Case 005Hedging with futuresCore

A Rs 500 crore equity fund with a beta of 1.15 wants its beta at 0.6 through a results month using index futures at 22,000 with a 50 unit contract. How many contracts, which side, and what is the fund still exposed to?

The situation

Salher Equity Fund runs Rs 500 crore of Indian large-cap stocks with a measured beta of 1.15 to the Satpura 50. The manager likes the holdings but expects a volatile results month and wants the fund's beta to the index at 0.6 for the next four weeks without selling any stock.

The near-month Satpura 50 future trades at 22,000 and one contract is 50 units of the index, so each contract carries Rs 11 lakh of index exposure. Ignore the difference between the futures price and the spot level for the sizing.

Your task

How many contracts does the fund trade, on which side, how do you check the answer with a 5% index fall, and what risks does the fund still carry?

Quick check

Before computing: does the fund buy or sell futures, and roughly how much notional?

Worked solution

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

30-second answerThe answer to give first

Sell 2,500 contracts, Rs 275 crore of index notional. The fund needs to shed 0.55 of beta on Rs 500 crore, which is Rs 275 crore of index exposure, and each contract carries 22,000 times 50, Rs 11 lakh. Check: a 5% index fall costs the stocks about Rs 28.75 crore and the short futures earn Rs 13.75 crore, a net loss of Rs 15 crore, 3% of the fund, which is 0.6 times 5%. The hedge leaves stock-specific risk, beta error, basis and daily cash calls.

Step 1How do you size the hedge without selling stock?

A shopkeeper who owns the shop but worries about the next month can insure the building without selling it. The fund keeps its stocks and sells enough index futures that the combined position moves like a 0.6 beta portfolio: the number of contracts is the change in beta times the fund value divided by the value of one contract. The change is 0.6 less 1.15, minus 0.55; times Rs 500 crore that is minus Rs 275 crore; divided by Rs 11 lakh a contract it is minus 2,500. The minus sign is the side: sell. Note the betaThe sensitivity of a portfolio to the index: a beta of 1.15 means the portfolio is expected to move 1.15% for every 1% move in the index. of 1.15 means the fund already carries more index exposure than its size, Rs 575 crore of index-equivalent on Rs 500 crore of stock.

The relationship

N = \frac{(\beta^{*} - \beta)\,V}{F \times m} = \frac{(0.60 - 1.15) \times 500\text{ crore}}{22{,}000 \times 50} = -2{,}500

\beta^{*}, \beta	the target beta 0.60 and the current beta 1.15
V	the fund value, Rs 500 crore
F \times m	the futures price times the contract multiplier, Rs 11 lakh

What it says in wordsThe number of contracts is the beta the fund wants to remove, times the fund, divided by the index exposure in one contract. A negative answer means sell.

Selling 2,500 contracts, Rs 275 crore of index notional or 55% of the fund, takes the beta from 1.15 to 0.60, and leaves stock-specific risk, error in the beta estimate, basis and the daily cash flows on the futures untouched.

Step 2How do you prove the number with one scenario?

Run a 5% index fall. The stocks, at beta 1.15, lose 5.75%, about Rs 28.75 crore. The short futures gain 5% of Rs 275 crore, Rs 13.75 crore. Net, the fund is down Rs 15 crore, 3% of its value, which is exactly 0.6 times the 5% index fall, so the hedge does what was asked. Say it the other way too: in a 5% rally the fund makes only 3% instead of 5.75%, and the manager has to be comfortable with that cost before the trade, because the hedge is symmetric.

Index falls 5%	Rs crore
Stocks, beta 1.15, lose 5.75%	-28.75
Short futures on Rs 275 crore gain 5%	+13.75
Net, 3.0% of the fund = 0.6 x 5%	-15.00

A 5% index fall costs the stocks Rs 28.75 crore and the short futures earn Rs 13.75 crore, leaving a net loss of Rs 15 crore, 3% of the fund, which is the 0.6 beta the manager asked for.

Step 3What is the fund still exposed to?

Four things, in order of size. Stock-specific risk is untouched: if one holding falls 20% on its own results, the index hedge pays nothing, and that is the whole point of a results month. The beta of 1.15 is an estimate from past returns; if the true beta this month is 1.3, the fund is hedged to about 0.75, not 0.6. Basis risk is the gap between the futures and the index, which moves with rates, dividends and roll, small over four weeks but not zero. And the futures settle daily, so a rally that costs Rs 13.75 crore on the hedge must be paid in cash while the gain on the stocks is only on paper, which means the fund needs a cash buffer or a line to fund margin calls.

Add the practical limit: 2,500 contracts is Rs 275 crore of notional in one month's futures, and the fund should confirm its position limits and the liquidity of that contract before assuming it can trade the full size in a day.

Where candidates lose it

Candidates divide the fund value by the contract value and sell all 4,545 contracts, which takes the beta to about minus 0.4 rather than to 0.6. The hedge size is the change in beta times the fund, not the fund.

The second loss is to describe the fund as hedged and stop. The interviewer wants the list of what is left: stock-specific risk above all, because a results month is precisely when single names move independently of the index.

What the interviewer asks next

The fund also holds Rs 50 crore of cash. Does that change the number of contracts?
After the results month the manager wants beta back at 1.15. What does the unwind cost if the futures basis has moved from 100 points to 40?
Why might the fund use options on the index instead, and what would that cost?
How would you estimate the beta you are hedging, and over what window?

Company names and figures are illustrative.