Finance

Homework #5

Problem #1

An analyst developed the following probability distribution of the rate of return for a common stock:

Scenario Probability Rate of Return

1 0.20 0.18

2 0.35 0.22

3 0.45 0.26

Using the table above, find expected return, standard deviation and variance.

Problem #2

State of the World Probability (P) Return (R )

Expansion 0.15 15%

Normal 0.55 25%

Recession 0.30 35%

Using the table above, find expected return, standard deviation and variance.

Problem # 3

An investor holds the following portfolio which is invested in three stocks: Adidas, Victoria’s Secret and Nike.

Security Number of Shares Share Price Expected Return

Adidas 25,000 $ 20 8 %

Victoria’s Secret 10,000 $ 30 11%

Nike 30,000 $ 10 12%

Calculate the expected return for this portfolio.

Problem # 4

Which of the following portfolios has the best Sharpe ratio? What does this mean?

Portfolio Expected return Expected Standard

deviation

A 7% 14%

B 9% 25%

C 12% 23%

Risk Free 4% 0%

Problem # 5

Define risk aversion and discuss evidence that suggests that individuals are generally risk averse.

Problem #6

a) If your nominal return was 14.8% during the year and the inflation rate was 6.8%; what was your real rate of return. Calculate the exact and approximate answers.

b) If your nominal return was 7% during the year and the inflation rate was 3%; what was your real rate of return. Why is the difference between the approximate and exact answer smaller than in part a?

Problem #7

Bear Market Normal Market Bull Market

Probability 0.2 0.5 0.3

X -15% 20% 40%

Y -10% 15% 10%

Using the table above find:

a) Expected return for Stock X and Stock Y

b) Variance and StdDev of Stock X and Stock Y

Problem #8

If an investor has $50,000 to invest in the stocks X and Y (from problem #7) in proportions 55% and 45% respectively and additional $5000 in T-bills (R=3.44%), what is the expected rate of return for this portfolio?

What can you...