How Big Is Too Big

Building

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Better

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COMMENTARY 73

OCTOBER

HOW BIG

2OO2

TOO BIG?

'S

Success to-a1 investment manager means growth in fee income, most often the result of successful -markeling bolste6d by excdllent performance. ihe clients, however, recognize that growth in assets inhibits the mana'qer's abilitv to continue to qeneratd superior returns, and would prefer the manager to-remain small

The problem ari ses because.transaction costs are proportional to trade size, while investment acumen is not. In this commentarv wb use the Plexus databbse to investigate the relationship of transaction costs to assets under management. Cost/Return Tradeoff Determines Decision Size

How Big Is Too Big? The award for an outstanding performance by a money manager is dramatic asset growth, a boon to fee revenue and a possible bane to future

returns.

As assets grow,

research acumen

Average

ti th

remains constant while transaction costs balloon. Increased costs lead to eroding returns, and managers attempt to compensate by shifting toward more liquid, broadly based styles. All too

often the initial winning combination

is

compromised, and estrangement between money managers and their clients results. As Andre Perold and Robert Salomonl point out, sponsors and mutual fund holders prefer that the manager limit asset growth to preserve the performance edge, while managers, who earn fees on total assets, seek to maximize asset growth.

The horizontal blue line is the expected marketadjusted return of the manager's ideas (vertical scale.) The location of this line varies according to the manager's style, skill and horizon. Note that the potential return is the same whether the manager buys one share or a million.

eost (red line) is the cumulative execution cost per share. As the average size of A parallel struggle occurs within the management a decision grows, so does the cost. But the rise is firm between portfolio managers and trading on gradual; the initial shares have low costs that one side and marketing/business development on offset the higher costs of additional shares. At the other. Some small cap managers, for point AC, the average cost line crosses the example, close their funds to new assets when expected return line. Adding more shares leads to size targets are reached. More often, funds are total costs that exceed the expected return. not capped, and deteriorating returns trigger the Trades of any larger size will detract from maximum asset size debate. performance. The issue can be addressed prospectively and quantitatively. In the following chart, asset size, as reflected in the size of the average purchase/sell decision, shows on the horizontal axis. Expected returns and costs in basis points show on the vertical axis.

Average

fVlargina! Cost (green line) shows the cost of trading each incremental share. While the first share may have minimal impact, the 250,0001h share might cost 2o/o. Thus marginal costs rise

more quickly than average costs. Point

[Ue

determines the optimal decision size; the cost of

an additional share traded beyond point MC exceeds the underlying return for that share, leading to deteriorating total return.

Expected Average Costs (bp) for lncreasing Trade Size Shares (000's) Large Gap

Gathering assets up to point AG leads to lower returns but higher manager fees. Stopping asset growth at ffi* increases expected returns, but does not maximize current fee income.

Estimating Returns and Costs The above model requires estimates of both returns and costs. Fortunately, Plexus clients have both. The data covers 6 quarters (3Q, 2000 to 4Q, 2001) and 140 client cuts categorized into vaiue, core ancj growth styles, separated into large and small cap funds.

The table below shows the average

30-day market-adjusted decision return over the analysis period. Since quarterly returns for each style show surprising consistency over time, we average the six quarters.

Average Return in bp (Top 25% in parentheses)

Large Cap Small Cap

cap

25

Value

+1

-10

19

-55

Core

-33

-48

-60

-87

Value Gore

Growth

cto*ir't

-93 : -114 : -130 : -169

-115 -199 -183 -341 , , -300 -464 '

-378

-582 -743

Again, the results intuit. Growth orders cost more than value or core, and small caps are more costly than large caps. Unlike the linear cost lines depicted in the picture on Page 1, costs rise at a decreasing rate. Demand pushes prices yet attracts additional supply, so costs do not double as size doubles.

The next table shows the marginal cost of increasing shares. Here cost grows more dramatically with increasing size. Trading a 500K share large cap core position might cost -124 bp, but the incremental cost above 250k shares is closer to -175 bp. Given a 75 bp average core decision return, a 50 bp differential looms large. Expected Marginal Costs (bp) for Increasing Shares Shares (000's) 10 25 50 , 100 ' 250 500 1000

Average 30 Day Return by Style

Large

Core

Growth

-50 (26)

+7s (178)

+236 (286)

-4e (25)

+167 (2431

+371 (465)

Value

Small

50 ; 100 : 250 : 500 1000 -5 -10 -36 -66 -133 +6 -1 -21 -31 -35 -44 -75 -124 -215 -59 i -73 : -81 i -92 ] -138 : -202, -342 10

cap

c;;; Growth

+6 1 -6 . '9 I -15,'53,

-96'-170

-21: -ge i -39: -53: -96:-173:-306 -59 . -82 . -Sg r -tOS I -169 -266 :

-482

-17 -28 -91 -155 -285 -557 72 114 -247 -499 -823 -93 -128 -146 -208 -387 -628 -1022 +1

Small

cap

The returns are mostly intuitive, with

Value

-33

-58

growth leading the way, and small caps showing stronger returns than large caps. lt also makes sense that the small cap funds have greater dispersion around the mean than the large cap funds.

Determining maximum and optimum decision sizes is a simple matter of finding the point where ihe average and marginal costs exceed the expected return, as illustrated below. Expected return (236 bp) is the horizontal blue line, while the cost lines represent the marginal (green) and The intuition breaks down when looking at the average cost (red). Where the cost lines intersect negative returns for value managers, an artifact of the average return determines the optimal and the maniacal markets of the end of the last maximal decision sizes. decade. We will adjust for this anomaly later. Finding Maximal and Optimal Per-Decision Sizes

The following table shows expected costs for each of the styles. We use the PAEG/L@ cost estimator to compute how size impacts expected cost. We use client data to estimate how trade size growth causes orders to become less liquid while creating higher momentum.

The average cost line crosses the return at a size of 617K shares. Trading more than this leads to total costs that exceed the expected return. The optimal share size, where marginal costs exceed returns, is 414K shares. Trading up to this amount maximizes client returns.

numbers

for value

managers

are

larger, confirming the intuition that value portfolios are more amenable to larger asset size: Optimal and Maximal Per-Decision Shares by Style (000 shares) Value Maximum

881

Maximum

35.2 26.8

Large Cap Growth Core 262 617 414 175

value 474

Small Gap Core Growth 403 234

157 275 320 670 These numbers represent averages for all large Optimal cap growth clients. The range of individual client We're almost ready for the key question: Given returns is diverse enough that it makes sense to this data, what is the maximum asset size for a use your own estimates based on style/skill manager? To convert the above table into dollars, history. In general, large cap growth managers we multiply large cap by $40/share and small cap tend to run concentrated portfolios, making large by $28: bets in individual names. The graph shows that to Maximal Per-Decision Dollars by Style ($mil) a certain size the returns exceed the costs by a Small Gap Large Cap Growth Value Core Value Core Growth large enough margin to justify active portfolio

construction.

Optimal

Using the process defined above, we compute the intercepts for returns and costs for the various styles. The table below shows the maximum share sizes, based on historical returns and costs: Optimal and Maximal Per-Decision Shares by Style (000 shares)

Maximum

??

Optimal

??

Large Cap Core Growth 262 617 175 414

24.7 16.6

13.3 9.0

606 4.4

11.3

7.7

Answering the "How Big ls Too Big?" question requires us to pull more numbers out of the hat for turnover and number of holdings:

Finding the Maxirnum Shares for AllSfyles

Value

10.5 7.0

Value

Small Cap Core Growth 234 403 t3/

ztJ

Value is blank for a reason: we measure negative expected return over our 6-week

Estimated Turnover and Number of Holdings Value

Core

Growth

Turnover

25%

33%

100o/o

# of holdings

100

300

100

Applying these numbers for both large and small cap portfolios leads to the following table of maximal and optimal asset sizes (in billions). Maximum Dollars Under Management by Style ($bil) Value

a

evaluation term, which falsely suggests that value managers should never buy and sell. While growth and core managers strive to capture current price opportunities, value returns develop over longer, often unforecastable, periods. These longer horizon returns are not captured in our data.

Furthermore, the period we are using for data was one in which value managers under performed. Morningstar data indicates that value managers often outperform growth managers after costs over longer periods. Perhaps the next few years are ones in which value managers will shine, so we will replace the negative expectations with a number equal to half that experienced by growth managers. The resulting

Maximum

14.1

Optimal

10.7

Large Cap Growth Core 9.5 6.3

Value

Small Gap Growth Core

2.5

5.3

5.9

1.1

1.7

3.6

4.0

0.7

The conclusions are obvious, although

not necessarily attractive. Active strategies that rely on stock-specific bets (rifle shooting) require large positions. For a 100 stock large cap growth portfolio, a safe optimal amount of assets under these assumptions ends up at only $1.7 billion peanuts relative to today's funds. Value and core funds, which trade less and in less costly situations, are less compromised by asset growth.

Needless to say, we've made a plethora of assumptions to get to this point. We think the process itself is instructive, irrespective of specific estimates and forecasts. We suggest you retrace the computations and experiment with homegrown numbers.

penalizes returns. A growth manager who trades passively shifts transaction costs to search costs: delay costs or missed trades. Appropriate trading speed is dictated by the

Maximum Shares for Top Pertormers The table below performs the same calculations for the top quartile of managers in each group. Managers with top quartile returns did not have

size or momentum characteristics relative to their peers. However, their costs were higher, reflecting the increased timeliness of their decisions. The news here is mostly good: those high-return managers most likely to attract new monies have capacity to grow assets. But not to the moon, of course.

information edge, not by trade size alone.

significantly different

Monitor your brokers and your analysts to see whether they are keeping pace with the new demands.

. .

Maximum $ Under Management for Top Performers ($bil) Shares Maximum

Value

Optimal

13.0

Large Cap Core Growth

17.1

28.9 19.4

.2,

2.2

Value

Small Cap Core Growth

e.9

oa

4t

4.6

6.4

1.0

.

So how do managers cope when growing asset sizes challenge the ability to produce return? The most common response appears to be to ignore the bad news, produce mediocre returns with occasional spurts of over-performance, and hope clients can be kept docile through upgraded client servicing. There are better ways to deal with the problem:

Expand research to new areas such as global

markets. Seek out more trend ideas

Raise the management fee; make the clients pay the manager to remain small.

Go into the business of managing (smaller) hedge funds at substantially higher fees.

. Implications

Close the fund or otherwise limit asset totals.

Keep your clients informed. They see, they hear, they count - and they remember.

In the end, we suspect that many managers, especially those subject to high transaction costs, hold larger positions than they should. Increasing bets creates impediments to performance, and both manager and client need to explore the implications. Asset growth changes the process from a winner's game to a loser's game. As Charlie Ellis said so eloquently, in a loser's game, the victor is the one who makes the fewest (costly?) mistakes.

(as

contrasted to opportunity ideas) and lengthen the holding period.

' A. Perold and R. Salomon, "The Right Amount of Assets Under Manage-ment," Financial Analysts Journal, May-June 199'1 .

Shift to more liquid names than those showing the most attractive returns. This is a siqnificant hazard for small cap funds. Increase the number of stocks held. This may not be a problem for core funds, but most active funds that take stock specific bets are watered down by "closet indexing" part of the portfolio. Stop overtrading: good traders know when they don't know what their doing. Modify trading style to reduce costs. Be careful; a manager who lets costs dictate trading style

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