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Understanding Hedging Strategies with Futures and Forward Contracts for Effective Risk Management

This overview by Dr. Ali Nejadmalayeri focuses on measuring risks through effective hedging strategies using forward and futures contracts. It explores the methodology of forecasting change and volatility, emphasizing the significance of the hedge ratio in minimizing risk. Two key approaches to hedging—without basis risk and with basis risk—are discussed, highlighting the impact of market dynamics on hedge effectiveness. Statistical concepts used include Value at Risk (VaR), volatility calculation, and the importance of a deterministic relationship between cash positions and futures prices.

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Understanding Hedging Strategies with Futures and Forward Contracts for Effective Risk Management

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  1. Hedging with Forward & Futures Risk Management Prof. Ali Nejadmalayeri, a.k.a. “Dr N”

  2. Measuring Statistics • Suppose we have T observations of past changes and we need to forecast change and volatility in T+1. Let’s say change is ΔSi = Si – Si-1, then expected change is: • The volatility of the change is :

  3. Square Root Volatility • If a series of random variables are identically, independently distributed, i.i.d., with volatility per period of σ, the volatility of the series of random variables over N periods is σ√ N

  4. Hedging with no Basis Risk • Value of hedged position is the sum of Cash Position + Gain from Hedge • One-day VaR of hedged position is 1.65Vol(ΔPV of Hedged Position) • In perfect hedging, i.e., making the expected value change zero, then requires correct Hedge Ratio. As the forward price changes, the hedge ratio changes. To change the hedge due to marked to market is Tailing Hedge.

  5. Hedging with Basis Risk • Value of hedged position is the sum of Payoff of Cash Position + Payoff of Hedge • In any date Basis is the difference between spot and forward price. The Basis Risk is when the basis is not deterministic. • Volatility-minimizing hedge is Volatility-minimizing hedge ratio  Exposure to the risk factor

  6. Hedge with Basis Risk • Relationship between cash position and futures price is deterministic:

  7. Hedge with Basis Risk • Hedge Size • Hedge Position

  8. Hedging with Random Basis • When basis is random, then an approximate linear relationship between spot and futures is needed to figure out how changes in the spot and changes in the futures are linked with each other. • We need to a run a regression: • Simply put then, the hedge ratio is:

  9. Hedge with Random Basis • Relationship between cash position and futures price is only approximately deterministic:

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