	0
B	25	3.50	5
C	50	5.50	10
D	75	7.50	15
E	100	9.50	20

As the risk of Becky's portfolio increases, the average annual return on her portfolio __ ( rises, falls) .

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 3.5% to 7.5%. In order to do so, she must do which of the following? Check all that apply.

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

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

c)Accept more risk

d)Sell some of her stocks and place the proceeds in a savings account

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 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 5.5%, but given the standard deviation of 10%, the returns will typically (about 95% of the time) vary from a gain of

______ (-14.5%,1.1%,15.5%,25.5%) to a loss of______( -14.5%,-4.5%,1.1%,25.5%) .