Hedging a Beta-1.15 Portfolio with Nifty Futures: Sizing, Basis and Rollover
Meera manages a ₹50 crore equity portfolio whose measured beta against the Nifty 50 is 1.15. On 3 March the Nifty spot is 24,000 and the March futures trade at 24,045; the lot size is 25 and the contract expires on 27 March. She expects a sharp but temporary market correction over the next three weeks. She does not want to sell shares because several holdings carry large embedded gains and one is under a lock-in. The fund's mandate permits exchange-traded futures but bars naked option writing. Her broker quotes initial margin of ₹78,000 per Nifty futures lot and requires daily mark-to-market settlement. The fund has ₹9 crore of cash and liquid collateral available for margins; anything beyond that must come from selling portfolio holdings. The April futures are quoting at 24,105.
1. How many March Nifty futures should Meera sell, and why is a beta-adjusted rather than a rupee-for-rupee hedge appropriate? Show the arithmetic and comment on rounding.
Read the worked answer
Hedge notional = portfolio value × beta = ₹50 crore × 1.15 = ₹57.5 crore.
Contract value = 24,045 × 25 = ₹6,01,125.
Contracts = 5,75,00,000 ÷ 6,01,125 = 956.5, so she sells 957 contracts (slightly over-hedged by about 0.05%, immaterial).
Why beta-adjust: a rupee-for-rupee short of ₹50 crore would hedge only the market component equal to the portfolio's face value. Because the portfolio moves 1.15 times the index, a 6% index fall would cost roughly 6% × 1.15 × ₹50 crore = ₹3.45 crore, which only a ₹57.5 crore short can offset. The beta is an estimate from historical returns; it can drift, and individual stocks carry idiosyncratic risk that no index future hedges. Margin check: 957 × ₹78,000 ≈ ₹7.46 crore, within the ₹9 crore available, leaving about ₹1.54 crore of buffer.
2. The Nifty falls 6% and the March futures settle at 22,600 on expiry. Estimate the futures result, the portfolio result and the net outcome. Where does the hedge leak risk?
Read the worked answer
Futures: sold at 24,045, settled at 22,600 → gain of 1,445 points × 25 × 957 = ₹3,45,71,625, i.e. about ₹3.46 crore.
Portfolio: expected loss = 6% × 1.15 × ₹50 crore ≈ ₹3.45 crore. Net result is roughly flat, a small gain of about ₹1.7 lakh.
The futures captured 1,445 points while spot fell 1,400: the 45-point premium at inception decayed to zero, an extra gain for the short. Leaks: (i) beta error - actual portfolio loss may be 5% or 7% of value, not 6.9%; (ii) stock-specific news in the holdings; (iii) dividends going ex during the hedge reduce portfolio value without any offsetting index move; (iv) the hedge notional is fixed at inception while portfolio value changes; (v) basis risk if the futures do not converge exactly to spot. The hedge neutralises market direction, not tracking error.
3. On 26 March the March futures are at 23,900 and April at 23,960. Should she roll, given the fund's view that the correction continues into April? Include margin and cost considerations.
Read the worked answer
Roll cost = 60 points × 25 × 957 = ₹14.36 lakh, plus STT on the April sale at 0.0125% of (23,960 × 25 × 957 = ₹5.73 crore) ≈ ₹71,700, plus brokerage and impact - call it ₹15–18 lakh in total, roughly 0.3% of the hedged notional.
Margin: April needs about ₹78,000 × 957 ≈ ₹7.46 crore again. During the overlap the broker may allow a calendar-spread benefit between the two Nifty months, but she should assume both legs are margined for at least a day.
Judgement: rolling is justified only if she is confident the correction extends into April. The roll converts an unrealised hedge gain into a fresh short at a 60-point lower level - she is selling April 60 points below March, effectively paying to stay short. If her view is weakening, closing the hedge avoids the carry and the STT, and she can re-establish later. Note also that rolling resets the reference price: further protection only begins from 23,960, so any April rebound to that level first eats into the roll cost.