Question #25
Reading: Reading 40 Analysis of Active Portfolio Management
PDF File: Reading 40 Analysis of Active Portfolio Management.pdf
Page: 11
Status: Correct
Correct Answer: A
Question
Zeta fund has active return and active risk of 1.6% and 8% respectively. Benchmark portfolio has a Sharpe ratio of 0.35 and standard deviation of benchmark returns is 10.5%. What is the weight of benchmark portfolio in a portfolio consisting of Zeta fund and the benchmark portfolio assuming that the portfolio is constructed to have optimal active risk?
Answer Choices:
A. 0.1667
B. 0.2
C. 0.25 Ufton Wealth Management's Ranger fund has proved popular with clients. An extract from the prospectus of the Ranger fund is shown in Exhibit 1. Exhibit 1: Ranger Fund Asset Portfolio weight Benchmark weight Expected portfolio return Expected benchmark return U.S. equities 15% 20% 11% 9% U.S. corporate bonds 35% 35% 8% 7% International equities 8% 40% 14% 10% U.S. real estate 42% 5% 7% 7% Ufton awards its best performing fund manager with a large cash bonus each year. Details of the performance of three funds is shown in Exhibit 2. Risk-free rate is 2%. Exhibit 2: Selected Fund Performance
Explanation
Information Ratio = active return / active risk = 1.6% / 8% = 0.2
Active risk of Zeta fund = 8%
Weight of Zeta fund = 6% / 8% = 0.75
Weight of benchmark = 0.25
(Module 40.2, LOS 40.b)
Ufton Wealth Management's Ranger fund has proved popular with clients. An extract from
the prospectus of the Ranger fund is shown in Exhibit 1.
Exhibit 1: Ranger Fund
Asset
Portfolio
weight
Benchmark
weight
Expected
portfolio return
Expected
benchmark return
U.S. equities
15%
20%
11%
9%
U.S. corporate
bonds
35%
35%
8%
7%
International
equities
8%
40%
14%
10%
U.S. real estate
42%
5%
7%
7%
Ufton awards its best performing fund manager with a large cash bonus each year. Details of
the performance of three funds is shown in Exhibit 2. Risk-free rate is 2%.
Exhibit 2: Selected Fund Performance
Fund
Portfolio
return
Benchmark
return
Portfolio
standard
deviation
Benchmark
standard
deviation
Sharpe
ratio
Tracking
error
Optimal level of active risk = σ∗
A =
σB =
(10.5) = 6%
IR
SRB
0.2
0.35
Saltire
8.46%
5.80%
6.13%
4.50%
1.05
1.58%
Dragon
13.01%
11.56%
7.64%
5.15%
1.44
2.12%
Rose
11.39%
11.37%
11.01%
11.14%
0.85
0.21%