Notes S3 - hedging strategies using futures PDF

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Chap 3 notes – hedging strategies using futures Many are hedgers to reduce risk. A perfect hedge = eliminates all risk. They are rare. We assume the hedge-and-forget strategy: we won’t modify a hedge once it’s been put in place.

Basic principles EX: a company gains 10,000$ for each 1cent increase in price of commodity over the next 3 months. To hedge, we should take a short position: if the price drops 1 cent, we gain 10,000$ and lose 10,000 if the price climbs 1 cent. The gain of the futures position offsets the loss on the rest of the company’s business if the price drops. (50/50) Take a short if scared of price drop, take a long if scared of price increase Daily settlement has a small effect. Means payoff from futures contract is realized through the life of the hedge rather than at the end. Short hedges Short position. Appropriate when we already own (or will own) the asset and expect to sell it in the future. EX: an exporter will realize a gain if EUR increases in value compared to USD. A short futures leads to a loss if EUR increased. This offsets the exporter’s risk. Long hedges Appropriate when a company knows it will have to purchase a commodity in the future and wants to lock in the price now. Sometimes though, it is more worth it to buy the commodity straight away to have it on hand. However, there are interest costs and storage costs. All depends if we need it now.

To hedge or not To hedge: reduced risk. However, many risks are left unhedged. Shareholders: they can hedge directly without having the company doing it for them. However, they have to have as much info as the management about the risks faced by the company. Also, this ignores the commissions and transaction costs. (less expensive to hedge for large transactions than small ones). However, shareholders can diversify risk in their portfolio. Competitors: because of competitive pressures from within the industry, the prices can fluctuate (raw material costs, interest rates, exchange rates). So a company that doesn’t hedge has profit margins that are constant whereas a company that does hedge has profit margins that fluctuate. (no hedge = follow industry trend, hedge = taking a chance and securing a price – unaffected by industry trends). gotta look at the big picture when hedging. ** reasons to not hedge: 1. Competitors are not hedging, 2. Shareholders might not want them to hedge 3. Difficulty justifying a loss on hedge but gain in exposure

Basis risk In real life, 1. The asset that needs to be hedged is not exactly the same as the asset underlying in the futures contract. 2. The hedger may not know the exact date when the asset will be bought or sold 3. The hedge may require the futures contract to be closed out before its delivery month. Basis = spot price of asset to be hedged – futures price of contract used. If the asset to be hedged = the underlying asset of the futures contract, the basis = 0 at maturity. Before maturity, the basis can be positive or negative. As time passes, the spot doesn’t necessarily change by the same amount as the month’s futures price. So, the basis changes. Comes from the hedger’s uncertainty of the difference between spot price and futures price at maturity Increase in basis = strengthening of basis. Decrease of basis = weakening of basis.

effective price paid with hedging. **see paper example** ** if the company uses a short hedge, and the basis increases, the company’s position improves bc it will get a higher price for the asset after futures gains or losses are considered. Vice versa. ** for a long hedge, if basis increases, the company’s position worsens. It will pay a higher price for the asset after futures gains and losses are considered. Cross-hedging: when the asset we want to hedge is different than the underlying in contract. Leads to an increase in basis risk. Price of underlying asset is S*2.

Choice of contract: = key factor affecting the basis risk. The choice of contract has 2 parts: choice of underlying asset & choice of delivery month Usually, we chose the asset the delivery month later than actual delivery because the price of futures during delivery months can be unpredictable. Basis risk also increases as the time difference between the hedge expiration and delivery month increases Most times, if we need to use a long maturity futures contract, we take a short maturity futures contract and roll it forward. Because there is more liquidity in short maturity contracts.

Cross hedging When the asset to be hedged is not the same as the underlying asset. Hedge ratio: ratio of size of position taken in futures contracts to the size of exposure. When the asset to be hedged is the same as the underlying asset, ratio = 1.

We need to choose a value for the hedge ratio that minimizes the variance of the value of the hedged position. We od so by calculating the minimum variance hedge ratio

Minimum variance hedge ratio Depends on the relationship between changes in the spot price (delta S) and changes in futures price (delta F) Minimum variance hedge ratio = h* if the correlation between S and F = 1, and stdevS = stdevF, then h*=1 spot price mirrors the futures price perfectly hedge effectiveness: proportion of the variance that is eliminated by hedging. = R^2 = correlation^2 interpretation: we should hedge by taking a position in asset to be hedged corresponding to 78% of its exposure. The hedge effectiveness=correlation^2  the size of futures position should be 78% of the size of the company’s exposure. A minimum variance hedge leads to no hedging when the coefficient of correlation between changes in the futures price and changes in the price of the asset being hedged is zero.

optimal number of contracts

where settles daily – AKA using forward contracts

we assume that the futures contracts are not

Impact of daily settlement: There are a series of one-day hedges.  the optimal number of contracts or a 1 day hedge

the stdev of a 1 day change in the value of the position being hedged = VAstdevS, where VA = vaue of the position (asset price*QA) stdev of a 1 day change in value of futures position = VFstdevF where VF = futures price *QF

stock index futures stock index tracks changes in value of a hypothetical portfolio of stocks. Weight of a stock = proportion of the hypothetical portfolio invested in the stock. The portfolio may remain fixed, but the weight assigned to each stock in the portfolio is constantly fluctuating according to its price. Settled in cash. All contracts are marked to market to either opening or closing price.

Hedging an equity portfolio where VA = current value of portfolio VF = current value of 1 futures contract futures price*size of contract N* is the number of futures contracts that should be traded. When the portfolio does not exactly mirror the index, we use Beta.  also h* We use hedging in an equity portfolio because we feel we have chose the stocks well but is uncertain about the market performance. **what is the hedge that min risk = calculate N*

Changing the beta of a portfolio if Beta>Beta*, a short position is needed

If B...