# Finance - Stocks X and Y

You have estimated the following probability distributions of expected future returns for Stocks X and Y:

Stock X Stock Y

pj rj rj x pj pj rj rj x pj

0.1 -10% -0.01 0.2 2% 0.004

0.2 10% 0.02 0.2 7% 0.014

0.4 15% 0.06 0.3 12% 0.036

0.2 20% 0.04 0.2 15% 0.03

0.1 40% 0.04 0.1 16% 0.016

15% 10%

a. What is the expected rate of return for Stock X? Stock Y?

Stock X = 15%

Stock Y = 10%

b. What is the standard deviation of expected returns for Stock X? For Stock Y?

Stock X Stock Y

rj r rj - r (rj - r)2 pj (rj - r)2pj rj r rj - r (rj - r)2 pj (rj - r)2pj

-10% 15% -25% 625 0.1 62.5 2% 10% -8% 64 0.2 12.8

10% 15% -5% 25 0.2 5 7% 10% -3% 9 0.2 1.8

15% 15% 0% 0 0.4 0 12% 10% 2% 4 0.3 1.2

20% 15% 5% 25 0.2 5 15% 10% 5% 25 0.2 5

40% 15% 25% 625 0.1 62.5 16% 10% 6% 36 0.1 3.6

135 √135 = 11.61% 24.4 √24.4 = 4.94%

c. Which stock would you consider to be riskier? Why?

Stock X is risker because it has a higher standard deviation than Stock Y.

2

The return expected form Project No. 542 is 22 percent. The standard deviation of these returns is 11 percent.

If returns from the project are normally distributed, what is the chance that the project will result in a rate

of return above 33 percent? What is the probability that the project will result in losses (negative rates of return)?

Return expected 22%

Standard deviation 11%

Above rate 33%

33% - 22% 0.11 1 I'm not sure about this one

11% 0.11

0% - 22% -0.22 -2

11% 0.11

3

The expected rate of return for the stock of Cornhusker Enterprises is 20 percent, with a standard

deviation of 15 percent. The expected rate of return for the stock of Mustang Associates is 10 percent

with a standard deviation of 9 percent.

a. Which stock would you consider to be riskier? Why?

Cornhusker Enterprises 15% 0.75

20%

Mustang Associates 9% 0.90

10%

Mustang Associates would be riskier because they have a higher coefficient of variation.

b. If you knew that the beta coefficient of Cornhusker stock is 1.5 and the beta of Mustang is .9, how would

your answer to Part a change?

Cornhusker would not now have the higher coefficient so my answer would change because they would

become the risker of the two.

4

An investor currently has all of his wealth in Treasury bills. He is considering investing one-third of his funds

in General Electric, whose beta is 1.30, with the remainder left in Treasury bills. The expected risk-free rate

(Treasury bills) is 6 percent and the market risk premium is 8.8 percent. Determine the beta and the expected

return on the proposed portfolio.

Return on stock = Risk free rate x Market risk premium

R = 6% x 8.8%

R = 0.00528 I'm not sure where to go now.

5

The Mutual Assurance and Life Company is offering an insurance policy under either of the following two terms:

If you had investment opporunities offering an 8 percent annual return, which alternative would you prefer?

a. Make a seriers of twelve $1200 payments at the beginning of each of the next 12 years (the first

payment being made today).

PV = FV / (1 + i)t Very lost

14,400 / (1 + .08)12

14400*.93

b. Make a single lump-sum payment today of $10,000 and receive coverage for the next 12 years.

#### Solution Preview

Please see my response in blue. Hope it helps.

You have estimated the following probability distributions of expected future returns for Stocks X and Y:

Stock X Stock Y

pj rj rj x pj pj rj rj x pj

0.1 -10% -0.01 0.2 2% 0.004

0.2 10% 0.02 0.2 7% 0.014

0.4 15% 0.06 0.3 12% 0.036

0.2 20% 0.04 0.2 15% 0.03

0.1 40% 0.04 0.1 16% 0.016

15% 10%

a. What is the expected rate of return for Stock X? Stock Y?

Stock X = 15%

Stock Y = 10%

b. What is the standard deviation of expected returns for Stock X? For Stock Y?

Stock X Stock Y

rj r rj - r (rj - r)2 pj (rj - r)2pj rj r rj - r (rj - r)2 pj (rj - r)2pj

-10% 15% -25% 625 0.1 62.5 2% 10% -8% 64 0.2 12.8

10% 15% -5% 25 0.2 5 7% 10% -3% 9 0.2 1.8

15% 15% 0% 0 0.4 0 12% 10% 2% 4 0.3 1.2

20% 15% 5% 25 0.2 5 15% 10% 5% 25 0.2 5

40% 15% 25% 625 0.1 62.5 16% 10% 6% 36 0.1 3.6

135 √135 = 11.62% 24.4 √24.4 = 4.94%

I rounded the number for you.

c. Which stock would you consider to be riskier? Why?

Stock X is risker because it has a higher standard deviation than Stock Y.

2

The ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer the finance questions.