During this session we reviewed what type of dealers we can find in the Derivatives Markets (hedger, speculators, arbitrageurs) and we also had a look at how we could hedge with Futures. We gave an example of how a hedger/arbitrageur can become a speculator.
We focused on how to hedge a position. Hedging means buying or selling a financial instrument to offset potential losses/gains that may be incurred by a companion investment.
Usually, if the underlying asset of the Future and the asset that we want to hedge are the same, to determine the amount of contracts that we should buy/sell we should divide the amount (units) of the underlying asset that we want to hedge (in the example, 2,000,000 gallons of jet fuel) by the amount (units) of each contract (in the example, 42,000).
However, if the underlying asset of the Future and the asset that we want to hedge are not the same, we will have to do cross-hedging. When we cross-hedge, two questions arise:
1) What is the hedge ratio that we should apply to determine the number of contracts that we have to buy/sell?
- We use a linear regression where the variable to be explained (y) is the change in price of the asset that we want to hedge and the exogenous variable (x) is the change in price of the Future. With this analysis, we will determine how "y" moves when "x" moves.
- The hedge ratio will be equal to the beta parameter of the regression line (beta = correl. coef * sigma "y" / sigma "x"). Beta means how many units "y" moves when "x" moves by 1 unit.
- In our example, beta = 0.77 (meaning that when "x" moves by 1, "y" moves by 0.77). Then, the number of contracts that we will have to long (I am short the underlying asset, if prices go up, my P&L would be lower) would be 0.77 * 2MM / 42k.
2) How good will the hedge be?
- To determine how good the hedge will be, we must calculate R^2 (R^2 = (Covariance / (Sigma "y" * Sigma "x"))^2.
- Values above 0.75 should indicate that the hedge is quite good.
In the second part of the class, we reviewed how to extrapolate cross-hedging to hedge equity portfolios or single stocks with Futures on an Index.
Why would I want to hedge an equity portfolio?
Typically, if I am long an equity portfolio I would be convinced of the potential positive performance of the portfolio. Then, if I am thinking about hedging, maybe I should sell my portfolio and buy later... There are three reasons to hedge:
- Transaction costs (produced by selling and buying again) may be high.
- Hedging with a Future on an Index would eliminate systematic risk (market risk). I would only be exposed to the relative performance of the portfolio vs. the Index.
- The investment is designed for the long run, while I want to hedge the short run (maybe we are waiting for bad news).
The process of cross-hedging is very similar to the prevous case. First, we must determine the beta of the portfolio. To calculate the beta of the portfolio, we calculate a value-weighted average of the betas of the securities in the portfolio. The betas of the securities that compose the portfolio will be available in Reuters or Bloomberg as beta is a fundamental component of CAPM.
To hedge completely the portfolio, we should long/short a number of contracts equal to beta * Value of Portfolio / Euro Value of Future. Remember that to obtain the Euro Value of the Future we must use the Future multiplier. If I hedge completely my portfolio the beta of my new portfolio (old portfolio + Future) will be equal to zero (it does not matter how the market moves, my new portfolio will not move).
I can also change the beta of the portfolio (reduce/increase it). For instance, if the beta of my portfolio is 1.003 and I want to take it to 2, I will have to long a number of contracts equal to (Objective beta - Current beta) * Value of Portfolio / Euro Value of Future.
You can find the presentation used in class here. You can find the Excel file used in class here. You can find how beta minimizes the variance of the new portfolio here.
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