Case 057Manager evaluation and attributionWarm up

Ambeth Fund and Corlane Fund both returned 12% last year. Ambeth had 8% volatility and a beta of 0.2; Corlane had 15% volatility and a beta of 0.9. The market returned 10% and cash 6%. Which manager showed more skill?

The situation

You sit on the allocation team of a multi-manager platform. Two equity long-short managers are up for review. Both returned 12% last year after fees.

Ambeth Fund ran with 8% annualised volatility and a beta to the market of 0.2. Corlane Fund ran with 15% volatility and a beta of 0.9. The market index returned 10% and cash returned 6%. For one extra step, assume the market's volatility was 16%.

Your task

Which manager added more that the platform could not get more cheaply elsewhere, and how confident can you be after one year?

Quick check

How much of Corlane's 12% was alpha, the part not explained by cash and market exposure?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Ambeth showed more skill: about 5.2% of alpha against Corlane's 2.4%. Corlane's beta of 0.9 earned it 3.6 points from the market that any index fund would have delivered; Ambeth took almost no market risk and still made 12%. Ambeth's Sharpe ratio is 0.75 against 0.40. One year is thin evidence, though: at this information ratio it takes roughly 8 years to be statistically confident.

Step 1What part of a return counts as skill?

Only the part you could not have bought cheaply. Two students score 80% in an exam, one who studied the syllabus and one who happened to get a paper full of topics he already knew; you judge them on what they added, not the score. For a fund, cash is free and market exposure is nearly free through an index fund, so skill is the return left after both. The market beat cash by 4 points. Corlane's beta of 0.9 earned 0.9 x 4 = 3.6 points of that; Ambeth's 0.2 earned 0.8. That leaves alphaThe return a manager earns beyond what cash and their exposure to the market would have delivered on their own. of 5.2% for Ambeth and 2.4% for Corlane.

Same 12%, three layers: cash, market exposure, and what is leftAmbeth Fundbeta 0.2, vol 8%cash 6.0beta 0.8alpha 5.2Corlane Fundbeta 0.9, vol 15%cash 6.0beta 3.6alpha 2.412% total0%Market 10%, cash 6%: each point of beta earns 4 points
Both funds made 12%, but Corlane's return is 6% cash, 3.6% from market exposure and 2.4% alpha, while Ambeth's is 6% cash, 0.8% from the market and 5.2% alpha.
The relationship
α=R−Rf−β(Rm−Rf)αA=12−6−0.2(4)=5.2%αC=12−6−0.9(4)=2.4%\alpha = R - R_f - \beta(R_m - R_f) \qquad \alpha_A = 12 - 6 - 0.2(4) = 5.2\% \qquad \alpha_C = 12 - 6 - 0.9(4) = 2.4\%
Rthe fund's return, 12%
R_fcash, 6%
beta(R_m - R_f)what market exposure alone would have earned
What it says in wordsAlpha is what is left after paying for cash and for the market exposure the fund carried.
Step 2Does the risk each took change the picture?

It strengthens it. Ambeth earned 6 points over cash with 8% volatility, a Sharpe ratio of 0.75; Corlane earned the same 6 points with 15%, a Sharpe ratio of 0.40. A platform can lever Ambeth to Corlane's volatility and expect far more. The finer measure is the information ratioAlpha divided by the volatility that the market does not explain, the residual risk. It measures alpha per unit of stock-specific risk.: with market volatility of 16%, Ambeth's unexplained risk is about 7.3% and Corlane's 4.2%, so their ratios are 0.71 and 0.57. Corlane's is closer than its alpha suggests, because most of its risk was market risk.

MeasureAmbethCorlane
Return12.0%12.0%
From market exposure0.8%3.6%
Alpha5.2%2.4%
Sharpe ratio0.750.40
Residual volatility7.3%4.2%
Information ratio0.710.57
Years to t-stat of 2812
Ambeth leads on alpha, 5.2% against 2.4%, and on Sharpe ratio, but at information ratios of 0.71 and 0.57 it would take about 8 and 12 years of similar results to be statistically confident in either.
Step 3How much can one year tell you?

Very little on its own. To be reasonably sure alpha is not luck you want a t-statistic near 2, and the t-statistic grows only with the square root of the years observed: roughly the information ratio times the square root of years. At 0.71, Ambeth needs about 8 years; Corlane, at 0.57, about 12. So the honest answer is that Ambeth showed more skill last year, and the review should now look at how: the process, the source of the alpha and whether it holds across market conditions, before any allocation decision.

Where candidates lose it

The usual loss is saying the two are equal because the returns are equal, or picking Corlane because it took more risk and so seems bolder. Equal returns with unequal market exposure are not equal performance.

The second is forgetting cash. Subtracting beta times the market return, 0.9 x 10, instead of beta times the market's excess over cash, gives the wrong alpha for both funds.

What the interviewer asks next

  • Ambeth ran with net exposure near zero but 300% gross. Does that change your view of its 8% volatility?
  • Next year the market falls 20%. Roughly what does each fund return if its alpha repeats?
  • What would you ask each manager to explain their alpha?

Company names and figures are illustrative.