BENCHMARKING BENCHMARKS: MEASURING CHARACTERISTIC SELECTIVITY USING PORTFOLIO HOLDINGS DATA Adrian D. Lee ∗ School of Banking and Finance Australian School of Business The University of New South Wales Phone: 02 9385 7864 Fax: 02 9385 6347 Email: [email protected]∗ I am indebted to my supervisors Associate Professor David Gallagher and Dr. Kingsley Fong for their research direction and supervision. I am also grateful for the helpful comments from a number of individuals, including Doug Foster, Eric Smith and Scott Lawrence. I thank Vanguard Investments Australia for research support. This research was funded through an ARC Linkage Grant (LP0561160) involving Vanguard Investments Australia and SIRCA.
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BENCHMARKING BENCHMARKS: MEASURING CHARACTERISTIC … · SELECTIVITY USING PORTFOLIO HOLDINGS DATA Adrian D. Lee∗ School of Banking and Finance Australian School of Business The
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∗I am indebted to my supervisors Associate Professor David Gallagher and Dr. Kingsley Fong for their research direction and supervision. I am also grateful for the helpful comments from a number of individuals, including Doug Foster, Eric Smith and Scott Lawrence. I thank Vanguard Investments Australia for research support. This research was funded through an ARC Linkage Grant (LP0561160) involving Vanguard Investments Australia and SIRCA.
Preface
Title of Thesis: TBA
Supervisors: Associate Professor David Gallagher and Dr. Kingsley Fong
Active equity fund management performance is reliant on a fund’s ability to exploit
private information while minimizing transaction costs (both implicit and explicit). My
thesis first considers the robustness of a popular benchmark used in the academic
literature in capturing fund abnormal return (or alpha). Second, I look at a strategy
using active equity fund stock holding information to form an alpha superior portfolio.
Third I look at the extent of which funds use well-known anomalies to outperform the
market. Finally I look at the ability of funds minimise transaction costs through the use
of multiple brokers.
My thesis is structured as follows:
Chapter 1: Introduction
Chapter 2: Benchmarking Benchmarks: Measuring Characteristic Selectivity Using
Equity Portfolio Holdings
Chapter 3: The Value of Alpha Forecasts in Portfolio Construction
Chapter 4: The Use of Anomalies by Active Fund Managers
Chapter 5: The Performance of Multiple Broker Trade Packages
Chapter 6: Conclusion
The following paper is based on Chapter 2.
Abstract
This study proposes methodological adjustments to the widely adopted performance
benchmarking methodology of Daniel et al. (1997) as a means of improving the
precision of alpha measurement for active equity fund managers. We achieve this by
considering adjustments for style migration and monthly updating of characteristic
benchmarks to ensure neutrality to the broad-based index. Applying this new
benchmark to a representative sample of active Australian equity funds in the period
January 1995 to June 2002, we find tracking error is almost halved while stock
selectivity is 0.14% lower compared with using the standard characteristic benchmark
methodology. The reduction in tracking error is robust when benchmarking funds by
style and by characteristics of stocks held. We also find tracking error is improved with
more characteristic portfolio sorts and longer holding periods consistent with literature
showing characteristic returns occur in annual cycles.
1. Introduction
Do active equity managers possess skill? Academics, investors, investment
consultants and the financial press have been debating this issue since fees associated
with actively managed funds should be justifiable. At the centre of this argument is an
accurate benchmark to quantify fund manager skill. While the literature has
demonstrated the impossibility of constructing a perfect benchmark1, improving
benchmarking methods remains an important area of research. In the case of stock
portfolios, benchmark construction philosophy has evolved from market capitalization
indexing to returns-based regression and holding based methodologies that adjust for
stock characteristics (or investment styles).
Daniel, Grinblatt, Titman and Wermers (1997) (hereafter DGTW), propose an
important method of incorporating style information in the use of characteristic-based
benchmarks. Research findings based on such benchmarks has re-opened the debate on
the value of active management. For U.S. mutual funds, DGTW (1997), Wermers
(2000) and Avramov and Wermers (2006), and in the Australian context Pinnuck
(2003) and Gallagher and Looi (2006), find active fund managers possess sufficient
skill to earn returns to cover their costs, consistent with the Grossman and Stiglitz
(1980) information equilibrium. This is in contrast to the literature over a number of
decades documenting that active funds possess no skill when assessed on their
aggregate net returns2.
The characteristic-based benchmark developed by DGTW (1997) utilizes a stock
holding performance measure based on passive benchmarks incorporating size, book-
to-market and momentum characteristics. This benchmark also includes a measure of
1 Using ex-ante inefficient benchmarks in mean-beta space results in performance measures which are
benchmark dependent (Roll (1977, 1978)). Indeed, Green (1986) and Lehmann and Modest (1987) find
performance evaluation rankings are sensitive to the benchmark employed. Similarly Chen and Knez
(1996) show there are an infinite set of admissible benchmarks of which provide an infinite number of
ranking orders. Also, Kothari and Warner (2001) and Pástor and Stambaugh (2002a, 2002b) identify
possible biases in performance measurement where returns-based measures are used in the estimation of
risk-adjusted performance (measured as the intercept in a returns regression).
2 See for example Jensen (1968), Malkiel (1995), Gruber (1996), Ferson and Schadt (1996).
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Style Timing ability, as well as the average style return of a fund (the idiosyncratic
return a fund manager that is generated by simply holding stocks with particular
characteristics). A benefit of using benchmarks formed using portfolio holdings is the
ability of researchers to decompose a fund’s raw return into (1) stock selection ability,
(2) style timing, and (3) the returns accounted for by the characteristics of the actual
stocks held in a fund’s portfolio. They further argue that this improved ability to
explain the variance of fund returns reduces the standard error of estimating a fund's
skill.
The intuitive design and ease of implementation of the DGTW (1997) benchmark
has made it a popular choice by researchers with more granular portfolio information,
such as portfolio holdings3. Chan, Dimmock and Lakonishok (2006) also show
empirically that such benchmarking techniques work better in tracking passive styles
than either the regression or independent sorting techniques of Fama and French
(1996).
Our study proposes several modifications to the original DGTW benchmark
methodology in order to improve the benchmark’s ability to capture characteristic
returns. First, we consider weighting characteristic benchmarks based on the
composition of a commonly referenced broad-based index. In our case, this index is the
S&P/ASX 300 which Australian fund managers track. This design results in a
benchmark that assigns zero alpha to a pure capitalization-weighted index
representative of the investable universe. This feature is particularly relevant when a
fund’s mandate specifies a passive benchmark index that does not include all listed
securities to evaluate manager performance.4
3 See studies such as Chen, Hong, Huang and Kubik (2004) Coval and Moskowitz (2001) and
Kacperczyk, Sialm and Zheng (2005).
4 Chen and Knez (1996) state in Condition I that any portfolio return achievable by an uninformed
investor is automatically assigned zero performance. Most equity market indices such as S&P 500,
FTSE, Hang Seng, Nikkei, include far fewer stocks than all those listed in their corresponding market. In
the Australian context, we use month-end index weights to measure the alpha of the S&P/ASX 300, the
most commonly tracked and broad-based index in Australia cited by fund managers, using
characteristic-based benchmarks following DGTW (1997)/Pinnuck (2003) for the period January 1995
to June 2002. We find the alpha of the index to be on average 1.27% per year.
2
Second, by using a monthly portfolio formation approach, we incorporate more
timely characteristic-based information of a stock, compared with annual updating.
Also, we are able to assess the performance of a larger pool of stocks as opposed to the
annual portfolio formation approach. Using a monthly portfolio formation process also
improves tracking of the broad-based index due to monthly rebalancing of the
benchmark. Third, we employ an overlapping benchmark approach (similar to
Jegadeesh and Titman (1993, 2001)) to better match the characteristic return of a stock.
Fama and French (2007) find that stocks ‘migrating’ from value to growth (and vice
versa) and from small to large represents a significant factor in explaining the value
and size premiums. Thus, a stock’s return is assessed against a style benchmark
representing the stock’s average characteristic over the past L months, where L is the
number of periods of which a characteristic benchmark portfolio is held for. Using this
overlapping methodology also provides us with the flexibility to test different
We collect month-end portfolio holdings data from the Portfolio Analytics
Database (PAD). This database comprises the holdings of 38 active Australian equity
fund managers (PAD funds hereafter). Further details of this database are detailed in
Gallagher and Looi (2006). Our sample period is from January 1995 to June 2002.
Monthly dilution-adjusted share returns, month-end market capitalization data are
extracted from the CRIF Share Price and Price Relative (SPPR) database.
Monthly returns of the S&P/ASX 300 Accumulation Index (S&P/ASX300A) are
sourced from SIRCA. The Aspect Financial database is used for financial year end
book value (Aspect item ID 7010). Month-end weight compositions of the S&P/ASX
300 are sourced from Vanguard Investments Australia.
3. Descriptive Statistics
Table 1 presents the average monthly weight distribution of stocks held by our fund
sample on a value-weighted basis sorted by size (MCAP), book-to-market ratio (BMC)
and prior 1-year return (PR1YR) deciles. MCAP is the month-end market
capitalization; BMC is the prior financial year book value over the month-end market
capitalization and PR1YR is the past 1-year return with one month lag. Panel A reports
the distribution using the S&P/ASX 300 universe of stocks in benchmark formation
and Panel B using the CRIF SPPR universe (i.e. all stocks listed on the Australian
Stock Exchange at any given time). There are approximately 260 stocks in the
S&P/ASX 300 universe5 and 950 stocks in the CRIF universe at any given time that
fulfils our data requirement above.
5 Aside from being unable to account for IPO stock holdings due to lack of past returns data, our other
limitations are the absence of book value data from the Aspect database for some stocks and omitting
non-ordinary stocks which are not in the CRIF SPPR database.
4
Table 1 Descriptive Statistics
At the end of each month from January 1995 to June 2002, stocks are ranked by their market capitalization, book-to-market and past 1 year return (PR1YR) independently into decile groups. 1 is the lowest decile group and 10 the highest. The table reports the monthly average weightings of the PAD funds in stocks of different characteristic ranking, and their weighting differences against the CRIF SPPR and S&P/ASX 300 decomposed into these groupings. Panel A reports weighting decompositions in percentages for the S&P/ASX 300 universe and Panel B for stocks in the CRIF SPPR universe.
To highlight the importance of using similar frequency data to reduce standard
errors, in Table 2 we calculate an ‘implied’ S&P/ASX 300 accumulated index return as
per Equation 3 and compare it to the actual index return (using month-end price
levels). Table 2 Panel A reports the annualized average monthly returns of the
S&P/ASX300 accumulated index from index levels (ASX 300A) and from S&P/ASX
300 market benchmark weights (Implied ASX 300A). We also measure the value-
weighted PAD portfolio return. The returns of the Implied ASX300A and value-
weighted PAD fund are calculated by using month-end weights at t-1 and holding for
month t.
During this period, the Implied ASX 300A return of 11.38% per year is only
slightly lower than the ASX 300A return of 11.44%. Thus intra-month fluctuations in
market weights do not appear to greatly affect the return of the market10.
Our calculation of the excess PAD return of PAD less Implied ASX 300A and
PAD less ASX 300A return is more revealing. Despite the economically significant
magnitude of about 3% per year, the statistical significance greatly differs. The PAD
less Implied ASX 300A has a t-stat of 3.80, higher than that of PAD less ASX 300A of
2.64. This difference can be seen in the Pearson correlation matrix of monthly returns
in Panel B. There is a 98.09% correlation between Implied ASX 300A and PAD but
the correlation between Actual Market and PAD funds is only 96.26%. Thus, it is of
importance to use the Implied Market return when calculating our Excess Style
measure. The correlation between the ASX 300A and Implied ASX 300 is 99.01%
suggesting the implied return accurately describes the returns of the actual ASX
despite the slight discrepancies. The importance of this is shown in later sections when
10 One additional discrepancy is that we do not use the returns of non-ordinary stocks as this is
unavailable in the CRIF SPPR.
10
we test correlation of the Implied ASX 300A return from characteristic benchmark
weights against the actual ASX 300A return.
Table 2 Annualized Monthly Average Returns of Holding Returns
Panel A presents the raw annualized monthly average market and PAD returns from January 1995 to June 2002. The return of the ASX 300 Accumulation Index is calculated using month-end price levels. S&P/ASX 300 Accumulation Index Implied Return is calculated using lagged month index weights multiplied by the current month return. Implied PAD Return holdings is calculated using lagged month weights of value weighted stock holdings of all PAD managers multiplied by the current month’s return. Panel B shows the Pearson correlation matrix of returns. T-statistics are in parenthesis. **, * denotes statistical significance at the 1 and 5% level respectively. Panel A. Raw Return Averages
Panel B. Pearson Correlation Matrix of Returns Actual Market Implied Market
Implied Market 0.9901 PAD funds 0.9626 0.9809
5.2. Decomposition of Value-Weighted PAD Returns
This section tests the differences between the original characteristic benchmark and
the modifications we make. The aim is to show incremental differences in
benchmarking which occurs from the original benchmark to the overlapping
benchmark. To measure how well each characteristic benchmarks captures passive
style we measure the tracking error of value-weighted PAD funds as the annualized
standard deviation of Characteristic Selectivity (CS). Chan, Dimmock and Lakonishok
(2006) assert that tracking error should be low if a benchmark portfolio aligns with the
investment manager’s domain. We also measure the correlation of the monthly IM (i.e.
the Implied Market return from Equation 3) with the actual return of the S&P/ASX
300A in order to measure the deviation of the characteristic benchmark. Ideally,
correlation of IM to the S&P/ASX 300A index should be as close to 100% as possible.
Table 3 presents the results of our decomposition of PAD fund holding returns into
CS, Excess Style (ES), unadjusted return (Raw), IM, correlation of IM to the
S&P/ASX 300 (Corr.) and tracking error, using the different methodologies. The
measures are annualized monthly averages.
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Table 3 Characteristic-Based Performance Measures
Table reports the time series average monthly annualized Characteristic Selectivity (CS), Excess Style, Style Return, Raw and Implied Market (Market) and tracking error for value-weighted PAD funds from January 1995 to June 2002 using different characteristic benchmark methodologies. The Market return is the average monthly annualized return of the S&P/ASX 300 using lagged monthly index weights of stocks. Corr. Is the correlation of the Market Return to the return of the S&P/ASX 300 Accumulation Index from price levels. T-statistics are in parenthesis. **, * denotes statistical significance at the 1 and 5% level respectively. Panel A. Pinnuck (2003) benchmark
For our initial test in Panel A, we adopt the standard characteristic benchmark
methodology following Pinnuck (2003). Every December month end, stocks in the
CRIF SPPR that fulfill data criteria for ranking by market-capitalization, book-to-
market and momentum, are ranked by their current month-end market capitalization
into five groups. Within each of these five groups, stocks are ranked and sorted by its
book-to-market into four groups. Book-to-market is defined as the current year's book
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value divided by the current month-end market capitalization. Each group is then
further sorted into three groups by their past 1-year momentum (with one month skip).
This results in 60 portfolios. The portfolios are held for 12 months based on value-
weights by market capitalization. Note that value-weighting occurs at the beginning of
the formation period and is fixed for the 12-month period unless a stock delists. If a
stock delists at the end of a month, the remaining stocks in that portfolio are
reweighted by their past December-end market capitalization. Using this characteristic
benchmark, we find CS of 1.81% per year, statistically significant at the 5% level. This
is slightly lower than the sample used by Pinnuck (2003) of about 2% a year although
he uses a different sample and a sample period from June 1990 to June 1997. Note the
10.02% per year IM is also 1.42% lower than that of the S&P/ASX 300A of 11.44%
reported in Table 2 Panel A due to using the entire ASX sample to form characteristic
benchmarks rather than the investable benchmark S&P/ASX 300. The reported value-
weighted return of all stocks in the CRIF SPPR during this period is 10.05% per year
(t-stat 2.87) confirming the S&P/ASX 300A outperformed the broader benchmark
during this period11. As a result, the correlation of IM to the S&P/ASX 300A is only
91.30%, much lower than the 99.01% reported in Table 2 Panel B.
5.2.2. Restricting Characteristic Benchmark Stocks to the Broad-based Benchmark
In Table 3 Panel B, we use the same methodology as Table 3 Panel A except for
restricting to S&P/ASX 300 stocks and value-weighting is done through using index-
weights (although similar results are found when value-weighting by market
capitalization). Also as the Pinnuck 5/4/3 portfolio sort uses 60 benchmarks will result
in characteristic benchmarks with five or less stocks, we use a 4/3/2 sort instead. Using
this benchmark CS is 1.15% per year (t-stat 2.12) which is nearly half of that reported
in Panel A. Also the IM correlation is higher (93.70%) and tracking error significantly
reduced to 1.49% per year compared with 2.11%. This improvement in benchmarking
and the drop in CS is due to the Panel B characteristic benchmarks better capturing
most of the characteristic return in the benchmarks as each portfolio contains less
stocks which have similar characteristic returns and thus the lower tracking error in the
CS measure. This experiment shows that using a more applicable market benchmark 11 Again, the discrepancy between our reported 9.44% Market return with that of the CRIF SPPR is due
to filtering for stocks which meet our data requirements.
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provides more accuracy in forming characteristic benchmarks. However, as the
benchmark value weights are held constant throughout the holding period, this results
in the IM deviating from the actual market return. To measure the extent of deviation,
we calculate the CS of the S&P/ASX 300 using lagged S&P/ASX 300 month-end
weights (with appropriate re-weighting for only stocks in the characteristic benchmark)
and apply it to this benchmark. We find a CS of 1.00% per year suggesting the bias in
the benchmark is economically significant, despite the improvements upon the former
benchmark. This suggests a fund which tracks the S&P/ASX 300 would have its CS
overestimated by about 1% per year using this characteristic benchmark.
5.2.3. Non-overlapping Benchmark
In Table 3 Panel C we use the same methodology except that for every month,
stocks in a benchmark portfolio are rebalanced by their month-end index-weights and
held for the next month. We do this to avoid the IM deviating from actual market
weights. Notable improvements to the benchmark’s correlation of 94.08% and tracking
error of 1.34% are made to the benchmark used in Panel B. The statistically significant
CS of 1.01% is also lower than that of the former benchmark suggesting more of the
excess market return is being captured by the characteristic benchmarks.
5.2.4. Varying the Number of Characteristic Benchmark Sorting Groups
In this section, we use the same methodology as Panel C except in altering the
number of characteristic benchmark portfolios to measure the CS of PAD funds. In
Panel D we use more portfolios by employing a 3/3/3 = 27 sort and in Panel E, less
portfolios by using a 2/2/2 = 8 portfolio sort. The 3/3/3 benchmark has slightly lower
tracking error than the Panel C benchmark of 1.31% despite CS being slightly higher at
1.03% per year. The broader 2/2/2 however has increased tracking error and also
increased CS of 1.63% consistent with the above findings in Section 5.2.2. where using
a broader benchmark captures less of the characteristic returns.
5.2.5. Overlapping Benchmark
In Table 3 Panel F, we use the overlapping methodology as described in Section
4.1. in order to use up-to-date characteristic information and to capture stocks which
may enter a portfolio in the middle of the year. Essentially this not only results in
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monthly reweighting of characteristic benchmarks as used in the Panel C,D and E
benchmarks, but also a monthly resorting of characteristic portfolios. We use 4/3/2
groupings for comparability to the Panel C benchmark. The benchmark’s correlation to
the market of 94.06% is 0.02% lower than the Panel C benchmark although has lower
tracking error of 1.26%. However despite this lower tracking error, the CS is much
higher of 1.67% per year compared with the CS of 1.01% of the non-overlapping
benchmark in Section 5.2.3. We remove mid-entry stocks from the overlapping
benchmark to make it more comparable to the non-overlapping benchmark. While CS
falls to 1.51% (t-stat 3.26), this measure is not statistically different to the CS when
including mid entry stocks. However when comparing this CS to the Panel C
benchmark, the difference of 0.50% is statistically significant (t-stat 3.63) suggesting
the higher CS is systematic. This suggests there is higher CS towards stocks chosen by
PAD funds in the overlapping benchmark, while those not chosen have lower CS than
the non-overlapping benchmark.
5.2. Performance of Overlapping and Non-overlapping Benchmarks by Fund Style
This section compares the ability and reconciles the measurement differences of the
non-overlapping (as used in Section 5.2.3.) and overlapping (from Section 5.2.5.)
benchmarks to track characteristic returns by measuring the CS of funds by self-
reported style. A characteristic benchmark able to closely match the style returns of
funds will result in low tracking. Table 4 reports the average CS, percentage of total
PAD assets in a style (% PAD) and tracking error using the non-overlapping
benchmark in Panel A and using the overlapping benchmark in Panel B.
Both benchmarks show Growth, Style Neutral and Value funds earn statistically
significant CS while GARP (Growth at a Reasonable Price) and Other funds do not.
However the benchmarks differ by the magnitude of measured CS. The CS of Value
funds measured by the non-overlapping benchmark is 1.85% per year (t-stat 2.26)
while using the overlapping benchmark is nearly 1% higher at 2.75% (t-stat 3.75). As
Value funds account for some 41% of total fund assets, this partially explains the
0.66% difference in CS of value-weighted PAD funds using the two benchmarks in the
previous section. Similarly CS of Style Neural funds is 2.71% (t-stat 2.26) using the
non-overlapping benchmark and is lower using the overlapping benchmark 2.26% (t-
stat 2.33). However as Style Neutral funds constitute about only 5% of total PAD
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assets, this difference in CS does not greatly affect the magnitude of value-weighted
PAD fund CS.
As for the value-weighted PAD sample in the previous section, tracking error is
noticeably lower in all styles except GARP using the overlapping benchmark. For
Value funds, where CS is higher using the overlapping benchmark, tracking error is
2.13% compared with 2.26% using the non-overlapping benchmark. Similarly for Style
Neutral funds, tracking error is 2.67% for the overlapping benchmark compared with
3.29% using the non-overlapping benchmark. The evidence suggests the overlapping
benchmark has better ability to capture characteristic return.
Table 4 Comparison of Benchmark Measurement of CS by Fund Style
Table reports the average annualized monthly CS and tracking error of value-weighted PAD funds by fund style using two characteristic benchmarks. % PAD is the monthly average percentage of total PAD assets assessed by the benchmark by fund style. Panel A. uses the non-overlapping benchmark as described in Section 5.2.3. and Panel B using the overlapping benchmark as described in 5.2.5.. T-statistics are in parenthesis. **, * denotes statistical significance at the 1 and 5% level respectively. Panel A. Non-overlapping Benchmark
Style CS T % PAD Tracking Error GARP 0.03 (0.05) 35.37 1.57 Growth 2.05* (2.07) 17.45 2.72 Other 0.19 (0.28) 2.18 1.72
5.3. Testing Different Overlapping Benchmark Parameters
In this section we test various versions of the overlapping benchmark to see
whether results are robust across combinations. We use different portfolio sort
combinations (2/2/2, 3/3/3 and 4/3/2) and different holding period lengths of 1,3,6,9
and 12 months resulting in 18 overlapping characteristic benchmarks. Table 5 reports
our results for testing various portfolio combinations and overlapping lengths. The
4/3/2 L=12 benchmark is the same as that in Table 3 Panel F and is reported for
comparative purposes. CS in all benchmarks is statistically significant at the 1% level
and varies in magnitude from 1.45% per year (3/3/3, L=12) to 2.14% (2/2/2, L=6).
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Across portfolio combinations, the broader benchmarks of 2/2/2 portfolio sorts
generally have higher reported CS and tracking error. For example controlling for
overlapping length, the 2/2/2 L=6 benchmark shows a CS of 2.14% per year and
tracking error of 1.59%, while CS is 1.58% and tracking is 1.25% for the 3/3/3 L=6
benchmark. This is consistent with the previous findings where using broader spread
portfolios show reduced ability to capture characteristic returns.
Table 5 Characteristic Selectivity Measures Using Different Overlapping Benchmarks Every month from January 1995 to June 2002, stocks in the S&P/ASX 300 are ranked by their most current market capitalization, book-to-market and prior 1 year return and placed into characteristic benchmark portfolios and held for L months. The value-weighted return of each portfolio forms a stock's characteristic benchmark return. The equal-weighted return of L overlapping portfolios forms a stock's characteristic benchmark. Various benchmark portfolios are applied against value-weighted PAD monthly holdings. Port. is the composition of the benchmark portfolios where the first number is the number of sorts by market capitalization, the second by book-to-market and the third by momentum (past year return with one month skip). L is the holding period length of each benchmark portfolio. T-statistics are in parenthesis. **, * denotes statistical significance at the 1 and 5% level respectively.
Port. L= CS ES SR RR MR Corr. TE 3/3/3 12 1.45** 1.18** 13.12** 14.56** 11.93** 0.9407 1.21
When controlling for holding period lengths, we find correlation of IM linearly
improves as we reduce the holding period length from twelve to one month. However
at the same time tracking error also increases. This suggests reducing the holding
period length fails to systematically capture characteristic returns. This is consistent
with literature finding that characteristic returns occur over a one year horizon (e.g.
Fama and French (1992, 1996), Jegadeesh and Titman (1993, 2001)). The results thus
suggest overlapping benchmark with longer holding periods and more portfolio
combinations result in better matching of characteristic returns.
5.4. Where Do Fund Managers Outperform? Characteristic Selectivity across Stock
Characteristics
This section examines whether PAD funds earn CS in stocks with specific
characteristics and compares the results with using the non-overlapping monthly index
reweighted benchmark from Section 5.2.3. and using the overlapping benchmark
methodology as used in Section 5.2.5. Every period, depending on the frequency of
ranking12, stocks in a characteristic benchmark are ranked placed into quintiles by its
size by market capitalization, book-to-market or past year return. Stocks held by PAD
funds are placed into each quintile group and its value-weighted CS return calculated.
For example large stocks held by PAD funds in the highest size quintile are treated as
an individual portfolio and CS is measured.
Table 6 reports the average monthly annualized CS, average fund weight, average
number of stocks and average tracking errors. Panel A reports results using the non-
overlapping benchmark and Panel B for the overlapping benchmark for size (MCAP),
book-to-market (BMC) and momentum (PR1YR) quintile groups. For the non-
overlapping benchmark, stocks are grouped at December end and remain in the same
quintile group for 12 months. In the overlapping benchmark, stocks are ranked into
quintiles at the end of each month and remain in the group for the next twelve months.
The average quintile group of overlapping quintiles (rounded up) is then calculated to
determine the grouping.
12 I.e. annually in the non-overlapping benchmark, and every month using the overlapping benchmark.
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Table 6 Characteristic Selectivity across Stock Characteristics
Table reports the average monthly annualized Characteristic Selectivity (CS), average fund weight, number of stocks and tracking error of value-weighted PAD funds by quintile rankings of market capitalization (MCAP), book-to-market (BMC) and 1-month lagged past year return (PR1YR) respectively for the period January 1995 to June 2002. T-statistics are in parenthesis. **, * denotes statistical significance at the 1 and 5% level respectively. Panel A. Non-overlapping Benchmark
MCAP 1 2 3 4 5 CS -0.99 3.75 -0.82 3.21 0.89
T (-0.21) (1.21) (-0.33) (1.52) (1.93) Fund Weight 0.85 2.10 4.14 12.94 79.98
Number of Stocks 21 28 37 45 49 Tracking Error 12.97 8.55 6.83 5.82 1.26
BMC 1 2 3 4 5 CS 2.69 0.41 0.15 1.80 4.45
T (1.11) (0.30) (0.09) (1.07) (1.50) Fund Weight 13.69 31.20 32.11 16.65 6.35
Number of Stocks 34 40 43 35 28 Tracking Error 6.66 3.74 4.53 4.64 8.17
PR1YR 1 2 3 4 5 CS -1.62 1.65 0.49 0.14 1.07
T (-0.39) (0.94) (0.28) (0.08) (0.50) Fund Weight 6.13 18.79 21.47 30.00 23.61
Number of Stocks 28 36 37 38 40 Tracking Error 11.45 4.82 4.89 4.91 5.97