Consider the following 2 assets:
Share Index
9 190
10 199
10,2 155
9,8 165
Calculate:
a. Standard deviation for both
b. Covariance
c. Correlation
2. Describe the main differences between the CAPM model and Sharpe´s market
portfolio
3. You have decided to invest 40% of your wealth in McDonalds, which has an expected
return of 15% and a standard deviation of 15%, and 60% of your wealth in GE, which
has an expected return of 9% and a standard deviation of 14%.
a. What is the expected return of your portfolio?
b. If the correlation between McDonalds and GM is 0.5, what is the standard
deviation of your portfolio?
c. If you wanted an expected return of 13%, what percentage should you invest
in McDonalds?
d. Based on your percentages in part c, what would the standard deviation of
this portfolio be?
4. Stock 1 and 2 have the same beta of 0.90. But stock 1’s return has a standard
deviation of 20% and stock 2 has a standard deviation of 30%. How would you
compare the risk of these two stocks? Which one do you think should have the higher
expected returns? Explain briefly.
5. Which of the following common stock portfolios is best for a conservative, risk-averse
investor? Explain briefly.
Expected return Expected market
risk premium
Standard Deviation
of return
Portfolio A 10% 10,5% 23%
Portfolio B 14% 9,5% 14%
Portfolio C 9% 6,5% 10%
6. Complete the table below. Risk free is 5% (show the steps followed on your
calculations)
Fund
7. Mario may buy the fund Umbrellasperformsbetter, which last 3 years have had an
annual return of 14% with a volatility of 19%. Risk free market is 2%.
a. Calculate the Sharpe Ratio
b. Has performed better than the market, if the market in the same period has
had a return of 14% with a volatility of 12%?
c. If Beta is 1,10, calculate the Treynor Ratio for the fund and the market. Has
the fund performed better or not?
d. Calculate Jensen. Has performed better than the market?
8. Mario wants to build an investment portfolio with his savings. He is being offered to
buy 2 different funds, a fixed income fund and an equities fund, with the following
information:
Expected return Volatility Correlation
Fixed income fund 5% 4% -0,5
Equities fund 13% 20%
a. Which % would buy of each one if Mario wants to get the maximum return?
Which are the expected returns and volatility of this portfolio?
b. If Mario wants to follow a conservative path and have a portfolio that
minimizes risk (volatility) what % would buy of each fund (MINIMUM
VARIANCE PORTFOLIO? What would be the expected return and the
volatility of this portfolio of funds? And if correlation is 0,5? Explain the
difference
9. With the information below. What would be the portfolio that minimizes risk (volatility)
(minimum variance portfolio); Make the appropriate calculations and explain the
results.
Expected return Volatility
Fixed income fund 3,5% 3%
Equities fund 13% 19%
a. If Correlation between both funds is 1
b. If Correlation between both funds is 0
c. If Correlation between both funds is -1
10. You can build a portfolio of two assets, A and B, whose returns have the following
characteristics:
Expected return Volatility Correlation
Share A 12% 20% 0,5
Share B 15% 30%
If you demand an expected return of 11%, what are the portfolio weights? What is the
portfolio’s standard deviation?
11. Assume the following Characteristic Line equation for these 3 assets:
RBNPP = 0,20% + 1,50 * RCAC40 + UBNPP
RTotal= 0,05% + 1,10* RCAC40 + UTotal
REDF = 0,50% + 0,90 * RCAC40 + UEDF
Assume a portfolio of 20% BNPP, 40% Total and 40% EDF. Calculate:
– Portfolio Beta
– Portfolio Alpha
– Expected return if CAC40 growth is 3%
12. Stock A and B have the following characteristics:
Expected return Volatility
Bond A 5% 10%
Stock B 9% 20%
Their correlation is 0. The risk-free interest rate is 2%.
a. Consider a portfolio, P, with 80% in Bond A and 20% in the risk- free asset.
What is the portfolio´s expected return and standard deviation of portfolio P’s return?
b. Consider another portfolio, Q, which consists of 70% of Bond A and 30% of
Stock B. What is the portfolio´s expected return and standard deviation of portfolio
Q’s return?
c. Calculate Sharpe ratio for both
13. The asset risk free offers a return of 5%. If the Expected return for the market
portfolio is 17% with a volatility of 10%
a. Would it be reasonable buy shares on XYZ with a Beta of 0,70 with an
expected return of 11%? Explain why
b. And a share on ABC with a Beta of 1.3 with an expected return of 21%?
Explain why
c. And if risk free would be 2%?
14. Betty Cole is an aggressive investor. She has $100,000 capital but is borrowing
additional $50,000 to invest in S&P500 index fund. Although the current risk-free rate
is only 1%, her borrowing rate is 2%. The current expected return and standard
deviation of S&P 500 index are 10% and 20%, respectively. What is the expected
Sharpe ratio of Cole’s portfolio?