Hedge Ratio and Portfolio Hedge

Ravi held about Rs 12,00,000 of stocks - mostly mid-caps he believed in. A big event was coming, so he decided to hedge. He shorted index futures worth roughly the same rupee value as his book: twelve lakh of stock, twelve lakh of NIFTY short. "Rupee for rupee, I'm covered," he told himself. The market fell. NIFTY dropped about 10%, and his short earned him close to Rs 1,20,000. He felt smart - right up until he opened his portfolio and saw it had fallen 14%, a loss of Rs 1,68,000. He was "fully hedged" and still down Rs 48,000. Nothing had gone wrong with his hedge. He had simply ignored the one number that decides how big a hedge needs to be.

That number is beta. This chapter is about sizing a portfolio hedge properly - and about being honest that even a properly sized hedge is never perfect.

Two numbers that size every hedge

You only need two ideas to size a hedge. Learn them and most of the confusion disappears.

Beta is how much your portfolio moves compared with the index. A beta of 1.0 means your stocks move about the same as NIFTY. A beta of 1.2 means they move roughly 20% more - when NIFTY falls 10%, your book tends to fall about 12%. Mid- and small-caps often have a beta well above 1; large, steady names sit closer to 1 or below. Beta is an average from the past, not a promise, but it is the best single guess you have for how hard your portfolio swings with the market.

Notional value is the full rupee value a position represents - not the margin you put up, the whole exposure. One NIFTY futures lot is the index level times the lot size. At an index level of around 24,000 and a lot size of around 65 (lot sizes are revised periodically by the exchange - always check the current contract specs), one lot carries a notional of 24,000 x 65 = Rs 15,60,000. You may post far less as margin, but you are exposed to about fifteen and a half lakh of index movement. Hedging is about matching notional value, not margin.

Sizing an index hedge, step by step

Here is the whole calculation in plain rupees. Say you hold a Rs 10,00,000 portfolio and you have worked out its beta is about 1.2.

1. Find your real exposure. Portfolio value x beta = 10,00,000 x 1.2 = Rs 12,00,000. Your twelve-lakh book behaves, in the market's eyes, like twelve lakh of index. That is why Ravi's rupee-for-rupee hedge fell short - his real exposure was bigger than his cash value.
2. Match that with index notional. You want to be short about Rs 12,00,000 of NIFTY to offset the fall.
3. Convert to lots. Divide by one lot's notional: 12,00,000 / 15,60,000 = 0.77 lot. You cannot trade three-quarters of a lot, so you round to one lot (a small over-hedge) or skip it.

Full, partial, over and under

You do not have to take off all the risk. Hedging is a dial, not a switch.

A partial hedge removes only part of the risk on purpose. If you want to keep some upside and only soften a fall, hedge half: take your hedge notional and multiply by 0.5. For the book above, a 50% hedge is six lakh of index, not twelve. You will feel half the drop and keep half the bounce. This is often the sensible middle: you are nervous but not certain, so you take some risk off rather than all of it. A full hedge protects the most but gives up the most upside; a partial hedge is a deliberate "I want to stay a little in the game" choice.

The two ways to get it wrong are quieter. Under-hedging means your short is smaller than your real exposure - you are still partly exposed, and a fall still hurts (this was Ravi). Over-hedging means your short is larger than your exposure - and now you have flipped. You are net short the market. If it keeps falling you profit, but if it rises you lose money even though your stocks went up. An over-hedge stops being insurance and becomes a fresh bet in the other direction.

A worked portfolio-hedge sizing table

Same method, different books. Index level around 24,000, lot around 65, so one lot is about Rs 15,60,000 of notional. Watch how the lots rarely come out whole.

The lesson in the last column: small books and odd betas almost never divide into whole lots. You are forced to round, and rounding is a tiny over- or under-hedge every time. That is normal. The goal is close enough, not perfect.

How this differs by who you are

The same maths applies to everyone, but how much it matters changes with your seat.

When this fails

Even sized perfectly, a portfolio hedge is an approximation. Be honest about why.

Basis and tracking risk - your stocks are not the index. You hedge with NIFTY, but you do not own NIFTY. You own a specific basket. If your stocks fall while the index holds up (a sector problem, a single bad result), your hedge barely moves and you lose anyway. The index can only protect against the part of your fall that is market-wide. The stock-specific part is uncovered.

Beta drifts. The 1.2 you calculated is a backward-looking average. In a sharp crash, correlations jump and many stocks fall together harder than their calm-day beta suggested - so a hedge sized for normal times can under-cover exactly when you needed it most. Beta is a guide, not a guarantee.

Lots do not divide evenly. As the table showed, you are almost always forced to round to a whole lot, leaving a small over- or under-hedge baked in from the start.

A perfect hedge - one that cancels your loss to the rupee - is a textbook idea, not a market reality. The honest aim is to take most of the market risk off the table at a known cost, and to know which risks you are still carrying.

Quick self-check