DTU406 PORTFOLIO MANAGEMENT
Dr. Nguyen Thi Hoang Anh
Lecture 6:
Application: Portfolio Management and Style Analysis
Contents
 Introduction
 Passive portfolio management
 Active portfolio management
 Benchmarks
 Style analysis
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Introduction
 In the last lectures, we considered how to compute the optimal portfolio of risky assets, based on
estimates of expected returns, the variance-covariance matrix and the risk free rate; when all investors
have the same information about these inputs, they will all reach the same optimal portfolio, and this will
be the market portfolio, which comprises all risky assets in proportion to their market values
 When markets are efficient, the optimal strategy for any investor - whether individual or institutional - is
to invest in the market portfolio; this is known as passive portfolio management
 In practice, however, investors know that not all markets are perfectly efficient all of the time, and that
not all securities are priced correctly; there is therefore an opportunity to engage in active portfolio
management by identifying stocks that are mispriced in order to achieve a better trade-off between risk
and return than is provided by the market portfolio
 This lecture provides an introduction to the methods of portfolio management and the evaluation of
portfolio performance and style
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Passive portfolio management
 Passive portfolio management in principle amounts to investing in the market portfolio, but in practice,
this is infeasible given its size
 Instead, passive fund managers normally construct a relatively narrowly based portfolio that is designed
to track a broad based index (such as the FTSE 100 or S&P 500) over time
 The manager is assessed by how well the fund tracks the target index, or benchmark
 Passive fund construction techniques include
Full replication: investing in all of the stocks in the target index
Sampling: investing in a representative selection of stocks in the target index
Quadratic programming: investing in a portfolio whose composition is designed to track the target
index as closely as possible (i.e. to minimise the tracking error of the portfolio)
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Active portfolio management 1
 Active portfolio management is based on the premise that there exist, at any point in time, certain stocks
that, for various reasons, are either under- or over-priced
 Active portfolio management attempts to identify these stocks, and include them in an otherwise passive
portfolio, either with increased weight (if they are undervalued) or decreased weight (if they are
overvalued)
 Mispriced
stocks
may
be
identified using fundamental
analysis (such as cash flow
valuation, screening on the basis
of ratios), or using technical
analysis (such as chartism and the
use of moving averages trading
rules)
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Benchmarks
 So far, we have analysed portfolio performance in the context of the CAPM; specifically, portfolio (or
individual stock) performance is measured relative to the market portfolio; the risk of the portfolio (or
stock) is measured by its CAPM Beta
 In practice, fund managers do not typically invest in the market portfolio; instead, portfolio managers
specialise in countries, industries or types of stocks (such as value stocks or small stocks)
 Their objective is usually to create a portfolio that tracks a passive benchmark, such as an industry index,
or an index of value stocks, but to add value through stock selection
 Moreover, their performance is measured with respect to that same benchmark

In evaluating a portfolio manager’s performance, we need to know the style of the portfolio; if it is a
portfolio of value stocks, it would not make sense to evaluate it against a benchmark comprised of growth
stocks
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Style analysis 1
 In order to establish the appropriate benchmark for an active fund, we use style analysis
 The resulting benchmark is known as the style benchmark portfolio, which is a portfolio of individual
style indices, reflecting passive investments in the different styles, such as value, growth, small-cap,
large-cap, European equities, emerging market equities, government bonds, etc
 We can then decompose the performance of the active fund into (a) the performance of the fund that is
due to the fund’s style (i.e. the performance of the style benchmark portfolio) and (b) the performance
that is due to the fund manager’s stock selection ability
 We evaluate the active fund by comparing its performance with that of the style benchmark portfolio
using the performance measures, such as the Sharpe ratio, Treynor’s measure and Jensen’s alpha
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Style analysis 2
 Introduced by William Sharpe
 Regress fund returns on indexes
representing a range of asset
classes.
 The regression coefficient on each
index measures the fund’s implicit
allocation to that “style.”
 R –square measures return
variability due to style or asset
allocation.
 The remainder is due either to
security selection or to market
timing.
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Style analysis 3
 Suppose that we are analysing the style of the Allianz NFJ Small Cap Value A fund
 To undertake style analysis for the fund, we first choose a set of style indices. For example, we might
(rather narrowly) choose style indices for
Large cap/Growth
Large cap/Value
Small cap/Growth
Small cap/Value
 To replicate these style indices, we
can use data on exchange traded funds
(ETFs), which can be obtained from
http://finance.yahoo.com/etf
 Here we have five years of monthly
data on the fund and the four style
indices
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Style analysis 4
 We then construct a style benchmark portfolio from these style indices using arbitrary weights (here set to
25% in each index), and calculate the tracking difference (the difference between the fund return and the
benchmark return)
 The tracking error is the standard deviation of the
tracking difference
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Style analysis 5
 To complete the style analysis of the portfolio, we use Excel’s Solver to select the style benchmark
portfolio weights to minimise the fund’s tracking error, subject to the constraints that (a) the weights sum
to unity, and (b) the weights are positive (because this is a mutual fund and hence not permitted to take
short positions)
 After implementing Solver we have
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Style analysis 6
 Comparing the results of our style analysis with the
style box from Yahoo Finance, we see that we have
correctly classified the fund as a Small-cap/Value fund
 Note, however, that fund also has a non-negligible position in Large-cap/Value stocks, and in evaluating
the performance of this fund, we should take this into account
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Style-based performance measurement
 We are now in a position to evaluate the performance of this fund. In particular, we have estimated the
appropriate style benchmark for the fund, and we can compare the performance of the fund with the
performance of this benchmark
 We could use any of the standard evaluation measures described earlier, but here we will focus simply on
the absolute performance
 In particular, we can compute the annualised
average return of the fund, the component of
this that is due to the fund’s style (which is
given by the annualised average return of the
benchmark) and the component that is due to the
manager’s stock selection (which is the
difference between the two)
 This fund appears to have performed rather
well, with about a third of the fund’s return
coming from the manager’s ability to select
stocks
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Practice exercise
You are an analyst working for a fund management company. You have been asked to evaluate the style and
performance of a mutual fund.
1. Download five years of weekly data for these funds from http://finance.yahoo.com/funds, and calculate
simple returns.
2. Estimate a benchmark style portfolio for the fund, using style indices for value/growth and size. As
proxies for the style indices, use data on the respective exchange traded funds from
http://finance.yahoo.com/etf.
3. How does your classification of the fund compare with the classification given on Yahoo! Finance?
4. Evaluate the performance of the fund relative to the benchmark portfolio.
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