Case 010Risk limits and drawdownsWarm up

A Selvik Quant strategy earns gross alpha of 8% a year but turns over its book 20 times a year at 15 basis points a side. Halving turnover would cut gross alpha to 6%. Which version is better after costs?

Man GroupBoston · 2022

The situation

Selvik Quant runs a short-term equity strategy. Its signals produce gross alpha of 8% a year, measured before any trading costs. To capture that, it turns over its whole book 20 times a year: every turn means selling the old positions and buying new ones. Commissions, spread and market impact together cost 15 basis points each time it buys or sells, a side.

A researcher finds that trading only on the stronger signals halves turnover to 10 times a year, but gross alpha falls to 6%.

Your task

Which version earns more after costs, at what cost level would the answer flip, and what happens as the fund grows?

Quick check

What does 20 turns a year at 15 basis points a side cost?

Worked solution

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

30-second answerThe answer to give first

The slower version is better: it nets about 3% a year against 2% for the fast one. Twenty turns at 30 basis points a turn, 15 on each side, cost 6%, leaving 2% of the 8% gross alpha. Ten turns cost 3%, leaving 3% of 6%. The fast version wins only if costs fall below about 10 basis points a side, and as the fund grows costs rise, which widens the gap.

Step 1How much does trading actually cost each version?

Count the sides. Turning over the book once means selling every position and buying a new set, two trades for every rupee of capital. At 15 basis points a side, one turn costs 0.30% of the book, so 20 turns cost 6% a year and 10 turns cost 3%. A shopkeeper who buys stock in the morning and sells it by evening pays the wholesaler's margin and the delivery charge every single day; one who restocks weekly pays them a fifth as often, even if some of his goods sit a little longer.

At 20 turns a year, 15 basis points a side costs 6% and cuts 8% of gross alpha to 2%; at 10 turns the cost is 3% and 6% of gross alpha becomes 3%, so the slower version keeps half as much again.

Step 2At what cost level does the answer flip?

Set the two net alphas equal. The fast version earns 2 extra points of gross alpha but pays for 10 extra turns, 20 extra sides. The two break even when a side costs 2% divided by 20, which is 10 basis points; below that the fast version wins, above it the slow one does. At 15 basis points Selvik is well above break-even, so the answer is not close. The faster signal is real alpha; it simply costs more to harvest than it pays.

The relationship

\alpha_{net} = \alpha_{gross} - 2\,c\,n \qquad 8\% - 2 \times 0.15\% \times 20 = 2\% \qquad 6\% - 2 \times 0.15\% \times 10 = 3\%

alpha_gross	alpha before trading costs
c	cost per side, 15 basis points
n	turns of the book per year

What it says in wordsNet alpha is gross alpha less two sides of cost for every turn of the book.

Step 3What happens as Selvik grows?

Commissions stay flat as a fund grows, but market impactThe amount a trade moves the price against the trader while it is being done; it rises with the size of the order relative to normal trading volume. does not. A common rule of thumb has impact rising with the square root of trade size. If the fund doubles and the cost per side rises from 15 to about 21 basis points, the fast version's net alpha falls to -0.5% while the slow one still earns 1.8%. That is the capacity point: high-turnover alpha shrinks fastest as money arrives. The judgement for the platform is to run the slower version, and to keep measuring realised costs against the model, because the gap between assumed and actual costs is where most quant strategies quietly lose their edge.

Where candidates lose it

The common slip is counting one side per turn: 20 turns at 15 basis points is 3%, and both versions appear to net 5% and 4.5%, so the fast one wins. Every turn is a sale and a purchase.

The second is judging signals on gross alpha. A researcher who reports 8% without costs has reported a number nobody can earn, and the interviewer wants to hear that you would never compare strategies before costs.

What the interviewer asks next

What if the stronger signals also decay more slowly, so the positions can be held longer?
How would you measure the strategy's real cost per side from its own trade records?
At what fund size does the slow version's net alpha fall to zero, using the square root rule?

Asked at Man Group, Investment Management, Boston, 2022 (Wall Street Oasis): How to understand portfolio risk and transaction cost?

Company names and figures are illustrative.