Question 1

The expected rate of return for the coming year on FTC common stock is normally distributed with a mean of 14% and a standard deviation of 7%.Determine the probability of earning more than 21% on FTC common stock.(Note: Table V is required to work this problem.)

Accepted Answer

z = (21% - 14%)/7% = 1;From Table V, p = 15.87%

Question 2

Determine the beta of a portfolio consisting of equal investments in the following common stocks:
$$\begin{array} { l l } 
\text { Securty } & \text { Bete } \
\hline \text { Apple Computer } & 1.15 \
\text { Coca-Cola } & 1.05 \
\text { Harley-Devidson } & 1.50 \
\text { Hamestalke Mining } & 0.50 
\end{array}$$

Accepted Answer

The answer of Determine the beta of a portfolio consisting...

Question 3

The expected rate of return for 3COM is 18 percent, with a standard deviation of 10.98 percent.The expected rate of return for Just the Fax is 26 percent with a standard deviation of 15.86%.Which firm would be considered the riskier from a total risk perspective?

Accepted Answer

3COM: v = 10.98%/18% = 0.61
Just the Fax: v = 15.86%/26% = 0.61

Question 4

An investor plans to invest 75 percent of her funds in the common stock of Gamma Industries and 25 percent in Epsilon Company.The expected return on Gamma is 12 percent and the expected return on Epsilon is 16 percent.The standard deviation of returns for Gamma is 8 percent and for Epsilon is 12 percent.The correlation between the returns for Gamma and Epsilon is +0.8.Determine the standard deviation of returns for this investor's portfolio.

Accepted Answer

σp = [(0.75)²(8%)² + (0.25)²(12%)² + 2(0.75)(0.25)(0.8)(8%)(12%)].⁵ = 8.59%

Question 5

Over the 10-year period from 1978 through 1987, the compound annual rate of return on U.S.Treasury bills was 9.17 percent.Over the same time period, the average annual inflation rate was 6.39 percent.Therefore,

Accepted Answer

9.17% - 6.39% = 2.78%

Question 6

Don has $3,000 invested in AT&T with an expected return of 11.6 percent;$10,000 in IBM with an expected return of 12.8 percent;and $6,000 in GM with an expected return of 12.2 percent.What is Don's expected return on his portfolio?

Accepted Answer

E(Rp) = (3/19)11.6% + (10/19)12.8% + (6/19)12.2% = 12.42%

Question 7

Sally's broker told her that the expected return from her portfolio was 14.2%.If 40% of her securities have an expected return of 10.3 percent and 20% have an expected return of 12.8 percent, what is the expected return of the remaining portion of her portfolio?

Accepted Answer

14.2% - 0.4(10.3%) - 0.2(12.8%) = 0.4 X
X = 18.8%

Question 8

The real rate of interest is expected to be 3 percent and the expected rate of inflation for next year is expected to be 5.5 percent.If the default risk premium is 1.1 percentage points, and the seniority risk premium is 0.4 percentage points, what is the required return on a 1 year U.S.Treasury security?

Accepted Answer

Required return = 3% + 5.5% = 8.5%

Question 9

An investor plans to invest 75 percent of her funds in the common stock of Gamma Industries and 25 percent in Epsilon Company.The expected return on Gamma is 12 percent and the expected return on Epsilon is 16 percent.The standard deviation of returns for Gamma is 8 percent and for Epsilon is 12 percent.The correlation between the returns for Gamma and Epsilon is +0.8.Determine the expected return on the investor's portfolio.

Accepted Answer

E(Rp) = 0 .75(12%) + 0.25(16%) = 13%

Question 10

Elephant Company common stock has a beta of 1.2.The risk-free rate is 6 percent and the expected market rate of return is 12 percent.Determine the required rate of return on the security.

Accepted Answer

kⱼ = 6% + 1.2(12% - 6%) = 13.2%

Question 11

A college student owns two securities: Apple and Coca- Cola.Apple has an expected return of 15 percent with a standard deviation of those returns being 11 percent.Coca-Cola has an expected return of 12 percent, and a standard deviation of 7 percent.The correlation of returns between Apple and Coca-Cola is 0.81.If the portfolio consist of $6,000 in Coca-Cola and $4,000 in Apple, what is the expected standard deviation of portfolio returns?

Accepted Answer

σp = [(.6)²(.07)² + (.4)²(.11)² + 2(.6)(.4)(.07)(.11)(.81)].⁵
= 0.0818

Question 12

The yield to maturity on ACL bonds maturing in 2005 is 8.75 percent.The yield to maturity on a similar maturity U.S.Government Treasury bond in 7.06 percent and the yield on Treasury bills is 6.51 percent.What is the default risk premium on the ACL bond?

Accepted Answer

Risk premium = 8.75% - 7.06% = 1.69%

Question 13

The expected rate of return for the coming year on FTC common stock is normally distributed with a mean of 14% and a standard deviation of 7%.Determine the probability of earning a negative rate of return (i.e.less than 0%) on FTC common stock.(Note: Table V is required to work this problem.)

Accepted Answer

z = (0% - 14%)/7% = -2.0;From Table V, p = 2.28%

Question 14

The return expected from a risky investment is 24 percent, and the standard deviation of this return is 17 percent.If returns from this investment are normally distributed, what is the probability that the investment may earn a negative rate of return? (Note: Table V is required to work this problem.)

Accepted Answer

z = (0% - 24%)/17% = - 1.41;From Table V, p = 7.93%

Question 15

The risk-free rate of return is 5.51 percent, based on an expected inflation premium of 2.54 percent.The expected return on the market is 12.8 percent.What is the required rate of return for Envoy common stock which has a beta of 1.35?

Accepted Answer

kⱼ = 5.51 + 1.35(12.8 - 5.51) = 15.35%

Question 16

Dana has a portfolio of 8 securities, each with a market value of $5,000.The current beta of the portfolio is 1.28 and the beta of the riskiest security is 1.75.Dana wishes to reduce her portfolio beta to 1.15 by selling the riskiest security and replacing it with another security with a lower beta.What must be the beta of the replacement security?

Accepted Answer

To find the beta for the 7 securities:
1.28 = 7/8(x) + 1/8(1.75)
x = 1.21
New security's beta would be:
1.15 = 7/8(1.21) + 1/8 beta
beta = 0.73

Question 17

Compute the risk premium for the stock of Omega Tools if the risk-free rate is 6%, the expected market return is 12%, and Omega's stock has a beta of .8.

Accepted Answer

Risk premium = 0.8(12% - 6%) = 4.8%

Question 18

If the return on U.S.Treasury bills is 7.02%, the risk premium is 2.32%, and the inflation rate is 4.16%, then the real rate of return is:

Accepted Answer

7.02% - 4.16% = 2.86%

Question 19

Assume you want to construct a portfolio with a 14 percent return from the following two securities:

What percentage of your portfolio should be invested in Security 1?

Accepted Answer

0.14 = X(0.16) + (1 - X)(0.125)
X = 0.43

Question 20

Twin City Knitting (TCK) pays a current dividend of $2.20 and dividends are expected to grow at a rate of 7 percent annually in the foreseeable future.The beta of TCK is 1.2.If the risk-free rate is 9.2 percent and the market risk premium is 6 percent, at what price would you expect TCK's common stock to sell?

Accepted Answer

kₑ = 0.092 + 1.2(0.06) = 0.164 or 16.4%
kₑ = $2.20(1.07)/P₀ + 0.07 = 0.164
P₀ = $2.354/0.094 = $25.04

Quiz 8: Analysis of Risk and Return