Question 8 Chapter 14 Risk and return
Suppose Dina is choosing how to allocate her portfolio between two asset classes: risk-free government
bonds and a
... [Show More] 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 1.50 0
B 25 3.50 5
C 50 5.50 10
D 75 7.50 15
E 100 9.50 20
If Dina reduces her portfolio's exposure to risk by opting for a smaller share of stocks, he must also accept a
average annual return.
Points: 1 / 1
Suppose Dina currently allocates 25% of her portfolio to a diversified group of stocks and 75% of her portfolio
to riskfree bonds; that is, she chooses combination B. She wants to increase the average annual return on
her portfolio from 3.5% to 7.5%. 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
Sell some of her bonds and use the proceeds to purchase stocks
Sell some of her stocks and place the proceeds in a savingsaccount
Accept more risk
Points: 1 / 1
Explanation: Close Explanation
Note from the table that a portfolio consisting entirely of government bonds with no stocks
(combination A) offers Dina an average annual return of 1.5% and zero risk. At the opposite extreme,
on E) offers a substantially higher average annual
-14.5%
Explanation: Close Explanation
The standard deviation of the return for a portfolio consisting of 50% stocks and 50% bonds is 10%.
The average annual return for the same portfolio is 5.5%. The returns for this portfolio will typically
stay within two standard deviations, or 20% , of the average annual return. The
returns will typically vary from a gain of 25.5% (two standard deviations above the mean) to a loss of
-14.5% (two standard deviations below the mean).
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 Dina 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 5.5%, but given
the standard deviation of 10%, the returns will typically (about 95% of the time) vary from a gain of
to a loss of .
Points: 0.5 / 1
return of 9.5% but comes with considerable risk. Specifically, the return on the all-stock portfolio has a
standard deviation of 20%, compared to 0% for the all-government-bond portfolio. Recall that the
standard deviation of a portfolio's return is an indicator of its volatility. Higher standard deviations are
associated with more volatile returns.
Dina faces a tradeoff between risk and return in selecting her portfolio. She can obtain higher returns
only by accepting the higher levels of risk associated with a stock-intensive portfolio. She can obtain
lower risk levels only by accepting the lower returns associated with a bond-intensive portfolio.
25.5% [Show Less]