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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.