Question

Suppose Caroline 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 (Percent) Average Annual Return (Percent) Standard Deviation of Portfolio Return (Risk) (Percent)A 0 2.50 0B 25 3.50 5C 50 4.50 10D 75 5.50 15E 100 6.50 20As the risk Caroline's portfolio increases, the average annual return on her portfolio _____ (rises or falls).Suppose Caroline 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 combinations B. She wants to increase the average annual return on her portfolio from 3.5% to 5.5%. In order to do so, she must do which of the following? Choose all that applya. Sell some of her stocks and place the proceeds in a savings accountb. Sell some of her stocks and use the proceeds to purchase bondsc. Sell some of her bonds and use the proceeds to purchase stocksd. Accept more riskThe table uses the standard deviation of the portfolio's return as a measure of risk. A normal random variable,e such as a portfolio's return, stays within two standard deviations of its average approximately 95% of the time.Suppose Caroline 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 4.5%, but given the standard deviation of 10%, the returns will typically (about 95% of the time) vary from a gain of _____( -15.5% , 0.9% , 14.5% , 24.5% ) to a loss of _____ ( -15.5% , -5.5% , 0.9% , 24.5% ).

Answer 1

Answer:

Ans 1)

As Average Annual return increases from Combination A to E we can observe that Standard deviation also increases from A to E

Therefore it is clear that there is positive relationship between the Risk of Caroline's portfolio and the average annual return.

Ans 2)

IF Caroline needs to reduce the risk associated with portfolio combination D from 15 to 5 then he can do 2 things such that he should sell some portion of portfolio invested into stocks and ultimately accept lower returns because as we see in Part 1) answer risk and returns are positively correlated.

Option 2) and Option 3) are correct

Ans 3)

95% confidence interval gives us range of -2*SD, 2*SD

therefore range of return for given scenario with portfolio return equals to 3.5% and SD=5%

(Mean- z value*SD , Mean value*SD)=

(3.5%-2*5% , 3.5%+2*5%)=(-6.5%,13.5%)

Gain of 13.5% and Loss of -6.5%