Attempts $$

Average $\frac{?}{3}$

$8.$ 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.

$\backslash$table$[[,\backslash$table$[[$Fraction of Portfolio in Diversified$],[$Stocks$],[$Combination$]],\backslash$table$[[$Average Annual$],[$Return$],[($Percent$)]],\backslash$table$[[$Standard Deviation of Portfolio Return$],[($Risk$)],[($Percent$)]]],[$A$,0,4\mathrm{.}00,0],[$B$,25,7\mathrm{.}00,5],[$C$,50,10\mathrm{.}00,10],[$D$,75,13\mathrm{.}00,15],[$E$,100,16\mathrm{.}00,20]]$

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

Suppose Becky 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.

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

Place the entirety of her portfolio in bonds

Accept a lower average annual rate of return

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

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 wi$$hin 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 $10\%,$ but given the standard deviation of $10\%,$ the returns will typically $($about $95\%$ of the time$)$ vary from a gain of $q,$ to a loss of $$