Solutions for Chapter 15: Questions and Problems
CHAPTER 15
EQUITY PORTFOLIO MANAGEMENT STRATEGIES
Answers to Questions
1.
Passive portfolio management strategies have grown in popularity because investors are
recognizing that the stock market is fairly efficient and that the costs of an actively
managed portfolio are substantial.
2.
Numerous studies have shown that the majority of portfolio managers have been unable
to match the risk-return performance of stock or bond indexes. Following an indexing
portfolio strategy, the portfolio manager builds a portfolio that matches the performance
of an index, thereby reducing the costs of research and trading. The portfolio manager’s
evaluation is based upon how closely the portfolio tracks the index or “tracking error,”
rather than a risk-return performance evaluation.
Another passive portfolio strategy, buy-and-hold, has the investor purchase securities and
then not trade them—i.e., hold them—for a period of time. It differs from an indexing
strategy in that indexing does require some limited trading, such as when the composition
of the index changes as firms merge or are added and deleted from the index.
3.
There are a number of active management strategies discussed in the book including
sector rotation, the use of factor models, quantitative screens, and linear programming
methods.
Following a sector rotation strategy, the manager over-weights certain economic sectors,
industries or other stock attributes in anticipation of an upcoming economic period or the
recognition that the shares are undervalued.
Using a factor model, portfolio managers examine the sensitivity of stocks to various
economic variables. The managers then “tilt” the portfolios by trading those shares most
sensitive to the analyst’s economic forecast.
Through the use of computer databases and quantitative screens, portfolio managers are
able to identify groups of stocks based upon a set of characteristics.
Using linear programming techniques, portfolio managers are able to develop portfolios
that maximize objectives while satisfying linear constraints.
Any active management technique incorporates fundamental analysis, technical analysis,
or the use the anomalies and attributes. For example, based upon the top-down
fundamental approach, a factor model may be used to tilt a portfolio’s sensitivity toward
those firms most likely to benefit from the economic forecast. Anomalies and attributes
- 122 Copyright © 2010 by Nelson Education Ltd.
Solutions for Chapter 15: Questions and Problems
can be used as quantitative screens (e.g, seek small stocks with low P/E ratios) to identify
potential portfolio candidates.
4.
Three basic techniques exist for constructing a passive portfolio: (1) full replication of an
index, in which all securities in the index are purchased proportionally to their weight in
the index; (2) sampling, in which a portfolio manager purchases only a sample of the
stocks in the benchmark index; and (3) quadratic optimization or programming
techniques, which utilize computer programs that analyze historical security information
in order to develop a portfolio that minimizes tracking error.
5.
Managers attempt to add value to their portfolio by: (1) timing their investments in the
various markets in light of market forecasts and estimated risk premiums; (2) shifting
funds between various equity sectors, industries, or investment styles in order to catch the
next “hot” concept; and (3) stockpicking of individual issues (buy low, sell high).
6.
The job of an active portfolio manager is not easy. In order to succeed, the manager
should maintain his/her investment philosophy, “don’t panic.” Since the transaction costs
of an actively managed portfolio typically account for 1 to 2% of the portfolio assets, the
portfolio must earn 1-2% above the passive benchmark just to keep even. Therefore, it is
recommended that a portfolio manager attempt to minimize the amount of portfolio
trading activity. A high portfolio turnover rate will result in diminishing portfolio profits
due to growing commission costs.
7.
The four asset allocation strategies are: (1) integrated asset allocation strategy, which
separately examines capital market conditions and the investor’s objectives and
constraints to establish a portfolio mix; (2) strategic asset allocation strategy, which
utilizes long-run projections; (3) tactical asset allocation strategy, which adjusts the
portfolio mix as capital market expectations and relative asset valuations change while
assuming that the investor’s objectives and constraints remain constant over the planning
horizon; and (4) insured asset allocation strategy, which presumes changes in investor’s
objectives and constraints as his/her wealth changes as a result of rising or falling market
asset values.
8.
A price momentum strategy is based on the assumption that a stock’s recent price
behaviour will continue to hold. Thus an investor would buy a stock whose price has
recently been rising, and sell (or short) a stock whose price has been falling.
An earnings momentum strategy rests on the idea that a firm’s stock price will ultimately
follow its earnings. The measurement of earnings momentum is usually based on a
comparison to expected earnings. Thus an investor would buy a stock that has
accelerating earnings relative to expectations and sell (or short) a stock whose earnings
fall below expectations.
These two approaches may product similar portfolios if company’s P/E ratios remain
stable as their earnings (or price) exhibits momentum characteristics.
- 123 Copyright © 2010 by Nelson Education Ltd.
Solutions for Chapter 15: Questions and Problems
9.
There are tradeoffs between using the full replication and the sampling method. Fully
replicating an index is more difficult to manage and has higher trading commission costs,
when compared to the sampling method. However, tracking error occurs from
sampling, which should not be the case in the full replication of the index.
10.
The portfolio manager could emphasize or overweight, relative to the benchmark,
investments in natural resource stocks. The portfolio manager could also purchase options
on natural resource stocks.
- 124 Copyright © 2010 by Nelson Education Ltd.
Solutions for Chapter 15: Questions and Problems
CHAPTER 15
Answers to Problems
1.
Using a spreadsheet and its functions we obtain the following values:
R2 : 0.98
alpha or intercept term: 0.08
beta or slope: 0.96
Average return difference (with signs): 0.08
Average return difference (without signs) 0.28
Portfolio
Return
Jan
5.0
Feb
-2.3
Portfolio
Mar
-1.8
Apr
2.2
May
0.4
Jun
-0.8
Jul
0
Aug
1.5
Sep
-0.3
Oct
-3.7
Nov
2.4
Dec
0.3
S&P
Return
5.2
-3
-1.6
1.9
0.1
-0.5
0.2
1.6
-0.1
-4
2
0.2
Difference Absolute
in Returns difference
in returns
R2
0.9834
-0.20
0.20
0.70
0.70
S&P 0.0822
500
Intercept
-0.20
0.20[Ri – E(Ri)] x
Slope
0.9571
0.30
0.30
0.30
0.30
-0.30
0.30
-0.20
0.20
-0.10
0.10
-0.20
0.20
0.30
0.30
0.40
0.40
0.10
0.10
average
0.08
0.28
2(a).
Portfolio turnover is the dollar value of securities sold in a year divided by the average
value of the assets:
Fund W: 37.2/289.4 = .1285 or 12.85%
Fund X: 569.3/653.7 = 0.8709 or 87.09%
Fund Y: 1,453.8/1,298.4 = 1.1197 or 111.97%
Fund Z: 437.1/5,567.3 = 0.0785 or 7.85%
(b)
Passively managed funds will have low portfolio turnover ratios and should have low
expenses ratios. On this basis, Funds W and Z are the most likely passively managed
portfolios; X and Y are most likely to be actively managed.
- 125 Copyright © 2010 by Nelson Education Ltd.
Solutions for Chapter 15: Questions and Problems
(c)
(d)
3(a).
The tax cost ratio is compute as [1 - (1 + TAR)/(1+PTR)] × 100 where TAR represents
tax-adjusted return and PTR is the pre-tax return. Our calculations are as follows:
Fund W: [1 - (1 + 0.0943)/(1+0.0998)] × 100 = 0.50%
Fund X: [1 - (1 + 0.0887)/(1+0.1065)] × 100 = 1.61%
Fund Y: [1 - (1 + 0.0934)/(1+0.1012)] × 100 = 0.71%
Fund Z: [1 - (1 + 0.0954)/(1+0.0983)] × 100 = 0.26%
The tax cost ratio represents the percentage of an investor’s assets that are lost to taxes
on a yearly basis due to the trading strategy employed by the fund manager. Funds Z
and W are the most tax-efficient (least assets lost to taxes) and Funds X and Y were
the least tax-efficient.
EUpk = ERp – (p2/RTk)
Portfolios
1
2
3
4
Ms. A
8 - (5/8) = 7.38
9 - (10/8) = 7.75
10 - (16/8) = 8.00
11 - (25/8) = 7.88
Mr. B
8 – (5/27) = 7.81
9 – (10/27) = 8.63
10 – (16/27) = 9.41
11 – (25/27) = 10.07
3(b).
The optimal portfolio is the one with the highest expected utility. Thus, portfolio 3
represents the optimal strategic allocation for Ms. A, while Portfolio 4 is the optimal
allocation for Mr. B. Since Mr. B has a higher risk tolerance, he is able to pursue more
volatile portfolios with higher expected returns.
3(c).
For Ms. A:
4a)
The table below shows that Manager A’s average return is less than the index while
Manager B’s average exceeded that of the index. But performing several t-tests (matched
pairs; t-test on differences assuming equal variances; t-test on the tracking errors) show
that neither manager’s performance differed significantly from that of the index.
b)
Portfolio 1 = Portfolio 2
8 – (5/RT) = 9 – (10/RT)
RT = 5
In other words, a risk tolerance factor of 5 would leave Ms. A indifferent between having
Portfolio 1 or Portfolio 2 as her strategic allocation.
The table below shows the difference between Manager A’s performance and the index,
as well as the difference between Manager B’s performance and the index. Manager A
did the better job of limiting the client’s exposure to unsystematic risk as the difference
between A’s returns and those of the index has a smaller standard deviation than that of
the difference between B’s returns and those of the index.
- 126 Copyright © 2010 by Nelson Education Ltd.
Solutions for Chapter 15: Questions and Problems
Period
1
2
3
4
5
6
7
8
9
10
Average
Std Dev
Paired tstatistic
t-test,
same var
Manager
A
12.80%
-2.10%
15.60%
0.80%
-7.90%
23.20%
-10.40%
5.60%
2.30%
19.00%
Manager
B
13.90%
-4.20%
13.50%
2.90%
-5.90%
26.30%
-11.20%
5.50%
4.20%
18.80%
Index
11.80%
-2.20%
18.90%
-0.50%
-3.90%
21.70%
-13.20%
5.30%
2.40%
19.70%
5.89%
6.38%
6.00%
11.41%
11.77%
11.66%
0.872825 0.697977
0.983224 0.942993
A minus
Index
1.00%
0.10%
-3.30%
1.30%
-4.00%
1.50%
2.80%
0.30%
-0.10%
-0.70%
B minus
Index
2.10%
-2.00%
-5.40%
3.40%
-2.00%
4.60%
2.00%
0.20%
1.80%
-0.90%
-0.11%
2.11%
-0.16469
0.38%
3.00%
0.400714
t-statistic
t-test
difference 0.872825 0.697977
from zero
- 127 Copyright © 2010 by Nelson Education Ltd.