Case 095Portfolio construction and sizingHard
Zorvek Defence has no listed peer. Its returns regress on the market with a beta of 0.9 and on a capital goods basket with a beta of 0.6, with an R-squared of 45%. You are long Rs 20 crore. How do you hedge it, and how much risk is left?
1The situation
Zorvek Defence makes radar and electronic warfare systems and has no close listed peer. You are long Rs 20 crore on a view about its order book. To hedge, you regress three years of Zorvek's weekly returns on two things you can short: the market index and a basket of capital goods stocks. The coefficients are 0.9 on the index and 0.6 on the basket, and the two together explain 45% of the variance; the index alone explains 30%.
Zorvek's volatility is 40% a year. The basket itself has a beta of 1.1 to the index. The pod's risk budget allows Rs 2 crore of stock-specific risk, one standard deviation a year, per name.
2Your task
How do you size the hedge, how much risk is left after it, and how big should the position be?
Quick check
The hedge removes 45% of Zorvek's variance. By how much does the rupee risk, measured as standard deviation, fall?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Short Rs 18 crore of the index and Rs 12 crore of the capital goods basket; that removes the 45% of variance the regression explains, and the 55% left is the stock-specific bet. Because risk scales with the square root of variance, rupee risk falls only about 26%, from Rs 8.0 crore to Rs 5.93 crore a year. To fit a Rs 2 crore budget for specific risk, the position would be about Rs 6.7 crore, not Rs 20 crore.
Step 1How do you hedge a stock that has no twin?
Build the twin from parts. Think of a tailor with no cloth that matches a customer's suit exactly: he blends two cloths that between them get the colour close. A regression on things you can short, here the index and a capital goods basket, tells you how much of each behaves like Zorvek: 0.9 of the index and 0.6 of the basket for every rupee of Zorvek. On Rs 20 crore that is Rs 18 crore of index and Rs 12 crore of basket, sold short.
Step 2Why short Rs 30 crore against a Rs 20 crore long?
Because the two coefficients are partial betas, measured together. The basket itself moves 1.1 with the market, so Zorvek's total market beta is 0.9 plus 0.6 x 1.1, about 1.56, and the hedge's market exposure, 18 plus 12 x 1.1, is Rs 31.2 crore, matching Rs 20 crore x 1.56. The book is net short in rupees but flat in market beta. The same fact is a warning: the index and the basket move together, so the regression cannot cleanly separate their roles, and the split between 0.9 and 0.6 can swing a lot from one sample to the next.
| r M | return on the market index |
| r CG | return on the capital goods basket |
| epsilon | the part of Zorvek's return neither explains |
| R squared | share of variance explained, 45% |
Step 3How much risk is really left?
More than most people expect. R-squared measures variance, and risk in rupees follows the square root of variance: 55% of the variance is 74% of the volatility, 29.7% a year against 40%. On Rs 20 crore, one standard deviation of yearly P&L falls from Rs 8.0 crore to Rs 5.93 crore, a 26% cut. That is still worth doing, since the part removed is risk you had no view on, but a hedge built on 45% R-squared leaves you running mostly Zorvek-specific risk.
Step 4So how big should the position be?
Size to the risk that is left. If the pod allows Rs 2 crore of stock-specific risk a year per name, and the residual volatility is 29.7%, the position is about Rs 6.7 crore, a third of Rs 20 crore. Then keep the hedge honest: re-run the regression on rolling windows to see how stable the 0.9 and 0.6 are, check that the basket can be shorted cheaply through a swap, and watch for defence-specific news, such as budget announcements, that moves Zorvek without moving either hedge. Say the limitation plainly: a hedge estimated from the past is a hedge against the past's relationships.
Where candidates lose it
The common miss is reading an R-squared of 45% as 45% less risk. Risk in rupees falls with the square root of the remaining variance, so the cut is about 26%, and a position sized as if it were half as risky is sized too big.
The second is hedging only with the index at 0.9 because it is simplest. That ignores the basket leg and understates the total market beta, leaving the book long the market through the capital goods exposure.
What the interviewer asks next
- The basket costs 3% a year to short through a swap. Is the second leg still worth it?
- How would you orthogonalise the two regressors, and what would it change?
- Zorvek wins a large export order. Which part of the return is that, and does the hedge touch it?
Asked at Balyasny Asset Management, Equity Research, New York, 2026 (Wall Street Oasis): How would you hedge this name that doesn't have a very similar public comp?
Company names and figures are illustrative.