perf1 asset allocation

8/4/2019 Perf1 Asset Allocation

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Performance Analysis

Loriana Pelizzon

University of Venice

Overview

Asset allocation

Performance Analysis

Attribution analysis

Mutual Funds Analysis

Benchmarks

Peer group analysis

Style analysis


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Asset allocation

how one decides to allocate assets among various

asset classes such as stocks, bonds, and cash. How do you decide how to allocate your assets?

The goal of asset allocation is to create adiversified portfolio with an acceptable level ofrisk and the highest possible return given that levelof risk.

A portfolio or asset allocation that maximizesreturn for the level of risk is called an efficientportfolio

Asset allocation

The most difficult aspect of this procedure is toaccurately predict expected returns.

In the case study we used long term historicalreturns, but is it reasonable to expect that historywill repeat itself?

There are a number of other ways to make suchpredictions.

One of the most promising methods is a modeldeveloped by Fischer Black and Robert Littermanwhile they were at Goldman Sachs.


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Performance analysis

Risk-adjusted measures based on absolute

benchmark

Risk adjusted measures based on relative

benchmark

Risk adjusted measures based on

Customized Benchmark

Risk-adjusted measures based

on absolute benchmark

Sharpe ratio

Treynor ratio

returnexcessfundofdeviationstandard

returnexcessaveragesfund

RatioSharpe

'=

returnexcessaveragesfundRatioTreynor

'=


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Risk-adjusted measures based

on absolute benchmark

Sortino ratio:

where:

deviationdownside

returnexcessfund'sRatioSortino =

( )[ ]returnexcessfund'sVARdeviationdownside ,0min=

Risk adjusted measures based

on relative benchmark

Morningstar Risk-Adjusted Rating.

Bill)TorReturnExcessCategory(AverageofHigher

BillTFundtheonReturnAdjustedLoadReturnrMorningsta

=

CategoryitsofrmanceUnderperfoAverage

rmanceUnderperfoAveragesFund'rRiskMorningsta =


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on relative benchmark

To calculate a funds summary star-rating,

the Morningstar Risk scores are thensubtracted from the Morningstar Return

scores.


on Customized Benchmark

The information ratio, which is the ratio of excess

return to standard deviation of excess return (or

tracking error), is a measure of a managers skilland the consistency with which the manager has

been able to outperform

ErrorTracking

AlphaRationInformatio =


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Manager performance: practice

One way to measure manager performance is

by looking at how an initial investment wouldhave grown over a specific time period



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The rolling window graph is also helpful fordetecting structural changes in a portfolio.

A risk control process that was initiated bya manager several years ago, for example,would probably lower the portfolio'stracking error.

As a result, the symbols would shift to theleft as they do for Active Manager A (blue).



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Manager performance:

practice


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Manager performance:

practice



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Attribution Analysis

To what do we attribute a managers

performance?

Is it stock picking, investing in the right

style, or market timing?

Were certain sectors over or

underweighted?


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Most of a managers returns are attributed to asset

class returns. A US equity managers returns depend mostly on

how well the US stock market does.

The second most important factor for an equitymanager is investment style.

Most growth stock managers perform well whengrowth stocks are in favor. Conversely theyperform badly when growth stocks are out offavor.


The first goal is to find out how much of the

managers return comes from the general

market and investment style

We accomplish this using a technique called

style analysis


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Example.

Using only the monthly returns for The

Needham Growth Fund and the monthly

returns from the four Russell style indices

and T-Bills, we find the combination of

indices that best describes Needhams

behavior/style.



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In Figure 2 the red portion of the pie chart shows

that these indices account for 77.5% of thevariance in Needhams return.

The variance of Needhams return that cant be

explained by the market and style is represented

by the green portion of the pie.

This residual variance or behavior is likely due to

the managers stock selection or sector bets.



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The portion of the managers returns that are

explained by exposures to the style indices couldbe passively replicated by buying the appropriatepercentages of index funds or ETFs that representthe style indices.

The managers alpha is generated by the portion ofthe fund that we cannot passively replicate.

This represents the managers active bets.

They could be stock bets, sector bets, or evenmarket timing bets.


In an attempt to identify these sources of returns, we startby constructing a custom benchmark called a stylebenchmark that is based on the index weights in Figure 1.

The performance graph and table (Figure 3) show thatNeedham beat its custom style benchmark by anannualized 16.92%.

This is the excess return Needham achieved over what wecould passively construct to represent Needhamsinvestment style.

This is the result of either manager skill or luck (how wedifferentiate between the two is explained in Mutual FundAnalysis). For now we assume manager skill.


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Attribution Analysis: stock

selection


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Should Needhams excess return be attributed to stock

selection, sector weightings, and/or market timing? To see the impact of sector bets we perform another style

analysis using sector indices rather than style indices.

Because we are using returns and a rolling window wedont expect to precisely identify the sector weights at anyspecific time but rather get an idea of what the sectorexposures have been over the life of the fund and how theyhave changed over time.

Attribution Analysis: sector

weightings


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Figure 4 above contains the results of the sector

analysis, which shows that Needham is heavilyweighted in technology, health care, and T-Bills.

T-Bills represent cash or anything that makes theportfolio behave like cash.

Based on the Needham Fund's prospectus the fundis run somewhat like a hedge fund. It shorts stocksand uses derivatives to reduce risk. Once again,using the exposure to the indices used in the style

analysis, we construct a custom style benchmark.



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Figure 5 below shows that Needham

outperforms this benchmark by 13.84%annualized.

So of the 16.92% outperformance, about 3%

is from their sector bets.

The balance, 13.8%, is the result of either

stock selection or market timing



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Market timing doesnt necessarily mean

moving from 100% stocks to 100% cash.

It can be as subtle as buying low beta stocks

when one perceives the market is over

valued.

It could also be a value manager building

cash because he cant find good valuations.



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One way to evaluate the results of market timing is

to see how managers do in both up and downmarkets.

If a manager goes up more than the benchmarkwhen the benchmark goes up, the manager plotsabove the horizontal line in Figure 6 above.

If a manager goes down more than the benchmarkwhen the benchmark goes down, he plots to theright of the vertical line. If the manager goes down

less he plots to the left of the vertical line.


Aggressive managers who go up more and downmore plot in the northeast quadrant. Defensive

managers who go up less and down less plot in thesouthwest corner.

Managers that go up more and down less, as is thecase with Needham, plot in the northwestquadrant. We believe that this is the result of goodmarket timing particularly if there is a consistentpattern of such behavior, as seen in Figure 7below.


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Managers with bad market timing that go up

less and down more fall into the southeast

quadrant.

Needham went up 26% more than the

benchmark when the benchmark had a

positive return. When the benchmark went

down the fund declined about 22% less.


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Mutual Fund Analysis

When investing in non-index mutual funds,

investors make two critical assumptions: 1) that skillful managers exist,

2) that they have the ability to recognize them.

If an investor is not willing to make these two

assumptions, they should invest in non-active

funds like index funds or exchange traded funds

(ETFs).


Mutual fund analysis, both qualitative and

quantitative, attempts to identify skillful active

managers. Qualitative analysis looks at factors such as the

background and experience of the manager and the

mutual fund company.

Here, we look only at the quantitative factors such

as manager performance, style, style consistency,

risk, risk-adjusted performance, etc.


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What is the best way to analyze, and ultimately select,

mutual funds? Financial journalists are not equipped to analyze mutual

funds. In most cases they are simply reporting theperformance figures they received from the managersthemselves or the marketing/public relations people.

Mutual fund rating services are good data collectors butlack any real sophistication in fund analysis. Theseservices are oriented toward the retail fund investor.Consequently sophisticated advisors, plan sponsors andconsultants must perform their own mutual fund analysis.


The two biggest mistakes in quantitative

mutual fund analysis are improper:

benchmarking

end point bias.

How can you avoid these mistakes?


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Benchmark

The most common error made when

measuring a managers performance is theselection of an improper benchmark.

Morningstars star ratings, for example, are

based on funds performance relative to a

broad group of fund returns, as opposed to a

more specific benchmark that reflects the

manager's true style.

Benchmark

Because of this, on February 28, 2000, at the very

peak of the growth stock bubble, most of

Morningstars five star funds were growth fundswhile there were no five star value funds.

Two years later, after the value funds did well and

the growth funds crashed, most of the five star

funds were value funds.

What makes a good benchmark?


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Benchmark

At the heart of a quality manager analysis is a

good benchmark. In order for a benchmark to be avalid and effective tool for measuring a managersperformance, it must be:

Unambiguous

Investable

Measurable

Appropriate

Reflective of current investment opinions

Specified in advance

Benchmark

A benchmark with all of these characteristics is the stylebenchmark.

The style benchmark is the result of Nobel LaureateWilliam F. Sharpes returns-based style analysis.

The style benchmark is a custom benchmark produced byweighting a set of indices in a unique combination thatreflects the style of the manager.

The most important advantage of a custom stylebenchmark over a standard market benchmark is that itaccounts for the style characteristics of the manager.


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Benchmark

If the manager specializes in small cap growth stocks thenthe benchmark should be made up of small cap growthstocks.

In fact, the ideal benchmark explains all of the returns ofthe manager that come from systematic factors such asstyle and market movements.

If this is the case, any performance over (or under) thebenchmark can be attributed to manager skill.

A benchmark that does not do a good job of capturing thestyle of the manager will always leave you wondering did the manager outperform because of style differenceswith the benchmark?

Benchmark

The investment industry uses a number of inappropriatebenchmarks, the most common of which is a manageruniverse or peer group.

Manager universes are not investable, not specified inadvance, and since they are made up of active managersthey are not the passive equivalent of an active manager.

Additionally, manager universes suffer from survivor bias(the poor performing managers drop out and / or aremerged with better performing funds).

Most importantly, they are usually too broadly defined toaccurately judge the skill of a specific manager.


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Benchmark

Broad market indices such as the S&P 500,

Russell 3000, Wilshire 5000 etc. are notgood benchmarks for most active non-large

core managers.

Even style indices such as the Russell 1000

Growth, 1000 Value, 2000 Growth, or 2000

Value are not appropriate for the vast

majority of managers

Style Benchmarks vs. Market

Benchmarks

Style benchmarks are superior to singleindex benchmarks for the majority of

managers. Figures 1 and 2 show the result of a style

analysis of the Dodge & Cox Fund.

The combination of Russell style indicesand T-Bills that best defines the style of thisfund is shown in Figure 1.


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Benchmarks


Benchmarks The Manager Style graph, shown in Figure 2, maps the

funds style relative to the four Russell style indices.

As explained earlier, the analytic technique that enables us

to determine the funds effective asset mix, create theManager Style Map, and build the custom style benchmarkis called returns-based style analysis.

The custom style benchmark is made up of the styles andweights shown on the bar chart.

For Dodge & Cox, the style benchmark is a compositereturns series made up of 2.1% in T-Bills, 76.5% in theRussell Large (1000) Value Index, and 21.4 % in theRussell Small (2000) Value Index.


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Benchmarks

Can we prove that this is a

better benchmark?

A good test of a benchmark is to see howcorrelated the benchmarks returns are to themanagers returns.

The higher the correlation the better thebenchmark.

The red portion of the left pie chart on Figure 3shows the R-squared (correlation squared) of themanagers returns to the custom style benchmark,90.0%.

The pie chart on the right shows that the R-squared to the S&P 500 is only 67.5%.


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Benchmark

The green portion of the pie chart measures the

variance in the funds returns that is not explainedby the benchmark. Notice for the S&P 500 it ismore than three times greater than for the stylebenchmark.

A good benchmark includes all of the systematicfactors (market, style) so that the unexplainedvariance is due exclusively to nonsystematic oridiosyncratic factors that are primarily the result of

the managers stock selection.

End Point Bias

The other common mistake made in performance analysisis called end point bias. Most of the funds recommended

by various financial publications are ones that recently

performed well.

When looking at cumulative statistics, recent performanceabove the benchmark creates the illusion that the fund hasconsistently outperformed.

Cumulative statistics are calculated through the mostrecent time period. Annualized return for one, three, five,and seven years, for example, is often used to evaluatemutual funds.


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End Point Bias

Notice that the most recent year is included in all

of these periods. Due to the nature of thesestatistics, recent performance often hides pastperformance.

Here is an example.

The September 15, 2003 Forbes magazineheralded the Mairs & Power Growth fund as oneof the three best funds to own based on its longterm record. In Figure 1 the long term annualized

returns for this fund look quite good.

End Point Bias


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End Point Bias

End Point Bias

Because this fund outperformed its benchmark (the S&P500 is a reasonable benchmark for this fund) for 2, 3, 5, 7,10, 15, 20, and 25 year periods, one would think that the

fund is a consistently good performer. Now look at Figure 2 below.

The red and green shaded area at the bottom of theperformance graph shows the cumulative return relative tothe benchmark.

If you had purchased this fund twenty five years ago youwould have spent all but the last couple of years belowyour benchmark.

It has only been the very good performance in the last fewyears that give it the high annualized rates of return found

in Figure 1.


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End Point Bias

This is what we mean by an end point bias.

We could also call it the broken clock syndrome (abroken clock will be right twice a day).

Similarly, if a manager has been managing moneyfor twenty five years, even with no skill, there islikely to be several years of good performance.

If your end point (the date on which your analysisends) is particularly good, cumulative statisticsmay create the illusion of consistently goodperformance.

End Point Bias


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End Point Bias

Would Forbes have recommended this fund

three years earlier?

We doubt it. Figure 3 shows us that through

February 2000 the fund had under

performed its benchmark by 831 percentage

points.

End Point Bias


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End Point Bias

One way to avoid end point bias is to look at

rolling time periods. Figure 5 shows rolling three year periods of excess

returns.

Here you can see an almost equal amount of timeunderperforming and outperforming thebenchmark.

To have confidence that a manager is skillful andthat the skill will likely result in beating thebenchmark in the future, we prefer managers that

consistently outperform.

End Point Bias


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End Point Bias

Lets take a look at a consistent

outperformer. Figure 6 shows theperformance of the Fidelity Low Priced

Stock Fund. It outperformed its benchmark

by 6.58% annually!

End Point Bias


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End Point Bias

Mutual fund analysis


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The bottom panel of Figure 6 contains some useful statistics. Onestatistical measure of consistency is tracking error, which is the

volatility (standard deviation) of excess return. All things equal, theless volatile the excess returns the greater the chance the manager isskillful rather than lucky.

Tracking error is used to calculate a risk-adjusted measure ofperformance called the information ratio.

The information ratio is the annualized excess return divided by thetracking error. The information ratio for the Fidelity fund is a very highat 1.48.

What are the chances that a manager could have achieved thisinformation ratio by being lucky? Part of the answer will depend onhow long she achieves a high information ratio.

The longer the good performance persists, the less chance of luck and

the more chance of skill.


Significance Level statistic measures the probability of luck vs.skill.

To have confidence that the manager was skillful and not just lucky thesignificance level should be at least 95%.

For the Fidelity Fund it is 100% (see the bottom panel of Figure 6).

The most important first step is to select the proper benchmark. If thatis not done all of the fancy statistics we have discussed will bemeaningless.

Investors can accurately measure a managers performance, evaluatethe consistency of the performance, and determine the probability thatthe managers performance is the result of skill.

Such an analysis dramatically improves the likelihood that our secondassumption our ability to pick skillful managers is true and in doingso that our selections may lead to superior future performance.


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Peer Group Analysis

Investors often try to gauge a managers skill by

comparing the managers performance to theperformance of a group of similar managers.

This is typically called a universe or peergroup analysis. Many consider a universe oruniverse composite to be a good benchmark for amanager.

In fact, manager universes do not have thequalities that make a good benchmark.

They are not investable, they are not specified in

advance, and they are usually too broadly defined.

Peer Group Analysis

Universes also suffer from what is known assurvivor bias because many of the poorperforming managers drop out of the universe.

Poorly performing mutual funds, for example, areoften merged with more successful funds.

When this happens only the successful fundstrack record is maintained, so the poorperformance is not represented in any universethat includes the fund.

Once a product no longer exists, for whateverreason, it is dropped out of the universe.


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Peer Group Analysis

Despite these limitations, peer group comparisons continue

to be popular with investors. Figure 1 is a peer group analysis using the standard

floating bar chart.

Notice that the floating bar graph shows where FidelityMagellan ranked in the universe for only six time periods.

The RHS graph shows where Magellan ranked everymonth for the last twenty five years.

Looking at the LHS graph one might conclude thatMagellan had never been in the bottom quartile of the

universe.

Peer Group Analysis


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Peer Group Analysis

With the LHS graph we can see that there

are two such periods. Managers may not want to show all the

periods, so for them the floating bar graphmight be best.

Sponsors, consultants, and advisors shouldalways use the more comprehensive graphwhere no time periods can be hidden.

Peer Group Analysis

Another thing to be aware of is the

difference between cumulative time periods

(last one year, three years, five years etc)

and rolling time periods.

This relates to end point bias, which is

discussed in Mutual Fund Analysis.


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Peer Group Analysis

Peer Group Analysis

There is no reason to limit peer group

comparisons to returns


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Peer Group Analysis

Peer Group Analysis


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Peer Group Analysis

A discussion of peer groups wouldnt be

complete without some discussion aboutuniverse construction.

One methodology is to create universes of

managers with similar styles.

Peer Group Analysis

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