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 (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

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. Transfer Coefficient

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

Optimal turnover to maximize net alpha 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Assets in $ Billion Turnover

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 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? 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% Assets in $ Billion Alpha Net of Costs 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. Alpha +0.2 IR Base case -0.2 IR Costs +0.2 IR Base case -0.2 IR

Capacity is very sensitive. Expected alpha is not CAPACITY ($ billion) ALPHA (%) at $100 billion 1.0 IR 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

The difference between 1.4% and 1.15% alpha Active Return Distribution %-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.