Submitted by: Submitted by dossymova
Views: 500
Words: 816
Pages: 4
Category: Business and Industry
Date Submitted: 04/24/2012 09:52 AM
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...