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Risk Management with Futures

Risk Management with Futures. Risk Management: Hedging. Activity that controls the price risk of a position Combine the derivative with the underlying asset Position in derivative is the opposite to that in the underlying asset

emily-decker
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Risk Management with Futures

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  1. Risk Management with Futures

  2. Risk Management: Hedging • Activity that controls the price risk of a position • Combine the derivative with the underlying asset • Position in derivative is the opposite to that in the underlying asset • Hedge ratio is the number of units of the derivative to the underlying asset • Hedge ratio minimizes the overall exposure to price risk

  3. Problems with Simple Hedging Strategy • The “commodity” you are interested in does not have a futures contract • Use a futures contract with an underlying that is closely related to the “commodity” • Due to unpredictable variations in the convenience yield of a commodity, the Futures price is less than perfectly correlated with the spot price. • Use futures contracts on the commodity but adjust the number of contracts according to correlation between F and S. • The date you need the “commodity” does not match the delivery date • Use a futures contract that has delivery as close to (and greater than) the date you are interested in.

  4. Adjustments to the Simple Strategy • Mismatch implies that risk cannot be reduced to zero. • Assume that we combine 1 long unit of the underlying with h units of the futures contract. • Change in position value is DS-hDF. • This change will be zero if h = - DS/DF, as long as F will change only due to changes in S. • This optimal hedge ratio is the beta of S with respect to F, which can be estimated as the slope of a regression of DS on DF. • It can be shown that the slope of such a regression will be h = Cov(S,F)/Var(F) or h = SF[S/ S] where r is the coefficient of correlation between S and F.

  5. Hedging: An Example • Problem 4.16 (p.95): beef producer is committed to purchasing 200,000 lbs of live cattle in one month. • The standard deviation of the monthly changes in the spot price of live cattle (cents per lb) is 1.2 • The standard dev. of monthly changes in the futures price of live cattle for the closest contract is 1.4. • The correlation between the two is 0.7. • Each contract is for the delivery of 40,000 lbs • Hedge ratio = ? • Number of contracts, long or short?

  6. Managing the Risk of a Portfolio • Assume that you are managing a $5.5 million portfolio of stocks, with a beta of 1.5. • You want to hedge the portfolio over the next three months against market movements, using futures contracts on the S&P 500 index. • Current index level is 1100. • Contract is for $250 units times the index price • i.e., Current price of one contract is 1100*$250 = $275,000 • # of contracts to short = (1.5)($5.5 million/275,000) = 30 contracts • Interpretation: since beta of portfolio is 1.5, then $5.5 million of the portfolio will have the variability of 5.5*1.5 = $8.25 million worth of the index. Since each contract covers $275,000 of the index, $8.25 million of the index requires shorting 30 contracts.

  7. Performance of the Hedge • The portfolio is immune to market movements over the next three months, but not to idiosyncratic movements. • If portfolio returns are perfectly correlated to index returns, portfolio will earn only r over the next three months. Index futures can be used for market timing: • Suppose you want to reduce the beta of your investment from 1.5 to 1. Typically, you would liquidate 1/3 of your $5.5 million investment (or $1,833,333) and invest the proceeds in T. Bills, hence reducing beta by 1/3 its original value. • Alternatively, you can short index futures: • #contracts to sell is (1.5 -1)*$5.5 million / $275,000 = 10 contracts. • Note, 10 contracts cover $2,750,000 of the index, which can neutralize only $1,888,333 worth of the portfolio given the portfolio’s beta of 1.5.

  8. Rolling over the Futures • Hedge a long term exposure with relatively shorter-maturity futures contracts. • Such contract are more liquid than long-dated ones. • Roll the hedge forward (close out a maturing contract and immediately enter another one).

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