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Hedging with Forward & FuturesPowerPoint Presentation

Hedging with Forward & Futures

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Hedging with Forward & Futures

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Hedging with Forward & Futures

Risk Management

Prof. Ali Nejadmalayeri,

a.k.a. “Dr N”

- 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 :

- 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

- Value of hedged position is the sum of Cash Position + Gain from Hedge
- One-day VaR of hedged position is 1.65Vol(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.

- 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

- Relationship between cash position and futures price is deterministic:

- Hedge Size
- Hedge Position

- 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:

- Relationship between cash position and futures price is only approximately deterministic: