ProblemSet10 solutions v1

Econ 136: Financial Economics
Problem Set #10
Due Date: April 30, 2014
1. In the spreadsheet Markowitz-01.xlsx some of the entries in the long/short and longonly portfolio data sections are missing (the missing data locations are highlighted in yellow). Use the Solver to calculate the following to replace this data:
(a) The mean excess return, standard deviation, and portfolio weights for the minimum variance portfolio.
(b) The mean excess return, standard deviation, and portfolio weights for the optimum (maximum Sharpe ratio) portfolio.
(c) The mean excess return, standard deviation, and portfolio weights for the portfolio with an expected excess return of 0.073.
Note: Your results will differ slightly from those in the book because their expected excess returns and covariances have been calculated in another spreadsheet and are shown in rounded form. For a good summary of how these calculations are done, see
BKM, pp. 234-239.
The solutions I obtained are given in the table below. There may be some variation from these results if you started with different initial weights. Such variations are to be expected in a multidimensional optimization problem.
Long/Short
Min. Var.
E[rport ]
0.0383
σport
0.1132
US
0.6150
UK
0.8702
France
-0.1936
Germany
-0.5238
Australia
0.0774
Japan
0.2058
Canada
-0.0509

Long Only
Optimum E[rport ] = 0.073
0.0575
0.0730
0.1402
0.1939
0.6885
0.3500
0.0521
0.0000
0.0000
0.0000
0.0000
0.6500
0.1336
0.0000
0.1258
0.0000
0.0000
0.0000

2. BP PLC (NYSE: BP) has a current stock price of $37 and current dividend of $1.32.
The dividend is expected to grow at 5% annually. BP’s beta is 0.87. The risk-free rate is 1.5%, and the market risk premium is 5.0%.
(a) What is next year’s projected dividend?
The projected dividend D1 is
D1 = D0 (1 + g) = $1.32 × 1.05 = $1.386 or $1.39 .
1

(1)

(b) What is BP’s cost of equity capital based on the CAPM?
The cost of equity capital rBP is rBP = rf + β [E(rm ) − rf ] = 1.5% + 0.87 [5.0%] = 1.5% + 4.35% = 5.85% .