Case 068Investment and portfolio riskCore

A portfolio has a market beta of 0.9 and a size factor exposure of 0.6. In a month when the market falls 10% and small caps trail large caps by a further 10%, estimate its return, split it by factor, and propose how to cap the size exposure.

The situation

Halvero Asset Management runs a Rs 3,000 crore diversified equity fund benchmarked to a broad large-cap index. The fund manager describes the fund as slightly defensive, pointing to its market beta of 0.9. The risk team's factor model also shows a size exposure of 0.6: the fund behaves as if it holds a 0.6 weight in a portfolio that is long small caps and short large caps.

In the month under review the market falls 10%, and small caps underperform large caps by a further 10%, so the size factor return is minus 10%. Assume no stock-specific return.

Your task

Estimate the fund's return, split it by factor, and propose how to cap the size exposure.

Quick check

The market falls 10%. What does the fund lose?

Worked solution

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

30-second answerThe answer to give first

The fund falls about 15%: minus 9% from the market and minus 6% from its tilt to small caps. Beta of 0.9 times the market's minus 10% gives minus 9%; size exposure of 0.6 times the size factor's minus 10% gives minus 6%. On Rs 3,000 crore that is about Rs 450 crore, against Rs 270 crore on beta alone. Capping size exposure at 0.3 would have held the loss to about 12%.

Step 1Why does beta alone understate the fall?

Two people both say their commute is ten minutes shorter than average. One lives near a train line; the other drives on a road that floods every monsoon. On a normal day they look the same; on a rainy day they do not. Beta measures only how a portfolio moves with the market; a fund can have a low beta and still carry a large bet on another factor that falls in the same month. Halvero's 0.6 size exposureHow much a portfolio moves with the return of small companies over large ones, estimated from a factor model. is that second bet, and in a sell-off small caps usually fall harder than large ones.

The relationship
r≈βmrm+βsrs=0.9(−10%)+0.6(−10%)=−15%r \approx \beta_{m} r_{m} + \beta_{s} r_{s} = 0.9(-10\%) + 0.6(-10\%) = -15\%
\beta_mmarket beta, 0.9
r_mmarket return, minus 10%
\beta_ssize exposure, 0.6
r_ssize factor return, small minus large, minus 10%
What it says in wordsEach factor's contribution is exposure times that factor's return; add them for the total.
Halvero's month split by factor, % return0%-9%Market0.9 x -10%-6%Size0.6 x -10%-15%Total-9%Beta-only viewwhat beta says-12%Size capped at 0.30.9 x -10% + 0.3 x -10%
Halvero loses 9% from the market and a further 6% from its size exposure, 15% in total, against the 9% a beta-only view predicts; with size capped at 0.3 the loss would have been 12%.
Step 2What does the split tell the fund manager?

Two fifths of the loss came from a bet the manager did not describe. A fund sold as slightly defensive lost 15% in a month the market lost 10%, which is exactly the outcome its investors thought they were avoiding. The size tilt may be deliberate, because small caps can outperform over long periods, or it may have crept in through stock picks that happen to be smaller companies. Either way it should be measured, disclosed and limited, not discovered in a bad month.

SourceExposureFactor returnContributionRs crore
Market0.9-10%-9.0%-270
Size0.6-10%-6.0%-180
Total-15.0%-450
On a Rs 3,000 crore fund, the market factor costs Rs 270 crore and the size factor a further Rs 180 crore, a total loss of Rs 450 crore.
Step 3How would you cap the size exposure?

Set a limit on factor exposure, not just on beta. A size exposure cap of 0.3 would have cut the size contribution to minus 3% and the month's loss to about 12%. To get there the manager can shift weight from the smallest holdings to larger ones with similar characteristics, or, where the mandate allows, sell small-cap index futures against the book. Monitor the exposure monthly, because it drifts as prices move, and report it to investors alongside beta.

Say the limits of the model. Factor exposures are estimated from past returns and change over time, and in a sell-off small caps also become harder to sell, so the realised loss can exceed the factor estimate. A cap is a guardrail, not a guarantee.

Where candidates lose it

The fast answer is minus 9%, beta times the market. It ignores the second factor entirely, which is the lesson the question is built around.

The second is adding the two market moves before applying exposures, 0.9 x minus 20%. Each factor has its own exposure; multiply first, then add.

What the interviewer asks next

  • Small caps outperform large caps by 10% in a month the market rises 10%. What does the fund return?
  • How would you tell whether the size tilt is deliberate or accidental?
  • Why might the fund's beta itself rise in a sell-off?

Company names and figures are illustrative.