Case 083Pairs and relative valueWarm up

You 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?

The situation

You believe Menvik Steel will gain market share from Irvanta Steel over the next year, so you buy Rs 10 crore of Menvik and short Rs 10 crore of Irvanta. Menvik carries more debt and has a beta of 1.3 to the market; Irvanta has a beta of 0.9.

The next week the market falls 10% on a global growth scare. Nothing company-specific happens: each stock moves exactly as its beta says.

Your task

What is the pair's P&L, why, and what size of short would have made it neutral to the market?

Quick check

The market falls 10% and nothing else happens. What does the Rs 10 crore against Rs 10 crore pair do?

Worked solution

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

30-second answerThe answer to give first

The pair loses Rs 40 lakh, because a rupee-neutral pair is not market-neutral. Menvik falls 13%, costing Rs 1.3 crore, while Irvanta falls 9%, so the short makes only Rs 90 lakh. The position is effectively Rs 4 crore long the market. To neutralise beta, short Rs 10 crore x 1.3 / 0.9, about Rs 14.4 crore of Irvanta, so both legs carry Rs 13 crore of market exposure.

Step 1Why did a balanced pair lose money when nothing changed in your thesis?

Picture two people on a seesaw who weigh the same but sit at different distances from the middle. Equal weight does not balance them; weight times distance does. A pair is balanced against the market only when rupees times beta match on both sides. Here the long carries Rs 10 crore x 1.3, which is Rs 13 crore of market exposure, and the short carries Rs 10 crore x 0.9, which is Rs 9 crore. The gap, Rs 4 crore of beta-weighted exposureThe rupee size of a position multiplied by its beta: how many rupees of market index it behaves like., is a hidden long bet on the market.

Market down 10%: a rupee-neutral pair is still long the market0Long Menvik Rs 10 cr, beta 1.3-1.30Short Irvanta Rs 10 cr, beta 0.9+0.90Net, rupee-neutral pair-0.40 = Rs 40 lakhShort Irvanta Rs 14.4 cr instead+1.30Net, beta-neutral pair0.00loss, Rs croregain, Rs crore
In a 10% market fall the Rs 10 crore Menvik long loses Rs 1.3 crore and the Rs 10 crore Irvanta short gains Rs 0.9 crore, a Rs 40 lakh loss; shorting Rs 14.4 crore of Irvanta instead would gain Rs 1.3 crore and leave the pair flat.
Step 2How big should the short have been?

Match beta-weighted rupees. The short needs Rs 13 crore of market exposure at a beta of 0.9, which is Rs 13 crore divided by 0.9, about Rs 14.44 crore. In the same 10% fall, Irvanta falls 9% and the larger short gains Rs 1.3 crore, exactly offsetting Menvik. What is left is the thing you wanted to bet on: whether Menvik beats Irvanta for company reasons.

The relationship
Short=Long×βLβS=10×1.30.9=14.44 crore\text{Short} = \text{Long} \times \frac{\beta_{L}}{\beta_{S}} = 10 \times \frac{1.3}{0.9} = 14.44 \text{ crore}
LongRs 10 crore of Menvik
beta LMenvik's beta, 1.3
beta SIrvanta's beta, 0.9
What it says in wordsSize the short so that each leg moves the same number of rupees for a given move in the market.
Market moveRupee-neutral pair, Rs lakhBeta-neutral pair, Rs lakh
-10%-400
-5%-200
+5%+200
+10%+400
The rupee-neutral pair gains or loses Rs 4 lakh for every point the market moves, a directional bet you did not choose, while the beta-neutral pair is flat whatever the market does.
Step 3What does beta-matching cost, and where does it stop working?

Two costs. The pair is now Rs 24.4 crore gross and Rs 4.4 crore net short in rupees, so it uses more capital and more borrow, and it pays for being net short if the stock market drifts up over a year. And betas are estimates: they come from past returns, move over time and differ by the window you choose. Menvik's higher beta partly reflects its debt, and debt changes. So re-estimate the betas regularly, and treat a beta-neutral pair as neutral to ordinary market moves, not to a sector shock such as a steel price collapse, which would hit both legs in ways beta does not capture.

Where candidates lose it

The common miss is saying the pair is hedged because the rupees match. Interviewers set up exactly this scenario to hear whether you think in beta-weighted exposure.

The second is dividing the wrong way and shorting Rs 10 crore x 0.9 / 1.3, about Rs 6.9 crore, which doubles the market exposure instead of removing it.

What the interviewer asks next

  • Both stocks also carry a 1.0 beta to steel prices. Is the beta-neutral pair neutral to steel?
  • How would you estimate the betas, and over what window?
  • The market rises 10% instead. What does each version of the pair make?

Company names and figures are illustrative.