Capacity

The Capacity Challenge

• Investment ideas have limited capacity

• We must first understand capacity. Then we can see its impacts and how to mitigate them.

A Model of Capacity

• Understand the driving forces• Improve intuition• The model has many shortcomings:

– Extrapolates beyond experience– Ignores important market issues– Ignores relationship between liquidity and skill…We will come back to these later

• So why is it useful:– Captures many key effects– Provides a context to understand shortcomings (a la

Black-Scholes)

Basics

• Gross Alpha

• Costs

• Net Alpha

gross intIR TC

costs tcost

net gross costs

(Note that = turnover)

Theory• Ex-ante Alpha net of Costs

• Intrinsic Information Ratio depends on research and available inefficiencies. It is an ex-ante estimate.

• The Transfer Coefficient, TC, depends on turnover, • The average trade cost depends on A (the amount of assets under

management) and turnover• This is a great framework for understanding products• Capacity: the maximum asset level that delivers the expected

performance– Actual performance falls below expected half the time– This quantity is not always clearly agreed upon ex-ante by investors and

managers

,intIR TC tcost A

Example

• “Typical” US equity mutual fund• Long-only, 5% active risk• Investors expect 1.4% active return on

average, before fees• Intrinsic Information Ratio is 1.2

– In the absence of constraints and costs, fund could deliver 6% alpha on average

• Let’s examine transfer coefficient, trading costs, and optimal turnover

Transfer Coefficient

0%

10%

20%

30%

40%

50%

0% 50% 100% 150% 200% 250% 300%

Annual Turnover

At very high turnover, long-only transfer coefficient approaches 50%

Transfer coefficient has an inflection point around 60% turnover.

Tra

nsf

er C

oef

fici

ent

*1maxTC e Exp

Average trading costs ($10 billion in assets)

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

0% 50% 100% 150% 200% 250% 300%

Annual Turnover

Ave

rag

e T

rad

ing

Co

sts

A $10 billion fund with 100% turnover experiences about 0.75% average trading costs

,costs A a b A

Optimal turnover to maximize net alpha

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 20 40 60 80 100 120

Assets in $ Billion

Tu

rno

ver

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

0 20 40 60 80 100

Assets in $ Billion

Costs

Alpha

Alpha Net of Costs

Expected Alpha

Managing asset levels beyond our capacity will not generate negative performance. It will lead to eroded performance. Poor

performance is not a warning sign of capacity problems.

What is optimal expected alpha?What is optimal expected alpha?

Slow decay of net

Costs vary little with assets. Monitoring costs may tell us little about reaching capacity

Performance erodes because gross alpha erodes

The impact of sub-optimal portfolio management

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

1.8%

2.0%

0 20 40 60 80 100 120

Assets in $ Billion

Alp

ha

Net

of

Co

sts

Optimal Costs

Optimal Net Alpha

Sub-Optimal Net Alpha

Sub-Optimal Costs

At $50 Billion, sub-optimal portfolio management reduces net alpha from 1.26% to 0.99%, leaving $135 million per year on the table

Sensitivity Analysis: net

We can’t estimate capacity with much precision. We can provide a probable range. One issue: capacity is more sensitive to inputs than is expected alpha.

Sensitivity to IR

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

1.8%

2.0%

2.2%

2.4%

0 20 40 60 80 100 120

Assets in $ Billions

Alpha

+0.2 IR

Base case

-0.2 IR

Costs+0.2 IRBase case-0.2 IR

Capacity is very sensitive. Expected alpha is not.

2

20

100CAPACITY

($ billion)

ALPHA (%) at $100

billion

1.0

IR

1.2 1.4

•What if the true IR is 1.2, but we over-estimate it as 1.4? •We would mistakenly estimate capacity as $100 Billion, not $20 Billion. •Instead of delivering 1.4% alpha, we would only deliver 1.15% alpha.

0.90

1.15

1.40

The difference between 1.4% and 1.15% alpha

Active Return Distribution

0

1

2

3

4

5

6

7

8

9

-15% -10% -5% 0% 5% 10% 15% 20%

Active Return

1.4% Alpha

1.15% Alpha

Real world issues: why the model is optimistic

• Liquidity: we can’t extrapolate cost models far beyond experience.

• Stock borrowing availability for long-short portfolios

• More liquid stocks may be more efficient• Practical limits to position size, based on

liquidity, regulatory issues, poison pill provisions

• Market reaction to poor performance • Theoretical limits

One Final Issue• Competition

– Difficult to model.

– Very important practically.

– Sharing of capacity.

How Can We Increase Capacity?

• Increase IR:– Increase skill and/or breadth. Research new

and better investment ideas.

• Decrease costs:– Research trading strategies that lower costs.