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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
SOLUTION to questions 2 and 3
2. Checking E(RP) and σP through the identity of slopes:
Slope of the efficient frontier of risky assets:
p P
E Rp
= 0. 7024 2 · * ( 0. 7024 ·^2 * 0. 01620 )^1 /^2
P P
Slope of the line that starts at rf =5% on the vertical axis and is tangent to the efficient frontier of risky assets at P*:
2
* 0.^11750.^70240.^016200.^05
P
P P
ERP rf
Equalizing both slopes we calculate the standard deviation of P*:
2
2
* 0.^06750.^70240.^01620
P
P P
P
0.7024·σ^2 P* = 0.0675 [0.7024·σ^2 P* - 0.01620]1/2^ + [0.7024·σ^2 P* - 0.01620]
(0.01620/0.0675)^2 = 0.7024·σ^2 P* - 0.
0.24^2 + 0.01620 = 0.7024·σ^2 P* σ^2 P* = 0.105068 P * 0. 3242
And substituing P * 0. 3242 in the equation of the efficient frontier of risky assets we obtain the
expected return on P*:
E(R P* )0.1175 0.7024( 0. 3242 )^2 0.01620 0. 3576
Faculty of Economics and Business Department of Business FINANCE I (102329) – Group 3 – 2012 - 13 Study Guide. Dr. Maria-Antonia Tarrazon & Dr. Joan Montllor
3.a) Efficient investment: A combination on the efficient frontier with risky assets (EFRA) assuming a risk of 3 =p=50%:
E(Rp) = 0.1175 + [0.7024*0.5^2 - 0.01620]1/2^ = 0.516749 or 51.6749% > E(R 3 )=50%
which shows that investing 100% of the budget in stock 3 is inefficient, since for the same total risk (50%) the expected return is higher.
In this case we cannot calculate the composition of this new investment yielding 51.6749% because portfolios may consist of up to 4 stocks (opposite to Exercise 2, where only two stocks are involved and, therefore, one weight can be x and the other one ( 1-x )).
b) Efficient investment: A combination on the linear efficient frontier with lending and borrowing assuming a risk of 3 =p=50%:
p (^) 0.3242 σp E(R )0.050.35760.05 = 0.05 + 0.9488·0.50 = 0.5244 or 52.44% > E(R 3 )=50%
Composition of this investment:
0.5244 = 0.05·(1-) + 0.3576 · =1.542263 and (1-)= -0. This is 154.2263% invested in P* with 54.2263% of borrowing at rf=5%. Checking: 0.05(-0.542263) + 0.35761.542263 = 0. -2.7113% interests +55.1513% = 52.44%
Drawing on the next page.
