Investment Hw 7

Homework 7

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.

Er= 0.20*0.18+0.35*0.22+ 0.45*0.26=0.23

VAR = 0.20*(0.18-0.23)^2+0.35*(0.22-0.23)^2+ 0.45*(0.26-0.23)^2=0.00094

SD=0,03066

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.

Er=0.15*15%+ 0.55* 25%+ 0.30* 35%=26.5%

VAR=0.15*(15%-26.5%)^2+ 0.55* (25%-26.5%)^2+ 0.30* (35%-26.5%)^2=42.75 or 0.004275

SD=6.54 or 0.0654

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 % $40000

Victoria’s Secret 10,000 * $ 30 * 11% $33000

Nike 30,000 * $ 10 * 12% $36000

Calculate the expected return for this portfolio. Er =109000 or 0,099%

Problem # 4

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

Portfolio Expected return Expected SD Sharpe ratio

A 7% 14% (7%-4%)/14%= 0.214

B 9% 25% (9%-4%)/25%= 0.2

C 12% 23% (12%-4%)/23%= 0.348

Risk Free 4% 0%

A ratio developed by Nobel laureate William F. Sharpe to measure risk-adjusted performance. The Sharpe ratio is calculated by subtracting the risk-free rate - such as that of the 10-year U.S. Treasury bond - from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns.

The Sharpe ratio tells us whether a portfolio's returns are due to smart investment decisions or a result of excess risk. This measurement is very useful because although one portfolio or fund can reap higher returns than its peers, it is only a good investment if those higher returns...