Dynamic strategy and performance of german equity and bond mutual funds
©2009
Diplomarbeit
97 Seiten
Zusammenfassung
Inhaltsangabe:Introduction:
Measuring performance of fund managers is a topic equally interesting to practitioners and researchers. Most common performance measures rely on the assumption of constant risk during the entire evaluation period. The measure of risk is the beta from the Capital Asset Pricing Model (CAPM). In order to better assess a managers investment ability, additional factors could be employed to capture the different sources of risk. The manager owes each portion of the achieved return to a certain risk factor. The risks a manager is running can be summed up to form his personal benchmark, which thus reflects the investment style. Still, the exposures to the included risk factors are assumed to be constant.
The dynamics of the capital markets had not been captured by the prevailing performance measures before an approach that controlled for varying economic conditions was suggested. Models that are based on this approach deliver a beta conditional on the market state. The managers exposure to the risk of the own benchmark was thus allowed to vary in time. Consequently, the search for indicators of the market states was launched and a model framework which could accommodate the chosen indicators as part of the benchmark had to be chosen. Two model frameworks emerged and a couple of indicators established themselves as standard. This study largely follows the approach of Ferson and Schadt. They introduced a linear model that can be perceived as a conditional version of the CAPM.
The aim of this study is not only to obtain performance measures which result from the conditional models. Since the variation in the exposure to market risk is accounted for, one who employs conditional models gains insight into fund managers trading. If the trading is reflected in changes of the beta, then inference on fund strategy is made possible even though information on the portfolio structure is not provided. The explanatory power of a conditional model depends on the researcher selecting a representative benchmark for the funds in the sample and indicators of economic conditions that fund managers rely on in reality.
The structure of this paper is the following: chapter 2 builds the theoretical foundation of conditional models and presents their two forms; chapter 3 relates this study to previous literature in the area; chapter 4 employs conditional models to evaluate strategies and performance of German fund managers; chapter 5 sums up the […]
Measuring performance of fund managers is a topic equally interesting to practitioners and researchers. Most common performance measures rely on the assumption of constant risk during the entire evaluation period. The measure of risk is the beta from the Capital Asset Pricing Model (CAPM). In order to better assess a managers investment ability, additional factors could be employed to capture the different sources of risk. The manager owes each portion of the achieved return to a certain risk factor. The risks a manager is running can be summed up to form his personal benchmark, which thus reflects the investment style. Still, the exposures to the included risk factors are assumed to be constant.
The dynamics of the capital markets had not been captured by the prevailing performance measures before an approach that controlled for varying economic conditions was suggested. Models that are based on this approach deliver a beta conditional on the market state. The managers exposure to the risk of the own benchmark was thus allowed to vary in time. Consequently, the search for indicators of the market states was launched and a model framework which could accommodate the chosen indicators as part of the benchmark had to be chosen. Two model frameworks emerged and a couple of indicators established themselves as standard. This study largely follows the approach of Ferson and Schadt. They introduced a linear model that can be perceived as a conditional version of the CAPM.
The aim of this study is not only to obtain performance measures which result from the conditional models. Since the variation in the exposure to market risk is accounted for, one who employs conditional models gains insight into fund managers trading. If the trading is reflected in changes of the beta, then inference on fund strategy is made possible even though information on the portfolio structure is not provided. The explanatory power of a conditional model depends on the researcher selecting a representative benchmark for the funds in the sample and indicators of economic conditions that fund managers rely on in reality.
The structure of this paper is the following: chapter 2 builds the theoretical foundation of conditional models and presents their two forms; chapter 3 relates this study to previous literature in the area; chapter 4 employs conditional models to evaluate strategies and performance of German fund managers; chapter 5 sums up the […]
Leseprobe
Inhaltsverzeichnis
Nikola Jelicic
Dynamic strategy and performance of german equity and bond mutual funds
ISBN: 978-3-8366-4448-8
Herstellung: Diplomica® Verlag GmbH, Hamburg, 2010
Zugl. Universität zu Köln, Köln, Deutschland, Diplomarbeit, 2009
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© Diplomica Verlag GmbH
http://www.diplomica.de, Hamburg 2010
I
Table of Contents
Tables ... V
Graphs ... VI
Abbreviations ... VII
Symbols ... VIII
1
Introduction ... 1
2
Theoretical Background ... 2
2.1
Beta Variation and its Implications ... 2
2.1.1
Problems with Time-varying Beta ... 2
2.1.2
Sources of Beta Variation ... 3
2.1.2.1
Changes in betas of underlying assets ... 3
2.1.2.2
Changes in weights of passive strategies ... 4
2.1.2.3
Active manipulation of portfolio weights ... 5
2.2
Modeling Beta Variation ... 6
2.2.1
Single-beta Models... 6
2.2.2
Multi-beta Models ... 7
2.2.3
Market Timing ... 8
2.2.4
Conditioning Beta on Information ... 9
2.3
Market Efficiency... 9
2.3.1
The Hypothesis ... 9
2.3.2
Return Predictability and its Implications ... 10
2.3.3
Rational Expectations... 12
2.4
Information variables ... 12
2.4.1
Variation in Expected Returns ... 12
2.4.2
Enhancing Benchmarks through Information ... 13
2.4.3
Informative Value of Employed Variables ... 13
II
2.4.3.1
Short term interest rate ... 13
2.4.3.2
Dividend yield... 14
2.4.3.3
Term spread ... 15
2.4.3.4
Default spread ... 15
2.4.4
Other Variables ... 16
2.4.5
Seasonality ... 17
2.5
Conditional models ... 17
2.5.1
Linear Regression Model ... 17
2.5.1.1
The Assumptions ... 17
2.5.1.2
The Model ... 17
2.5.1.3
Model refinement ... 19
2.5.2
Stochastic Discount Factor Model ... 20
2.6
Summary ... 22
3
Discussion of Related Literature... 22
3.1
Literature on Conditional Asset Pricing ... 22
3.2
Literature on Conditional Performance Evaluation ... 24
3.2.1
Overview ... 24
3.2.2
Study by Ferson and Schadt (1996) ... 25
3.2.3
Studies of the German Fund Market ... 27
3.2.3.1
Study by Bessler et al. (2009) ... 27
3.2.3.2
Study by Silva et al. (2003) ... 27
3.3
Relating this Study to Existing Literature ... 28
4
Empirical Analysis ... 28
4.1
The Data ... 28
4.1.1
Fund Returns ... 29
4.1.2
Fund Groups and Indices ... 30
4.1.3
Information Variables ... 32
4.1.3.1
Description ... 32
III
4.1.3.2
Forecast power ... 33
4.2
The Models ... 35
4.2.1
Model Containing Time-varying Beta ... 35
4.2.2
Model Containing Time-varying Alpha ... 35
4.2.3
Conditional Market Timing Model ... 36
4.3
The Hypotheses ... 36
4.4
Excursus: Panel Data Estimation ... 38
4.4.1
Panel Data Specifics ... 38
4.4.2
Applicability of Panel Data Estimation Methods... 39
4.4.3
Panel Data Estimation Methods ... 40
4.4.3.1
Fixed-effects estimation ... 40
4.4.3.2
Random-effects estimation ... 40
4.4.3.3
Choice of estimation method ... 41
4.5
Dynamic strategy ... 42
4.5.1
Results of Cross Sectional Analysis: Fund Groups ... 42
4.5.2
Results of Regressions Using Panel Data Methods ... 45
4.5.3
Results of Cross Sectional Analysis: Individual Funds ... 47
4.6
Performance and Timing ... 47
4.6.1
Comparing Performance Results ... 47
4.6.1.1
Fund Group Performance... 47
4.6.1.2
Individual Fund Performance ... 49
4.6.2
Performance Persistence ... 50
4.6.3
Conditional Market Timing... 52
4.7
Robustness of the Results ... 53
4.7.1
Dynamic Strategy ... 54
4.7.2
Performance and Timing ... 55
4.8
Factor Model ... 56
4.9
Critical Acclaim ... 57
IV
4.9.1
Results versus Stylized Facts ... 57
4.9.2
Critique and Suggestions for Further Research ... 58
5
Summary ... 60
Appendices ... 61
Appendix 1: Unconditional vs. conditional beta ... 61
Appendix 2: Conditional beta of a portfolio ... 61
Appendix 3: Line graphs for the information variables ... 62
Appendix 4: Information variables and markets from 1991 to 2006 ... 63
Appendix 5: Dynamic Strategy ... 67
Appendix 6: Performance ... 71
Appendix 7: Dynamic Strategies, Performance and Timing 1999-2006 ... 75
Appendix 8: Factor Models ... 79
References ... 80
Curriculum Vitae
V
Tables
Table 1: Descriptive statistics on funds' raw and excess returns ... 29
Table 2: Descriptive statistics on indices ... 32
Table 3: Descriptive statistics on information variables ... 33
Table 4: Regressions of indices' excess returns on information variables' one-month
lags ... 34
Table 5: Means, medians and standard deviations of individual fund alphas across
models ... 49
Table 6: Performance persistence: correlation between alphas ... 50
Table 7: Performance persistence Model with time-varying alpha ... 52
Table 8: Conditional market timing ... 52
Table 9: Results of the cross-sectional regressions: evidence of dynamic strategy for
fund groups ... 67
Table 10: Results of the cross-sectional regressions: evidence of dynamic strategy
(robust standard errors) ... 68
Table 11: Results of regressions using panel data estimation methods ... 69
Table 12: Descriptive statistics on coefficients from individual fund regressions:
evidence of dynamic strategy ... 70
Table 13: Conditional alpha: Controlling for time-variation in the intercept ... 71
Table 14: Results of cross sectional regressions (Jan 1999 - Dec 2006) ... 75
Table 15: Results of regressions using panel data estimation methods (Jan 1999 - Dec
2006) ... 76
Table 16: Conditional alpha: Controlling for time-variation in the intercept (Jan 1999 -
Dec 2006) ... 77
Table 17: Conditional Market Timing (Jan 1999 - Dec 2006)... 78
Table 18: Risk factor models for bond funds ... 79
VI
Graphs
Graph 1: Line graph showing one-month lagged values on the information variables
one-month Euribor, Dividend Yield and Term Spread from 1991 to 2006 ... 62
Graph 2: Line graph showing the one-month lagged values of the Default Spread from
1991 to 2006 ... 62
Graph 3: Line graphs displaying each of the information variables with the indices from
1991 to 2006 ... 66
Graph 4: Distribution of individual EG fund alphas across models ... 73
Graph 5: Distribution of individual EI fund alphas across models ... 73
Graph 6: Distribution of individual BG fund alphas across models ... 74
Graph 7: Distribution of individual BI fund alphas across models ... 74
VII
Abbreviations
BG
Group of funds invested solely in German bonds
BI
Group of funds invested in international or German and international bonds
BofA
Bank of America
BP
Breusch-Pagan
BVI
Bundesverband für Investment und Asset Management
(English: Federal Organisation for Investment and Asset Management)
CAPM
Capital Asset Pricing Model
CPE
Conditional Performance Evaluation
EG
Group of funds invested solely in German equities
EI
Group of funds invested in international or German and international
equities
ETF
Exchange Traded Funds
Euribor Euro Interbank Offered Rate
FE
Fixed-effects (estimation)
Fibor
Frankfurt Interbank Offered Rate
HML
High-minus-low
ML
Merrill Lynch
MSCI
Morgan Stanley Capital International
OLS
Ordinary least squares (estimation)
RE
Random-effects (estimation)
S&P
Standard and Poor's
SDF
Stochastic Discount Factor
SMB
Small-minus-big
VIII
Symbols
Theoretical vector of average conditional alphas of a fund's portfolio
Intercept of a linear regression model on security or portfolio
Intercept of a linear regression model on a fund's portfolio
Portfolio 's conditional alpha
Theoretical vector of response conditional alpha coefficients of a fund's
portfolio
Theoretical vector of response conditional beta coefficients of a fund's
portfolio
Dividend paid on a security at time
Price of a security at time
Fund raw return (from stylized example)
Market raw return (from stylized example)
Gross return on an asset or portfolio at time
Return on the fund portfolio at time
,
Return of an individual security at time
Return on the market portfolio at time
Risk-free rate at time
Vector of public information variables at time
Theoretical vector of average conditional betas of a fund's portfolio
Coefficient - function of public information in SDF framework at time
Variant part of the error term from a regression model on portfolio at
time
Stochastic discount factor (SDF) at time
Excess return on a security or a portfolio at time
Excess return on the market portfolio at time
,
Vector of theoretical error terms in a regression model at time
Invariant part of the error term from a regression model on portfolio
individual specific variation
Weight of an individual security at time
Value of deviations from unconditional information variable means at time
IX
Regression coefficient related to the measure of timing at time
,
Regression coefficient related to the January dummy at time
Slope coefficient of a linear regression model on portfolio
Vector of securities' market betas
Portfolio 's conditional beta
Vector of regression coefficients in conditional regression model
,
Error term of a linear regression model on portfolio at time
Information set at time
,
Correlation between a portfolio 's and the return on the market portfolio
Volatility of the return on a portfolio
Volatility of the return on the market portfolio
Portfolio weight vector
Error term consisting of a variant (
) and an invariant ( ) part
1
1
Introduction
Measuring performance of fund managers is a topic equally interesting to practitioners
and researchers. Most common performance measures rely on the assumption of
constant risk during the entire evaluation period. The measure of risk is the beta from
the Capital Asset Pricing Model (CAPM). In order to better assess a manager's
investment ability, additional factors could be employed to capture the different sources
of risk. The manager owes each portion of the achieved return to a certain risk factor.
The risks a manager is running can be summed up to form his personal benchmark,
which thus reflects the investment style. Still, the exposures to the included risk factors
are assumed to be constant.
The dynamics of the capital markets had not been captured by the prevailing
performance measures before an approach that controlled for varying economic
conditions was suggested. Models that are based on this approach deliver a beta
conditional on the market state. The manager's exposure to the risk of the own
benchmark was thus allowed to vary in time. Consequently, the search for indicators of
the market states was launched and a model framework which could accommodate the
chosen indicators as part of the benchmark had to be chosen. Two model frameworks
emerged and a couple of indicators established themselves as standard. This study
largely follows the approach of Ferson and Schadt (1996). They introduced a linear
model that can be perceived as a conditional version of the CAPM.
The aim of this study is not only to obtain performance measures which result from the
conditional models. Since the variation in the exposure to market risk is accounted for,
one who employs conditional models gains insight into fund manager's trading. If the
trading is reflected in changes of the beta, then inference on fund strategy is made
possible even though information on the portfolio structure is not provided. The
explanatory power of a conditional model depends on the researcher selecting a
representative benchmark for the funds in the sample and indicators of economic
conditions that fund managers rely on in reality.
The structure of this paper is the following: chapter 2 builds the theoretical foundation
of conditional models and presents their two forms; chapter 3 relates this study to
previous literature in the area; chapter 4 employs conditional models to evaluate
strategies and performance of German fund managers; chapter 5 sums up the findings
and draws conclusions.
2
2
Theoretical Background
2.1
Beta Variation and its Implications
2.1.1
Problems with Time-varying Beta
A stylized example from Ferson and Warther (1996) is borrowed to illustrate how
performance is misjudged when relying on unconditional models. The same numerical
example is used in many subsequent studies to. In the following text, beta applies to the
exposure to market risk and alpha to the performance of a portfolio. Alpha is the
intercept of a regression on a performance model.
The assumptions for the model are as follows. First, investors expect two equally likely
states of the market called `bull' and `bear'. Second, a relevant index (originally S&P
500) has an expected return of 20% in the `bull' state and a 10% return in the `bear'
state. Third, the risk-free return to cash is 5% and lastly investors have the same
expectations. This implies that on average no abnormal returns can be achieved by
relying on the given information.
In the described world of two possible market states and a risk-free alternative, there is a
fund that holds the market during `bull' market periods and cash during `bear' market
periods. Next, the fund's performance is assessed based on the model of conditional
performance evaluation (CPE) and the Capital Asset Pricing Model (CAPM).
Considering a beta of 1.0 during a `bull' period and equal excess return of the fund and
its benchmark index (.2 less .05 gives .15 excess return on both portfolios), the
conditional model delivers a zero alpha. Conditional on the `bear' market, performance
captured by alpha is again zero.
1
On the other hand, the CAPM or "unconditional" approach incorrectly reports a non-
zero alpha. Without conditioning on the states of the market, the hypothetical fund has a
high market risk exposure of 1.5.
2
This is much higher than the average conditional beta
of .5. The unconditional fund alpha results as the difference between the fund and
market excess returns, with the market excess return multiplied by the average
beta:
. 125 .05 1.5 . 15 .05
.075 . According to the unconditional
model, the fund has negative abnormal performance. This is a clear misjudgment of the
manager's ability.
1
Note that beta equals zero for the bear state by assumption.
2
See Appendix 1.
3
The unconditional model fails to provide insight into the varying risk exposure. The
variation in the market premium and the exposure to market risk is common and often
related. In this example, beta is positively correlated with the premium on market risk.
The manager takes more risk when the premium is high, making average unconditional
exposure to market risk look higher. As a result, the manager isn't given any credit for
his ability to anticipate market states. On the contrary, the average beta risk of the held
portfolio makes the benchmark harder to beat. Investors who have access to the
information on economic states (and most do) would not use the "inflated risk
exposure"
3
and would not evaluate the manager's performance as negative.
The presented example indicates how varying risk leads to misjudgment of the
manager's performance in the unconditional model. This study concentrates on the
varying beta risk and its implications.
2.1.2
Sources of Beta Variation
According to Ferson and Schadt, time-variation in a managed portfolio beta comes from
three distinct sources:
1.
Changes in betas of underlying assets,
2.
Changes in weights of passive strategies due to changes of relative values of
held assets and
3.
Active manipulation of portfolio weights by the manager.
4
The first two sources arise from the dynamics of the assets that the fund manager trades
and are present even in buy-and-hold strategies. The third source relates to the
manager's deliberate departing from a buy-and-hold strategy. This is the behavior this
study aims to identify with German fund managers. The first two points are briefly
discussed and then the focus is placed on the active management that is dynamic
strategy.
2.1.2.1
Changes in betas of underlying assets
The portfolio beta is a weighted average of the securities' betas contained in the
portfolio. The weights are fractions of the portfolio each security represents.
5
The betas
of the securities a manager holds in the portfolio vary in time and thus the portfolio beta
itself changes.
3
Ferson/Qian (2004), p. 9.
4
Cf. Ferson/Schadt (1996), p. 428.
5
Cf. Elton et al. (2007), p. 657.
4
The most evident case of security beta variation is when the risk of a security measured
by the standard deviation of its price/return changes. Even if the standard deviation of
the security return is relatively stable, market indices are regularly updated to include
securities that better match or exclude those that no more conform to their criteria. This
remark applies to both stock and bond indices.
The fact that bonds have a maturity is their most troublesome property for performance
evaluation. Namely, the price of a bond closing on its maturity is being driven by its
face value rather than by the development of relevant interest rates. A fairly priced bond
quotes at the discounted value of its future cash flows. The cash flows from a bond are
certain, both in their amount and payout date. As the discounting is done for the few
remaining cash flows and over a shorter period, existing bonds will relate less and less
to the market as they draw closer to maturity.
6
Bond indices mostly have a very stable
maturity pattern. This "pattern" is described by duration, the average maturity of all
cash flows arising from a bond portfolio. In performance models that use a single-index
benchmark, beta is approximated by a duration ratio, relating the duration of the
portfolio to the one of the index.
7
For the beta to vary a manager does not have to depart from the buy-and-hold strategy.
Additionally, the fractions of the portfolio allocated to single securities do not have to
change. Securities and especially bonds possess risk dynamics of their own to which the
beta risk measure is not immune. However, the grounds for this study lie in dynamics
which exceed those present in buy-and-hold strategies.
2.1.2.2
Changes in weights of passive strategies
Even when the manager employs a pure buy-and-hold strategy, there are two ways for
the portfolio beta to change. The first one, previously discussed, is when the beta of
individual securities varies. The second one refers to the case when the weighting of the
securities included in the portfolio changes.
The weighting in a portfolio evolves with the changes in the relative values of the held
securities. A formula is provided for illustration:
(1)
,
1
,
,
1
,
/
6
The market is represented by a relevant index.
7
Cf. Elton et al. (2007), pp. 558-559.
5
where
,
refers to the portfolio weight of an individual security at time .
8
The term
,
denotes its corresponding return. For the weights to remain constant over time, the
returns on assets contained in the portfolio would have to move together, which is
unlikely.
2.1.2.3
Active manipulation of portfolio weights
Finally, a manager may deliberately depart from buy-and-hold strategies, thereby trying
to outperform his benchmark. An important decision parameter for including a security
in the portfolio is the manner in which it contributes to the fund's risk exposure, namely
its beta. Ferson and Schadt (1996) found that in a buy-and-hold strategy, the dynamics
of the fund beta exceed the dynamics of the betas of underlying securities.
9
Managers often try to earn their excess returns by riding on market cycles, thereby
changing their exposure to market risk. More precisely, managers increase their market
beta when the market premium is high, only to decrease it when the premium is low.
This is exactly the kind of manager behavior that this study is trying to isolate.
Anticipating market cycles and adjusting the portfolio beta accordingly is what will
further on be referred to as dynamic strategy.
Beta adjustments can be done in various ways. One of them is to buy stocks and sell
bonds, in times of `bull' markets. `Bear' market periods suggest selling stock holdings
and investing into bonds. Since funds used in this study are pure equity or bond funds,
the dynamics would have to result from adjustment on the level of individual securities.
This implies that managers would change the weighting of stocks or bonds he holds.
Securities that are more sensitive to market risk should be assigned higher weights in
`bull' markets and those less sensitive should be given greater proportions in `bear'
markets.
Changes in portfolio weights are not always a result of the manager's active behavior.
They can also be explained by flows of money into the fund. More inflows correspond
with periods when the investment public expects higher returns. If managers need time
to invest the new money according to their investment strategy, they will typically have
more cash holdings and therefore a lower beta. The effect of new money flows on the
8
Cf. Ferson/Schadt (1996), p. 443.
9
Cf. Ferson/Schadt (1996), p. 456.
6
beta will depend on the magnitude of the flows, their relation to fund size and the time
the manager needs to invest new money according to the fund strategy.
10
2.2
Modeling Beta Variation
2.2.1
Single-beta Models
In order to be able to identify outperformance, some model of "normal" returns on
assets is required. Traditional performance analysis uses the Capital Asset Pricing
Model (CAPM) from Sharpe (1964). The most appealing CAPM performance measure
is the "alpha" suggested by Jensen (1968). Jensen's alpha is equal to the difference
between the fund's average return and the expected return implied by the CAPM. This
means that the fund's performance is measured against a single benchmark, consisting
of the risk-free asset and a broad market portfolio. In fund performance studies, an
index representing the fund's investment universe comes in place of the practically non-
replicable market portfolio introduced by the CAPM. Single-beta models, also called
single-index models, are described by the following equation:
(2)
,
,
.
The term
is the excess return on a portfolio
,
the excess return on the
market
.
11
The beta resulting from the classical single-index model averages
over the entire period that the performance has been measured for. This is described as
the "unconditional" performance measurement because the expected returns in the
model are calculated as unconditional means which are based on past averages.
12
The
risks are unconditional second moments of return, incorporated in the unconditional
beta:
,
/ . The denotes standard deviation and represents correlation.
If expected returns and risks vary over time, the unconditional approach will mistake
variation in the fund's risk exposure and expected market returns, for manager ability.
This makes the classical performance measure unreliable, especially when it is
calculated over long assessment periods. Throughout longer periods, risks and expected
returns would likely vary more and the resulting alpha would lose even more of its
informative value. Solutions to these problems have primarily resulted in the inclusion
of multiple sources of risk.
10
Cf. Ferson/Warther (1996), p. 25.
11
The term
represents the risk-free rate.
12
Cf. Ferson (2006b), p. 385.
7
2.2.2
Multi-beta Models
Controlling for sources of risk and return other than the market has long been
recognized as an issue both for asset pricing and performance evaluation. These sources
can be represented by risk factors or additional indices. Concerning performance, the
multi-beta approach explicitly models the sources of risk, rather than modeling the
variation in expected returns based on a single benchmark.
The most famous model incorporating additional risk factors for stocks was introduced
by Fama and French (1993). It incorporates firm size and its book-to-market ratio as
relevant risk factors driving stock returns.
13
The two factors are calculated as
differences in returns between portfolios of stocks representative as "small" and "big"
companies (factor known as small-minus-big or SMB) and between those with "high"
and "low" book-to-market ratios (called high-minus-low or HML).
14
An enhancement
of the model was provided by Carhart (1997) which controls for managers making use
of persistence of returns in the short run. This factor is known as momentum.
Analogously, there are common risk factors in the bond market. They are related to
shifts in the yield curve and changes in the likelihood of default.
15
The first factor
structure is represented by the term spread, a difference in returns between high
qualities bond at opposite ends of the yield curve. The spread in return between a high-
yield and a high quality index usually serves as a proxy for the "default" factor. There
is also evidence of predictability of stock market returns based on the two factors.
16
The dynamics in the risks the fund manager takes can also be modeled by employing a
model that contains more than one index. In a heterogeneous group of funds, different
indices capture different exposures and therefore, by relating returns to risk, better
assess performance. A study from Blake et al. (1993) introduces several multi-index
models for measuring performance of bond funds. The indices are chosen to capture
exposures to different maturities and default risks. Following Sharpe' style analysis
(1992), Blake et al. also provide a model which imposes regulatory restrictions on the
betas, regarding them as portfolio weights. A quadratic programming problem is then
13
Cf. Fama/French (1993), p. 4 et seq.
14
Cf. Fama/French (1993), p. 7 et seq.
15
Cf. for example Fama/French (1989, 1993) or Gebhardt et al. (2004).
16
Cf. for example Fama/French (1989) or Fama/French (1993), p. 26 et seq.
8
solved for the benchmark of every fund, revealing weights that closely match fund
holdings that is mimic its style.
17
Multi-index linear models as well as the model containing the customized benchmark
tackle the problem of beta variation. This is done only indirectly because the goal of
Blake et al. (1993) is to test for robustness of performance results across different
models and to identify factors that describe the performance of bond funds. This
approach reveals the investment style of the fund by offering insight into the average
weights assigned to certain risk carriers over the examination period. What is missing is
the insight into the time variation of the exposure to the fund's own benchmark.
2.2.3
Market Timing
Traditional performance analysis distinguishes between two investment abilities:
security selection and market timing. Security selection refers to the ability of the
manager to pick "undervalued" securities from the market. Market timing means
anticipating which asset class would perform better in the future and thus switching the
portfolio (e.g. between stocks and bonds) to achieve higher returns.
The most commonly used model of market timing is the one from Treynor and Mazuy
(1966). It captures the effect of managers' trading stocks with different volatilities. If a
manager thinks the market is going to rise, he would pick stocks with higher volatility,
thereby increasing his exposure to the market.
18
In expectation of a falling market he
would shift his portfolio to hold less volatile securities. The variable defined by Treynor
and Mazuy (1966) to detect this behavior is the square of the excess return on the index
provided in an extension of the single-index model:
(3)
,
,
,
.
The coefficient on the market timing variable reveals how successful the manager was
in his anticipation. A
,
0 indicates market timing ability. The relationship between
the fund's return and risk would in this case be convex. The non-linearity is captured by
the coefficient on the timing variable.
An alternative model of market timing introduced by Merton and Henriksson (1981) is
even more intuitive. The manager targets two betas: one for the case of the market
premium being positive and the other for the premium being negative. Technically, the
17
Cf. Blake et al. (1993), p. 403.
18
Cf. Treynor/Mazuy (1966), p. 132.
9
quadratic term in the equation above is replaced with the payoff of a long call option:
,
; 0 , where the exercise price is equal to the risk-free rate.
Subsequent studies that have dealt with the problem of varying beta find that there are
various nonlinear effects that could be confused with timing ability.
19
There are findings
of a perverse ability to predict market trends, but systematically in the wrong
direction.
20
This calls for models that would address the sources of beta variation more
directly. Nonlinearities obviously exist and instead of merely controlling for them, one
could use them to find out about dynamic trading strategies that are reflected in
responses to market developments.
2.2.4
Conditioning Beta on Information
The idea behind conditioning on information is to pick up time-variation in beta by
linking it to information that indicates developments in the market. Conditioning of the
beta on chosen indicators directly tackles the problem of performance evaluation under
changing risk exposure. Furthermore, it provides insight into fund strategy based on the
"response of the exposures to public information, without the need for asset holdings
data"
21
. The pre-eminent goal this study is to emphasize the potential benefits from
using such models for the assessment of fund strategy and performance.
The chosen indicators are a subset of information available in the market. Bearing in
mind that controlling for information will affect the reported performance, there have to
be criteria for choosing the variables.
The information that is controlled for will be part of the expected return. No longer will
it be possible for a manager to have superior performance from trading based on the
changes in value of the chosen variables. Conditional models are flexible to
accommodate whatever standard of information is considered appropriate. Advocates of
conditional models look for this standard in the market efficiency hypothesis.
2.3
Market Efficiency
2.3.1
The Hypothesis
The market efficiency hypothesis states that "security prices fully reflect all available
information"
22
. For this hypothesis to hold there would have to be "no costs of getting
19
Cf. for example Chen et al. (2003).
20
Cf. Ferson/Schadt (1996), p. 450.
21
Ferson/Schadt (1996), p. 456.
22
Fama (1991), p. 1575.
10
prices to reflect information"
23
. This is, of course, unrealistic. A weakened version of
the hypothesis says that a certain piece of information will not be priced if marginal
benefits of acting on it do not exceed the accompanying marginal costs. This version is
economically intuitive and opens the way for different levels of efficiency in different
markets. In the general form market efficiency can be defined in the following way:
"A market is efficient with respect to information set
if it is impossible to make
economic profits by trading on the basis of information set
."
24
Fama (1970) distinguishes between three forms of market efficiency: the weak form
with the relevant information set consisting of historical data, the semi-strong form,
which states that all publically available information is priced and the strong form,
where the information set also includes private information. Conditional models are
compatible with the semi-strong form of market efficiency, which means that returns
are conditioned on publicly available economic variables.
All forms of information efficiency can be empirically tested, although only jointly with
an asset pricing model. It is only possible to say whether information is properly priced
in the context of a suitable pricing model. As a consequence, shortcomings of the
underlying asset pricing model can be mistaken for evidence against information
efficiency. As such, the implications of the results from empirical research for the
efficiency hypothesis are disputed. Nevertheless, empirical research on market
efficiency has proved to be both scientifically useful and practically relevant.
25
The area
of research that addresses the theme of this study is further discussed.
2.3.2
Return Predictability and its Implications
With the aim of identifying dynamic strategies, this section explores the predictability
of returns in order to provide ground for the use of public information in performance
studies. Chosen variables must be carriers of information on market developments in
order to assume that managers rely on these as indicators when making their investment
decisions in a dynamic setting.
The area of research that challenges semi-strong information efficiency is characterized
by tests for return predictability and by event studies. Reaching beyond the weak form
of efficiency and predictability based on past returns, the first area of research works
23
Ibid.
24
Jensen (1978), p. 96.
25
Cf. Fama (1991), p. 1576.
Details
- Seiten
- Erscheinungsform
- Originalausgabe
- Jahr
- 2009
- ISBN (eBook)
- 9783836644488
- DOI
- 10.3239/9783836644488
- Dateigröße
- 1 MB
- Sprache
- Englisch
- Institution / Hochschule
- Universität zu Köln – Fakultät für Wirtschafts- und Sozialwissenschaften, Finanzierungslehre
- Erscheinungsdatum
- 2010 (März)
- Note
- 1,7
- Schlagworte
- german performance conditional empiric
