Question

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.

Combination	Fraction of Portfolio in Diversified Stocks	Average Annual Return	Standard Deviation of Portfolio Return (Risk)
	(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? Check all that apply.

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

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 Frances 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 9.5%, 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   .

Answer 1

Assumptions Average annual retum on bond \(=2 \%\) Average annual retum on diversified stocks \(=12 \%\) Standard deviation of retum on bond \(=0 \%\) Standard deviation of retur on diversified stock \(=20 \%\)

Answer A: Currently she is holding a portfolio of \(75 \%\) bond and \(25 \%\) of diversified stocks, in order to reverse this combination she needs to sell some of her bonds to buy stocks and in result she will be accepting more risk. Thus, correct answers are "sell some of her bonds and use the proceeds to purchase stocks" and "accept more risk".

Assumptions Retum \(=9.5 \%\) Standard deviation \(=15 \%\)

Answer B: At \(95 \%\) confidence level the retum of portfolio vary from \(\pm 2\) standard deviation. Compute the variation in retum for given information in the following manner.

Returns variation = Return \(\pm 2 \times\) standard deviation \(=9.5 \% \pm 2 \times 15 \%\)

\(=39.5 \%\) to \(-20.5 \%\)

Thus, the retums typically (at \(95 \%\) confidence level) vary from a gain of \(39.5 \%\) to loss of \(20.5 \%\)