Question

Suppose Deborah 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	2.50	0
B	25	4.50	5
C	50	6.50	10
D	75	8.50	15
E	100	10.50	20

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

Suppose Deborah 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.

1. Accept a lower average annual rate of return

2. Place the entirety of her portfolio in bonds

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

4. 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 Deborah 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 6.5%, but given the standard deviation of 10%, the returns will typically (about 95% of the time) vary from a gain of (-13.5%, 1.3%, 16.5%, 26.5%)   to a loss of (-13.5%, -3.5%, 1.3%, 26.5%)

Answer 1

Solution

Given that there are 2 asset classes available to Deborah that are risk-free government bonds and risky group of diversified stocks.

(a) She wants to reduce the level of risk associated with her portfolio from a standard deviation of 15 to a standard deviation of 5.So for this she has to reduce her fraction of portfolio in diversified stocks from the existing 75 % to 25%.For that , she must Sell some of her stocks and use the proceeds to purchase bonds.So in this process ,she will have to accept a lower average rate of return as the return on bonds is much lower when compared to return on stocks.

(b) The average annual return for this type of portfolio is 6.5%, but given the standard deviation of 10%, the returns will typically (about 95% of the time) in the range of :

6.5% + 10% =>16.5% return (i.e., a profit of 16.5%)

to

6.5% - 10% => -3.5% return (i.e., a loss of 3.5%)

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