# Risk & Return

6. Returns on an investment are uncertain. You estimate the likelihood of alternative returns based on the estimated probabilities of possible outcomes:

Outcome Return Estimated Probability of Outcome

1 3% .05

2 7% .25

3 10% .40

4 13% .25

5 17% .05

a. Calculate the expected return.

b. Calculate the standard deviation of the return

7. Dublin Plastics Inc.'s stock is selling for $17.60. Your research suggests it will pay dividends of $2.00 next year and $2.80 the following year, after which its stock price will have peaked at $21.00. You require a return of 20% on similar investment risk. Should you buy now and sell when the price reaches $21.00?

8. A four-stock portfolio is made up as follows:

Stock Current

Value Beta

A $15,300 .5

B $28,700 .9

C $19,600 1.2

D $10,400 1.7

a. Calculate the portfolio's beta

b. How relatively risky is this portfolio? Could the portfolio have more risk? Could the portfolio have less risk? Explain.

9. Given the following information, calculate the required return on MNO Corporation's common stock:

? MNO Corp.'s Common Stock Beta (ß) = 0.9

? Risk-free rate = 5%

? Required return on the overall market = 11%

#### Solution Preview

6. Returns on an investment are uncertain. You estimate the likelihood of alternative returns based on the estimated probabilities of f possible outcomes:

Outcome Return Estimated Probability of Outcome

1 3% .05

2 7% .25

3 10% .40

4 13% .25

5 17% .05

a. Calculate the expected return.

b. Calculate the standard deviation of the return

return Probability return x Probability Difference from mean, i.e.0.1 Difference 2 Prob x Difference 2

3% 0.05 0.0015 -0.0700 0.0049 0.000245

=0.03x0.05 =0.03-0.1 =-0.07^2 =0.05x0.0049

7% 0.25 0.0175 -0.0300 0.0009 0.000225

10% 0.4 0.0400 0.0000 0.0000 0.000000

13% 0.25 0.0325 0.0300 0.0009 0.000225

17% 0.05 0.0085 0.0700 0.0049 0.000245

Total 1.00 0.1000 0.000940

Expected return= 10%

Variance= 0.00094

Standard deviation=square root of ...

#### Solution Summary

Answers 4 questions:

1) Returns on an investment: Calculates the expected return and standard deviation of the return, given the probability distribution of return

2) Dublin Plastics Inc.'s stock: Answers should you buy now and sell when the price reaches $21.00.

3) four-stock portfolio: Calculates beta

4) MNO Corporation's common stock: calculates required return using CAPM.