Question 1

What is the expected return on this stock given the following information?
$\begin{array}{lcc}
\text { State of the Economy } & \text { Probability of } & \text { Rate of Return if } \
& \text { State of Economy } & \text { state occurs }\
\text { Boom } & .15 & 22 \% \
\text { Normal } & .60 & 11 \% \
\text { Recession } & .25 & -14 \%
\end{array}$

Accepted Answer

A) 6.40% 
B) 6.57% 
C) 8.99% 
D) 13.40% 
E) 14.25%

Question 2

An efficient portfolio is one that does which of the following?

Accepted Answer

A) offers the highest return for the lowest possible cost 
B) provides an evenly weighted portfolio of diverse assets 
C) eliminates all risk while providing an expected positive rate of return 
D) lies on the vertical axis when graphing expected returns against standard deviation 
E) offers the highest return for a given level of risk

Question 3

What is the variance of the expected returns on this stock?
$$\begin{array} { l c c } 
\text { State of the Economy } & \text { Erobability } & E ( R ) \
\text { Eoom } & .70 & 24\% \
\text { Recegaion } & .30 & 6\%
\end{array}$$

Accepted Answer

A) 48.75% 
B) 52.75% 
C) 61.53% 
D) 68.04% 
E) 70.03%

Question 4

A stock fund has a standard deviation of 16% and a bond fund has a standard deviation of 4%. The correlation of the two funds is .11. What is the weight of the stock fund in the minimum variance portfolio?

Accepted Answer

A) 3.47% 
B) 6.48% 
C) 11.92% 
D) 14.67% 
E) 18.22%

Question 5

What is the expected return on this stock given the following information?
$\begin{array}{lcc}
\text { State of the Economy } & \text { Probability of } & \text { Rate of Return if } \
& \text { State of Economy } & \text { state occurs }\
\text { Boom } & .05 & 16 \% \
\text { Normal } & .45 & 7 \% \
\text { Recession } & .50 & -12 \%
\end{array}$

Accepted Answer

A) 2.05% 
B) 1.08% 
C) .47% 
D) 1.22% 
E) 1.43%

Question 6

Rosita owns a stock with an overall expected return of 14.40%. The economy is expected to either boom or be normal. There is a 52% chance the economy will boom. If the economy booms, this stock is expected to return 15%. What is the expected return on the stock if the economy is normal?

Accepted Answer

A) 12.00% 
B) 12.83% 
C) 13.15% 
D) 13.75% 
E) 14.40%

Question 7

The risk-free rate is 2.05%. What is the expected risk premium on this stock given the following information?
$\begin{array}{lrr}
\text { State of the Economy } & \text { Probability of } & \text { Rate of Return if } \
& \text { State of Economy } & \text { state occurs }\
\text { Boom } & .35 & 16\%\
\text { Normal } & .65 & 6 \%
\end{array}$

Accepted Answer

A) 6.88% 
B) 6.95% 
C) 7.32% 
D) 7.45% 
E) 7.59%

Question 8

You are graphing the investment opportunity set for a portfolio of two securities with the expected return on the vertical axis and the standard deviation on the horizontal axis. If the correlation coefficient of the two securities is +1, the opportunity set will appear as which one of the following shapes?

Accepted Answer

A) conical shape 
B) linear with an upward slope 
C) combination of two straight lines 
D) hyperbole 
E) horizontal line

Question 9

You are graphing the portfolio expected return against the portfolio standard deviation for a portfolio consisting of two securities. Which one of the following statements is correct regarding this graph?

Accepted Answer

A) Risk-taking investors should select the minimum variance portfolio. 
B) Risk-averse investors should select the portfolio with the lowest rate of return. 
C) Some portfolios will be efficient while others will not. 
D) The minimum variance portfolio will have the lowest portfolio expected return of any of the possible portfolios. 
E) All possible portfolios will graph as efficient portfolios.

Question 10

You currently have a portfolio comprised of 70% stocks and 30% bonds. Which one of the following must be true if you change the asset allocation?

Accepted Answer

A) The expected return will remain constant. 
B) The revised portfolio will be perfectly negatively correlated with the initial portfolio. 
C) The two portfolios could have significantly different standard deviations. 
D) The portfolio variance will be unaffected. 
E) The portfolio variance will most likely decrease in value.

Question 11

To reduce risk as much as possible, you should combine assets which have one of the following correlation relationships?

Accepted Answer

A) strong positive 
B) slightly positive 
C) slightly negative 
D) strongly negative 
E) zero

Question 12

You have a portfolio which is comprised of 40% of Stock A and 60% of Stock B. What is the standard deviation of this portfolio?
$\begin{array}{lccc}
\text { State of the Economy } & \text { Probability } & \text { A } & \text { B } \
\text { Boom } & .15 & 22 \% & 19\% \
\text { Normal } & .80 & 12\% & 10\% \
\text { Recession } & .05 & -26 \% & -4\%
\end{array}$

Accepted Answer

A) 4.39% 
B) 5.68% 
C) 6.41% 
D) 7.14% 
E) 9.08%

Question 13

An investor owns a security that is expected to return 12% in a booming economy and 4% in a normal economy. The overall expected return on the security is 7.80%. Given there are only two states of the economy, what is the probability that the economy will boom?

Accepted Answer

A) 35.0% 
B) 37.5% 
C) 40.0% 
D) 45.0% 
E) 47.5%

Question 14

What is the variance of the returns on a security given the following information?
$\begin{array}{lcc}
\text { State of the Economy }&\text { Probability}&\text { E(R) }\
\text { Boom } & .25 & 16\% \
\text { Normal } & .45 & 10\% \
\text { Recession } & .30 & -8 \%
\end{array}$

Accepted Answer

A) 48.18% 
B) 56.23% 
C) 64.38% 
D) 72.87% 
E) 90.99%

Question 15

Which one of the following distinguishes a minimum variance portfolio?

Accepted Answer

A) lowest risk portfolio of any possible portfolio given the same securities but in differing proportions 
B) lowest risk portfolio possible given any specified expected rate of return 
C) the zero risk portfolio created by maximizing the asset allocation mix 
D) any portfolio with an expected standard deviation of 9% or less 
E) any portfolio created with securities that are evenly weighted in respect to the asset allocation mix

Question 16

You have a portfolio which is comprised of 48% of Stock A and 52% of Stock B. What is the standard deviation of this portfolio?

Accepted Answer

A) 1.98% 
B) 2.06% 
C) 2.13% 
D) 2.27% 
E) 2.30%

Question 17

Roger has a portfolio comprised of $8,000 of Stock A and $12,000 of Stock B. What is the standard deviation of this portfolio?

Accepted Answer

A) 4.67% 
B) 9.97% 
C) 7.23% 
D) 8.83% 
E) 10.42%

Question 18

As the number of individual stocks in a portfolio increases, the portfolio standard deviation:

Accepted Answer

A) increases at a constant rate. 
B) remains unchanged. 
C) decreases at a constant rate. 
D) decreases at a diminishing rate. 
E) decreases at an increasing rate.

Question 19

A portfolio consists of the following securities. What is the portfolio weight of Stock X?
$\begin{array}{ccc}
\text { Stock }&\text { Number of}&\text {  Price per Share } \
&\text { Shares }\
\text {X }& 600 & \$ 17 \
\text {Y }& 900 & \$ 23 \
\text {Z} & 400& \$ 49
\end{array}$

Accepted Answer

A) .183 
B) .202 
C) .219 
D) .246 
E) .285

Question 20

How will the returns on two assets react if those returns have a perfect positive correlation?
I. move in the same direction
II. move in opposite directions
III. move by the same amount
IV. move by either equal or unequal amounts

Accepted Answer

A) I and III only 
B) I and IV only 
C) II and III only 
D) II and IV only 
E) III only

Exam 11: Diversification and Risky Asset Allocation