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084

Case 084Portfolio construction and sizingCore

Tamsin Equity's book has a momentum factor exposure of 0.4. A momentum reversal of minus 15% hits the factor in a week. What does the book lose, and how would you hedge the exposure without selling your best ideas?

1The situation

Tamsin Equity runs a Rs 2,000 crore market-neutral long-short book on a multi-manager platform. The platform's risk model shows an exposure of 0.4 to the momentum factor: the book tends to move 0.4% for every 1% move in a portfolio that is long recent winners and short recent losers. The exposure has built up quietly, because Tamsin's best ideas have all worked and are now the market's recent winners.

In one week the momentum factor falls 15% as investors rotate into beaten-down stocks. Tamsin's stock picking, measured within its names, is positive by 1.2% of NAV that week.

2Your task

What does the factor cost the book, and how would you remove the exposure without selling the names you believe in?

Quick check

Roughly what does the momentum move alone cost the book?

Worked solution

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

30-second answerThe answer to give first

The factor alone costs about 6% of NAV, Rs 120 crore, and the week ends down 4.8% despite 1.2% of positive stock picking. The exposure of 0.4 times a 15% fall is the whole damage. To keep the names, short Rs 800 crore of a momentum factor swap, 0.4 times NAV, as an overlay: the factor risk goes, the ideas stay, at a cost of about 0.24% of NAV a year on an assumed fee.

Step 1How can a market-neutral book lose 6% in a week?

Think of a restaurant that has quietly become a cricket-screening venue: its menu is fine, but its takings now depend on whether India is playing. A book can be neutral to the market and still carry a large exposure to a style, such as momentum, that moves on its own. When your best ideas have all rallied, they become the market's recent winners, and the book starts behaving like a momentum factorA portfolio that is long stocks with the strongest recent returns and short those with the weakest. When it reverses, stocks that led fall and laggards rise. portfolio. 0.4 times minus 15% is minus 6%.

The week's P&L, % of NAV: the factor, not the names, did the damage-6.0%Momentum factor0.4 x -15%+1.2%Stock pickingwithin names-4.8%Week asreported+6.0%Swap overlayshort 0.4 x factor+1.2%Week withthe hedge0-6%
Tamsin's week: the momentum factor cost -6.0% of NAV and stock picking added 1.2%, a reported loss of -4.8%; a short momentum overlay of 0.4 times NAV would have offset the factor and left roughly the 1.2% gain.
Step 2How do you separate the factor from the stock picking?

Split the week's P&L into exposure times factor return plus what is left. The factor part is 0.4 x -15%, or -6.0%; everything else, +1.2%, is the stock-specific return that measures the analyst's skill. This split is what a platform's risk team runs every day, and it is why a pod can be told to cut its momentum exposure even in a week when its names outperformed their peers.

The relationship
rbook=βmom×rmom+rspecific=0.4×(−15%)+1.2%=−4.8%r_{book} = \beta_{mom} \times r_{mom} + r_{specific} = 0.4 \times (-15\%) + 1.2\% = -4.8\%
beta momthe book's momentum exposure, 0.4
r momthe factor's return that week, -15%
r specificstock picking net of factors, +1.2%
What it says in wordsThe book's return is the part the factor explains plus the part only the names explain.
Step 3How do you hedge it without selling the best ideas?

Sell the factor, not the names. Enter a swap that pays the momentum factor's return short, on a notional of 0.4 times NAV, Rs 800 crore, so the overlay loses when momentum rises and gains when it falls, cancelling the book's tilt. Many prime brokers offer factor baskets or swaps of this kind; a platform can also build a custom basket of the most crowded momentum names. After the overlay, the 15% reversal costs roughly nothing, and the 1.2% of stock picking comes through.

Same names, different exposure: the overlay removes the factor, not the ideasBefore: names onlyMomentum exposure0.4scale 0 to 0.515% factor fall costs 6.0% of NAVEvery name keptCost: noneAfter: names plus overlayMomentum exposure0.0scale 0 to 0.515% factor fall costs about 0%Every name still keptCost: about 0.24% of NAV a year
Before the overlay Tamsin carries 0.4 momentum exposure and a 15% reversal costs 6% of NAV; after a Rs 800 crore short momentum swap the exposure is near zero and every stock position is kept, for about 0.24% of NAV a year.
Step 4What does the overlay cost, and what does it not fix?

Assume fees and financing of 0.6% a year on the swap notional: Rs 4.8 crore, about 0.24% of NAV. You also give up whatever the momentum factor earns over time, which in normal years can be positive. And the 0.4 is an estimate: the exposure moves as prices move, so the hedge needs resizing, and a hedge of the index factor will not match the specific names that are most crowded. A strong answer adds the alternative: trim position sizes in the most momentum-heavy names while keeping the ideas, or add longs among recent laggards that the analyst likes on fundamentals.

Where candidates lose it

The common error is assuming a market-neutral book is safe from a style move. Market-neutral removes one factor, the index; momentum, value, size and crowding are separate exposures a risk model reports.

The second is solving it by cutting the winners. That removes the factor and the analyst's best ideas together, which is the answer the question was built to rule out.

What the interviewer asks next

  • How would you size the swap if the exposure estimate ranges from 0.3 to 0.5?
  • Momentum rallies 10% next week. What does the hedged book do?
  • Why might a platform set a hard limit on factor exposure rather than let each pod decide?
← Case 083You are long Rs 10 crore of Menvik Steel (beta 1.3) and short Rs 10 crore of Irvanta Steel (beta 0.9). The market falls 10% and both stocks move exactly with their betas. What is your P&L, and how should you have sized the short?Case 085 →Pallav Multi-Strategy Fund can buy a put spread costing 1.5% of NAV a year that pays 12% of NAV if the market falls 25%. You think such a crash happens once in eight years. Is the hedge worth buying?

Company names and figures are illustrative.

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