Chapter 7, Efficient Diversification Video Solutions, Investments

Problem 1

Which of the following factors reflect pure market risk for a given corporation?
a. Increased short-term interest rates.
b. Fire in the corporate warehouse.
c. Increased insurance costs.
d. Death of the CEO.
e. Increased labor costs.

Doris Bennett

Numerade Educator

01:15

Problem 2

When adding real estate to an asset allocation program that currently includes only stocks, bonds, and cash, which of the properties of real estate returns most affects portfolio risk? Explain.
a. Standard deviation.
b. Expected return.
c. Covariance with returns of the other asset classes.

Dominador Tan

Numerade Educator

Problem 3

Which of the following statements about the minimum-variance portfolio of all risky securities is valid? (Assume short sales are allowed.) Explain.
a. Its variance must be lower than those of all other securities or portfolios.
b. Its expected return can be lower than the risk-free rate.
c. It may be the optimal risky portfolio.
d. It must include all individual securities.

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01:37

Problem 4

What are the investment proportions in the minimum-variance portfolio of the two risky funds, and what are the expected value and standard deviation of its rate of return?

Anand Jangid

Numerade Educator

Problem 5

Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of $0 \%$ to $100 \%$ in increments of $20 \%$.

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Problem 6

Draw a tangent from the risk-free rate to the opportunity set. What does your graph show for the expected return and standard deviation of the optimal portfolio?

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01:37

Problem 7

Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio.

Anand Jangid

Numerade Educator

Problem 8

What is the Sharpe ratio of the best feasible CAL.?

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Problem 9

You require that your portfolio yield an expected return of $14 \%$, and that it be efficient, that is. on the steepest feasible CAL.
a. What is the standard deviation of your portfolio?
b. What is the proportion invested in the money market fund and each of the two risky funds?

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02:46

Problem 10

If you were to use only the two risky funds and still require an expected return of 14\%, what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimized portfolio in Problem 9. What do you conclude?

Breanna Ollech

Numerade Educator

Problem 11

Stocks offer an expected rate of return of $18 \%$ with a standard deviation of $22 \%$. Gold offers an expected return of $10 \%$ with a standard deviation of $30 \%$.
a. In light of the apparent inferiority of gold with respect to both mean return and volatility, would anyone hold gold? If so, demonstrate graphically why one would do so.
b. Given the data above, reanswer (a) with the additional assumption that the correlation coefficient between gold and stocks equals 1. Draw a graph illustrating why one would or would not hold gold in one's portfolio.
c. Could the set of assumptions in part (b) for expected returns, standard deviations, and correlation represent an equilibrium for the security market?

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Problem 12

Suppose that there are many stocks in the security market and that the characteristics of stocks $A$ and $B$ are given as follows:
$$
\begin{array}{lcc}
\text { Stock } & \text { Expected Return } & \text { Standard Deviation } \\
\hline \text { A } & 10 \% & 5 \% \\
\text { B } & 15 & 10
\end{array}
$$
Suppose that it is possible to borrow at the risk-free rate, $r_f$ What must be the value of the riskfree rate?

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Problem 13

True or false: Assume that expected returns and standard deviations for all securities (including the risk-free rate for borrowing and lending) are known. In this case, all investors will have the same optimal risky portfolio.

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Problem 14

True or false: The standard deviation of the portfolio is always equal to the weighted average of the standard deviations of the assets in the portfolio.

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03:07

Problem 15

Suppose you have a project that has a . 7 chance of doubling your investment in a year and a . 3 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment?

Narayan Hari

Numerade Educator

Problem 16

Suppose that you have $$\$ 1$$ million and the following two opportunities from which to construct a portfolio:
a. Risk-free asset earning $12 \%$ per year.
b. Risky asset with expected return of $30 \%$ per year and standard deviation of $40 \%$.
If you construct a portfolio with a standard deviation of $30 \%$, what is its expected rate of return?

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Problem 17

If your entire portfolio is now composed of stock $A$ and you can add some of only one stock to your portfolio, would you choose (explain your choice):
a. $B$
b. $C$
c. $D$
d. Need more data

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01:04

Problem 18

Would the answer to Problem 17 change for more risk-averse or risk-tolerant investors? Explain.

Achintya Suden

Numerade Educator

01:31

Problem 19

Suppose that in addition to investing in one more stock you can invest in T-bills as well. Would you change your answers to Problems 17 and 18 if the T-bill rate is $8 \%$ ?

Breanna Ollech

Numerade Educator

01:32

Problem 20

Input the data from the table into a spreadsbeet. Compute the serial correlation in decade returns for each asset class and for inflation. Also find the correlation berween the returns of various asset classes. What do the data indicate?

Tim Schmuhl

Numerade Educator

02:05

Problem 25

If the correlation coefficient between annual portfolio returns is actually 3 , what is the covariance between the returns?

Victor Salazar

Numerade Educator

Problem 26

Repeat Problem 23 using an annual correlation of 3 .

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Problem 27

Repeat Problem 24 using an annual correlation of 3 .

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Investments

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27