FNGB 7460 Portfolio Management Fordham University
A problem set in portfolio management, focusing on key financial strategies in the context of Fordham University's FNGB 7460 course.
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FORDHAM UNIVERSITY
Graduate School of Business
Portfolio Management Prof. Christopher Blake
FNGB 7460 Spring 2013
Problem Set 2
Consider the following data for assets 1 through 5 (i = 1, ..., 5):
Asset iiRi
1 7% 4%
2 12% 6%
3 18% 12%
4 20% 10%
5 22% 13%
Also,12
= −0.15,13
= 0.45,14
= 0.3,15
= 0.4,23
= 0.4,24
= 0.15,25
= 0.3,34
= 0.8,35
= 0.5, and45
= 0.2.
Answer questions 1, 2 and 3 using the above data. Show all work involved on separate sheets of
paper attached to this page.
1a) (30 points)
Using the formulas introduced in class, what are the investment weights, the expected return (R )
and the total risk ( ) of the least risky two-asset portfolio constructed from assets 1 and 5?
(Assume short sales are allowed.)
We want to find the weights that minimize the standard deviation, i.e. for an optimal risky
portfolio. The following formula is used :
𝑤1 = 𝑅1 ∗ 𝜎5
2 − 𝑅5 ∗ 𝜎15
𝑅1 ∗ 𝜎5
2 + 𝑅5 ∗ 𝜎1
2 − (𝑅1 + 𝑅5) ∗ 𝜎15
Where 𝜎15 is the covariance of the assets 1 and 5 :
Graduate School of Business
Portfolio Management Prof. Christopher Blake
FNGB 7460 Spring 2013
Problem Set 2
Consider the following data for assets 1 through 5 (i = 1, ..., 5):
Asset iiRi
1 7% 4%
2 12% 6%
3 18% 12%
4 20% 10%
5 22% 13%
Also,12
= −0.15,13
= 0.45,14
= 0.3,15
= 0.4,23
= 0.4,24
= 0.15,25
= 0.3,34
= 0.8,35
= 0.5, and45
= 0.2.
Answer questions 1, 2 and 3 using the above data. Show all work involved on separate sheets of
paper attached to this page.
1a) (30 points)
Using the formulas introduced in class, what are the investment weights, the expected return (R )
and the total risk ( ) of the least risky two-asset portfolio constructed from assets 1 and 5?
(Assume short sales are allowed.)
We want to find the weights that minimize the standard deviation, i.e. for an optimal risky
portfolio. The following formula is used :
𝑤1 = 𝑅1 ∗ 𝜎5
2 − 𝑅5 ∗ 𝜎15
𝑅1 ∗ 𝜎5
2 + 𝑅5 ∗ 𝜎1
2 − (𝑅1 + 𝑅5) ∗ 𝜎15
Where 𝜎15 is the covariance of the assets 1 and 5 :
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Document Details
University
Fordham University
Subject
Finance