Risk and return

Suppose Lucia 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.

There is a

relationship between the risk of Lucia's portfolio and its average annual return.

Suppose Lucia 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 $6\%$ to $13\%.$ 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

Accept more risk

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

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

within two standard deviations of its average approximately $95\%$ of the time.

Suppose Lucia 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 $13\%,$ 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