Case 082Manager evaluation and attributionWarm up

An analyst at Tavish Capital made 40 trades: 18 winners averaging Rs 1.8 crore and 22 losers averaging Rs 1.0 crore. What is the hit rate, the expectancy per trade, and what would you tell the analyst?

The situation

Tavish Capital runs a pod of four analysts. At the year-end review, one analyst's trade log shows 40 closed trades. 18 made money, averaging Rs 1.8 crore each. 22 lost money, averaging Rs 1.0 crore each. The analyst is worried: fewer than half the ideas worked, and a peer on the next desk wins 60% of the time.

The portfolio manager asks you to read the numbers and prepare the feedback conversation.

Your task

What are the hit rate and the expectancy per trade, what do they say, and what would you tell the analyst?

Quick check

With a 45% hit rate, is the analyst making or losing money on average?

Worked solution

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

30-second answerThe answer to give first

The hit rate is 45% and the expectancy is about Rs 0.26 crore a trade, positive because winners are 1.8 times the size of losers. Gains of Rs 32.4 crore beat losses of Rs 22.0 crore by Rs 10.4 crore. At that payoff ratio the break-even hit rate is 35.7%. Tell the analyst the pattern is sound, then add that 40 trades cannot yet prove skill.

Step 1Why is a 45% hit rate not bad news on its own?

Think of a shopkeeper who stocks a few expensive items. Most days they do not sell, but the days they do pay for the slow ones. What matters is the hit rate and the size of wins against losses taken together, which is the expectancyThe average profit per trade: the chance of winning times the average win, less the chance of losing times the average loss.. Here 45% of trades win Rs 1.8 crore and 55% lose Rs 1.0 crore, so each trade is worth 0.45 x 1.8 less 0.55 x 1.0, which is Rs 0.26 crore.

Fewer winners, bigger winners: 45% hit rate, positive expectancy18 winners x Rs 1.8 cr+32.422 losers x Rs 1.0 cr-22.0net +10.4What is leftRs 10.4 crore / 40 tradesExpectancy +Rs 0.26 crore a tradeWinners are 1.8x the size of losersBreak-even hit rate 35.7%
The analyst's 18 winners made Rs 32.4 crore and 22 losers cost Rs 22.0 crore, leaving Rs 10.4 crore, or Rs 0.26 crore a trade, because winners average 1.8 times the size of losers.
The relationship
E=p×W−(1−p)×L=0.45×1.8−0.55×1.0=0.26p∗=LW+L=12.8=35.7%E = p \times W - (1 - p) \times L = 0.45 \times 1.8 - 0.55 \times 1.0 = 0.26 \qquad p^{*} = \frac{L}{W + L} = \frac{1}{2.8} = 35.7\%
phit rate, 18 of 40
Waverage win, Rs 1.8 crore
Laverage loss, Rs 1.0 crore
p*hit rate at which expectancy is zero
What it says in wordsExpectancy weighs each outcome by how often it happens; with wins 1.8 times losses, anything above a 35.7% hit rate makes money.
Step 2Is 40 trades enough to call it skill?

Not yet, and saying so is what separates a reviewer from a cheerleader. With 40 trades, the hit rate is known only to within about 8 points either way, roughly 37% to 53%, and the low end sits close to break-even. Taking the spread of trade results into account, the Rs 0.26 crore average is only about 1.2 standard errors from zero, which a run of luck could produce. The sign is encouraging; the proof needs more trades.

Expectancy against hit rate, with the band 40 trades can pin downbreak-even 35.7%45%: +Rs 0.26 cr37% to 53%one standard error-0.5+0.5+1.0020%30%40%50%60%70%Hit rate (expectancy per trade, Rs crore, on the vertical axis)
At a win-to-loss ratio of 1.8, expectancy turns positive above a 35.7% hit rate; the analyst's 45% earns Rs 0.26 crore a trade, but 40 trades only pin the hit rate to about 37% to 53%.
Step 3What would you actually tell the analyst?

Three things, in this order. First, stop comparing hit rates with the peer: a 60% hit rate with winners half the size of losers loses money. Second, protect the payoff ratio, because it carries the whole result; check whether a handful of big winners made most of the Rs 32.4 crore, and whether losers are being cut at a plan or allowed to drift. Third, keep sizing steady until another 40 or 60 trades confirm the pattern. The profit factorTotal gains divided by total losses. Above 1 means the trades made money overall. of 1.47 is healthy; what would worry you is losers growing while winners shrink.

Where candidates lose it

The usual miss is treating the hit rate as the score, either by telling the analyst to raise it or by comparing it with a colleague's. A hit rate without the payoff ratio says nothing about whether money is being made.

The second is the opposite error: declaring skill from 40 trades. A good reviewer gives the positive expectancy and, in the same breath, the uncertainty around it.

What the interviewer asks next

  • The peer wins 60% of trades, averaging Rs 0.8 crore on winners and Rs 1.3 crore on losers. Who is better?
  • Three of the 18 winners made Rs 15 crore between them. Does that change your feedback?
  • How many trades would you want before you raised the analyst's capital?

Company names and figures are illustrative.