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  1. 015A Rs 50 crore equity portfolio has a beta of 1.2 to the index. How much index futures notional must you sell to bring the portfolio's beta down to 0.5?Portfolio risk mathsWarm upPortfolio implementationHedge funds

    Try it first

    How much notional do you sell?

    Show the worked solution

    Sell Rs 35 crore of index futures notional. At a beta of 1.2 the portfolio moves like Rs 60 crore of the index. At the target of 0.5 it should move like Rs 25 crore. The difference, (1.2 minus 0.5) x Rs 50 crore, is Rs 35 crore, assuming the futures move one for one with the index. At an assumed Rs 10 lakh a contract, that is about 350 contracts.

    Why is the portfolio's market exposure not simply Rs 50 crore?

    Think of a car that goes 1.2 km for every km a reference car goes. Holding Rs 50 crore of it is like holding Rs 60 crore of the reference. Beta converts a portfolio's value into index-equivalent exposure, so a Rs 50 crore book at beta 1.2 carries Rs 60 crore of market risk. Once you see the exposure in index rupees, the hedge is a subtraction: you want Rs 25 crore left, so you take away Rs 35 crore by selling futures, which carry a beta of one to the index.

    Hedge the change in beta, not the whole portfolioPortfolio value50its value in rupeesMarket exposure now6050 x 1.2Sell index futures-35(1.2 - 0.5) x 50Exposure left2550 x 0.5 = the target betaAt an assumed Rs 10 lakh a contract, Rs 35 crore is about 350 contracts.
    The Rs 50 crore portfolio at beta 1.2 carries Rs 60 crore of market exposure; selling Rs 35 crore of index futures leaves Rs 25 crore, which is a beta of 0.5 on the portfolio.
    The relationship
    N=(βtarget−βnow)×V=(0.5−1.2)×50=−35N=(\beta_{target}-\beta_{now})\times V=(0.5-1.2)\times 50=-35
    Nfutures notional to trade, Rs crore; negative means sell
    \beta_{now}, \beta_{target}the current beta 1.2 and the target 0.5
    Vthe portfolio's value, Rs 50 crore
    What it says in wordsThe futures notional equals the change in beta times the portfolio value, with a minus sign meaning a sale.

    What does the hedge not do?

    It removes market risk, not stock risk. After the hedge the portfolio still carries every stock-specific bet it had; only its sensitivity to the index has been cut. That is often the point: a manager who likes the stocks but not the market can keep the stock picks and trim the market bet. Say the limitations: beta is estimated from history and drifts, so the hedge is right only on average; futures need margin and must be rolled at expiry, and the futures price can move slightly differently from the index, which is called basis risk.

    Where candidates lose it

    The common answers are Rs 50 crore, hedging the whole value, and Rs 60 crore, hedging the whole beta-weighted value. Both take the beta to zero, not to 0.5. Hedge the change in beta.

    Candidates also forget the direction. Lowering beta means selling futures; raising it means buying them. Say the sign with the number.

    What the interviewer asks next

    • How much would you trade to raise the beta to 1.5 instead?
    • If the portfolio falls 10% in value, is the hedge still right?
    • Why might the hedged portfolio still lose money in a market fall?