Faculty of Economics and Business
Department of Business
FINANCE I (102329) – Group 3 – 2012-13
Study Guide. Dr. Maria-Antonia Tarrazon & Dr. Joan Montllor
EXERCISE 1 (standard exercise on the portfolio selection model)
Lucrècia Estiracabells decides upon her investment strategies applying the optimal portfolio
selection model constructed by Professor Markowitz. Her expectations about the return and risk of
the four existing stocks and the risk-free asset are summarized in the following table:
Assets
Expected return
Standard deviation
ρ Stock 1
ρ Stock 2
ρ Stock 3
ρ Stock 4
Stock 1
18%
20%
1
0.50
0.70
0.01
Stock 2
30%
30%
0.50
1
0.70
0.01
Stock 3
50%
50%
0.70
0.70
1
0.05
Stock 4
10%
40%
0.01
0.01
0.05
1
rf =
5%
The efficient frontier of risky assets that arises from the optimization model is:
E(Rp) = 0.1175 + [ 0.7024·σ2p – 0.01620 ]1/2
The optimal risky portfolio P* promises an expected rate of return of 35.76% with an associated
standard deviation of 32.42%.
P* consists of 6.12% of stock 1, 45.85% of stock 2, 40.24% of stock 3, and 7.79% of stock 4.
Questions:
1. Check the expected rate of return on the optimal risky portfolio, E(RP*), and its standard deviation,
P*, using the formulae of their definitions.
2. Once the risk-free asset is introduced, check again E(RP*) and P* through the identity of slopes
between the efficient frontier of risky assets and the linear area of lending.
3. Lucrècia Estiracabells loves assuming a risk of 50%. Her concern about this preference is to find
out if investing 100% of her budget in stock 3 is an efficient decision in:
a) a setting with only risky assets (first scenario of Markowitz model) and
b) when lending and borrowing at 5% are allowed in the model (third scenario).