Minimum Variance Portfolio
A portfolio manager may create a portfolio with the following two assets. Asset A
is an Asian-Stock-Index product and asset B is a BRIC bond-index product. The
expected return of asset A is 10% (asset B 7% ) and the volatility of asset A is 20%
(asset B 10%). According to historical data, the correlation is expected to be 0,4.
How is the loading of the MVP?
What is the expected risk and return of the MVP?
The Ideal Portfolio
A portfolio manager needs to create a portfolio for a new client who has a risk
aversion of a = 4. The manager can choose between two assets A and B. The
following information is being provided to the manager: µA = 10%, µB = 5%, σA =
20%, σB = 10%, ρA,B = 0,3.
Which is the ideal portfolio loading for the client?
Another client of the manager has already a portfolio set up.
The portfolio loading is 68,7% stocks and 31,3% bonds. Additional portfolio
information: µA = 10%, µB = 5%, σA = 20%, σB = 6%, ρA,B = 0,3.
What is the client’s risk-aversion factor that the manager needs to know to offer the
client an additional product?
MPT - Risky and Risk-Free Assets
An investors’ utility function is given by
U(RQ ) = f (µ Q ," Q ) = µ Q(w)# a
2 $" 2
What is the loading, which maximizes the investors utility?
The market portfolio (tangential portfolio) has µM = 10% and σM = 20%. The risk
free rate is given by an investment in a AAA government bond with rf = 5%.
Calculate the ideal asset allocation for client A who has a risk aversion of a=1,
client B (a=1,25), client C (a=3), and client D (a=4)
Capital Asset Pricing Model
Exp. Return in %
SD in %
a)Complete the above table (where it is possible).
b)Are all assets priced correctly according to CAPM?
Are the following statements true or false? Why?
1. The slope of the CML is equal to the beta of the market portfolio.
2. Diversification eliminates systematic risk in a portfolio.
3. Assets with a higher beta always offer a higher return than assets with a
Evaluate, if a real investment of € 100 Mio. is fairly priced according to the given
capital market information (in Mio. €):
Condition A Condition B Condition C
Asset A, E[r] in t1
Asset B, E[r] in t1
The risk-free rate is rf=10%. The market portfolio consists of asset A and B
with the shares xA=0,67 and xB=0,33.
a) Calculate the expected return of the market portfolio and the market portfolio
b) What are the expected cash flows and the expected return of the real investment?
c) Calculate the beta of the investment project.
d) What is the risk-adequate return of the project? Is it economically logical to
conduct the investment?