The standard deviation of monthly changes in the spot price...

The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4 . The correlation between the futures price changes and the spot price changes is 0.7 . It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15 . The producer wants to use the December live cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. What strategy should the beef producer follow?

Key Concepts

Basis Risk

Basis risk is the risk that the hedge may not move in perfect opposition to the underlying asset because of differences between the spot price and the futures price. This imperfect correlation, due to factors like timing differences or the use of a cross-hedge, can result in a residual risk even if a hedging strategy is implemented.

Optimal Hedge Ratio

The optimal hedge ratio is the proportion of the exposure that should be hedged to minimize risk, taking into account the statistical relationship between the spot price changes and the futures price changes. It is often computed using the formula: correlation multiplied by the ratio of the standard deviations of the spot and futures prices, ensuring that the hedge is neither under- nor over-sized.

Cross-Hedging

Cross-hedging is a strategy where a futures contract is used to hedge the risk of an exposure in a different but related asset. It is used when there is no direct futures contract for the asset being hedged, relying on the correlation between the asset’s price and the price of the hedging instrument.

Futures Contracts

Futures contracts are standardized agreements to buy or sell a specific quantity of an asset at a predetermined price on a set future date. They are widely used in hedging because they provide liquidity and a benchmark for price movements, allowing market participants to lock in prices and mitigate risk.

Hedging

Hedging is a risk management strategy used to offset potential losses in an underlying asset by taking an opposing position in a related financial instrument. It involves actions such as entering into futures contracts to protect against adverse price movements, thereby reducing uncertainty and stabilizing revenue or costs.

Transcript

00:01 Okay, for this problem, we're going to refer back to some context from a previous problem.

00:06 And we're going to do some adjustments to some mean information that we know about cattle, cow, and steers that are going to be sold at auction.

00:15 So we were told the angus weight, the mean weight of yearly angus steers is 1152 pounds.

00:23 So it's an average for these cattle.

00:28 And the standard deviation is 84 pounds.

00:34 And what we want to know in this case is we want to know, we want to know they want to sell 1 ,000 -pound cows.

00:42 So they want their cows to be over 1 ,000 pounds.

00:48 What they're going to do is they're going to subtract 1 ,000 pounds from the mean to see if we know how that's going to change the mean.

00:56 So that's what we're going to do for this problem.

00:58 So they're trying to get us to see the effect on the information.

01:01 And in the end, we're also going to, so they want us to find the new mean and standard deviation.

01:13 And in the end, they want us to do a little bit of cost analysis on this too.

01:19 So let's go ahead and do this.

01:21 I can write it out at the end.

01:23 So we're going to do this.

01:24 We're going to say, well, let's take this in our plan for this problem.

01:29 We're going to take the mean minus 1 ,000.

01:33 We can do that.

01:35 To just the mean, we want to know what the mean is going to be for if you take cows that are only over 1 ,000.

01:40 So we can take our 1152 minus 1 ,000.

01:47 So now we know our new mean just equals to 1502 pounds.

01:55 All right.

01:59 So you can do that with means...

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