Using Futures for Hedging

Introduction to Hedging with Futures

Welcome to one of the most practical chapters in your FRM Part I journey! In the world of finance, prices are constantly moving, which creates risk. Hedging is simply the act of taking a position in the futures market to offset or "neutralize" the risk of price movements in the spot market (the market where you buy things right now). Think of hedging like buying an insurance policy for your investments. You might have to pay a little or give up some potential profit, but you get peace of mind knowing that a sudden price crash won't ruin you.

In this chapter, we will explore how to protect yourself whether you are selling an asset, buying one, or managing a whole portfolio of stocks. Don't worry if the math looks a bit scary at first—we will break it down step-by-step!

1. Short Hedges vs. Long Hedges

The first step in hedging is knowing which direction to trade. It all depends on what you are trying to protect.

The Short Hedge

A short hedge involves taking a short position (selling) in a futures contract. You use this when you already own an asset and plan to sell it in the future, or when you expect to receive an asset soon.

When to use it: Use a short hedge if you are afraid the price of your asset will fall before you sell it.

Example: Imagine a farmer who is growing corn. He won't be ready to sell his corn for three months. If the price of corn drops during those three months, he loses money. To protect himself, he "locks in" a price now by selling corn futures.

The Long Hedge

A long hedge involves taking a long position (buying) in a futures contract. You use this when you know you will need to buy an asset in the future and want to lock in the price now.

When to use it: Use a long hedge if you are afraid the price of the asset will rise before you buy it.

Example: A bakery knows it needs to buy 1,000 bushels of wheat in six months to make bread. If the price of wheat spikes, the bakery's costs go up. To prevent this, the bakery buys wheat futures now to lock in today's price.

Quick Review:
- Own the asset? Short Hedge (Sell futures).
- Need the asset? Long Hedge (Buy futures).

2. Basis Risk: Why Hedges Aren't Perfect

In a perfect world, a hedge would perfectly offset your losses. However, in the real world, we deal with Basis Risk. The Basis is simply the difference between the spot price and the futures price.

The formula for Basis is: \( \text{Basis} = \text{Spot Price of asset to be hedged} - \text{Futures Price of contract used} \)

Why does Basis Risk happen?
1. Asset Mismatch: You are hedging an asset that is slightly different from the one underlying the futures contract (e.g., hedging jet fuel using heating oil futures).
2. Timing Mismatch: You plan to sell the asset on a date that doesn't perfectly match the futures contract's expiration date.
3. Location Mismatch: The asset is in one location, but the futures contract delivery is in another.

Strengthening and Weakening of the Basis

If the basis increases (the gap between spot and futures gets wider in favor of the spot price), we call this strengthening. If it decreases, we call it weakening.

Memory Trick:
- A Short Hedger (Seller) likes it when the basis strengthens.
- A Long Hedger (Buyer) likes it when the basis weakens.

Did you know? At the exact moment a futures contract expires, the basis should theoretically be zero because the spot price and futures price must converge (meet).

3. Cross Hedging and the Optimal Hedge Ratio

Sometimes, there isn't a futures contract for the exact asset you own. For example, there is no "Jet Fuel" futures contract, so airlines often use "Heating Oil" futures to hedge. This is called Cross Hedging.

Because the two assets aren't identical, we need to calculate the Optimal Hedge Ratio (\( h^* \)). This ratio tells us how many units of the futures contract we should buy or sell for every unit of the asset we have.

The formula for the Minimum Variance Hedge Ratio is: \( h^* = \rho \left( \frac{\sigma_S}{\sigma_F} \right) \)

Where:
- \( \rho \) (rho) is the correlation coefficient between the change in spot and futures prices.
- \( \sigma_S \) is the standard deviation of the change in the spot price.
- \( \sigma_F \) is the standard deviation of the change in the futures price.

Calculating the Number of Contracts (\( N^* \))

Once you have \( h^* \), you can find out exactly how many contracts to trade: \( N^* = \frac{h^* \times Q_A}{Q_F} \)

Where:
- \( Q_A \) is the size of the position being hedged (units).
- \( Q_F \) is the size of one futures contract (units).

Key Takeaway: The goal of the optimal hedge ratio is to minimize the variance (risk) of the total value of your position. If the correlation is 1.0 and the volatilities are equal, your hedge ratio is 1 (a perfect match).

4. Hedging Equity Portfolios (Beta Hedging)

If you manage a portfolio of stocks, you can use Stock Index Futures (like the S&P 500 futures) to hedge. To do this, we use the portfolio's Beta (\( \beta \)).

The number of contracts needed to hedge a portfolio is: \( N^* = \beta \times \left( \frac{V_P}{F} \right) \)

Where:
- \( V_P \) is the current value of the portfolio.
- \( F \) is the current value of one futures contract (Futures Price \(\times\) Multiplier).

Changing the Portfolio Beta

Sometimes you don't want to eliminate all risk; you just want to reduce it or increase it.
- To change Beta from \( \beta \) to \( \beta^* \), the number of contracts is: \( N^* = (\beta^* - \beta) \times \left( \frac{V_P}{F} \right) \)

Common Mistake: Forgetting the sign! If your target Beta (\( \beta^* \)) is lower than your current Beta, the result will be negative, meaning you should sell (short) futures. If you want to increase your Beta, the result will be positive, meaning you should buy (long) futures.

5. Rolling the Hedge Forward

What happens if you need to hedge for two years, but the longest futures contract available only lasts six months? You use a Rolling Hedge (also known as "Stack and Roll").

Step-by-Step Process:
1. Enter a futures contract that expires in 6 months.
2. Just before it expires, close out that position.
3. Immediately enter a new 6-month futures contract.
4. Repeat this until your 2-year horizon is reached.

Important Note: Rolling hedges introduce extra risk because every time you "roll" the contract, you are exposed to the basis at that specific time. If the market is in a weird state when you roll, it could cost more than expected!

Summary Checklist

Before moving on, make sure you can:
- Identify whether a Short or Long hedge is needed.
- Define Basis Risk and understand why spot and futures prices might diverge.
- Calculate the Optimal Hedge Ratio using correlation and standard deviation.
- Determine the number of Index Futures contracts needed to adjust a portfolio's Beta.
- Explain how Rolling a Hedge works for long-term protection.

Don't worry if this seems tricky at first! Hedging is all about matching what you have with an opposite position in the futures market. Practice the formulas a few times, and it will become second nature.