Hedging risk versus return diversification and options on futures

Download images options on futures

It might be good to diversify. It is a good idea to have large negative correlation. If you take a long position in short the other the correlation should be negative as long as the basis behaves reasonably. If the basis is high this is an ideal opportunity for diversification.

When you set up your portfolio for optimal hedge you will have a cash position of RC with the futures position of RF. This is the return on both positions in the change.

Three turn on the hedge is the difference between return on the cash position and return of the cash future. H would be that it hedge ratio on the fraction of the cash position which is hedged.if h is equal to one that hedge ratio is 100%. RC and RS will always be unknown at that point of knowing the hedge. If h is equal to one and the cash and future went up 10%, If you short futures there would be a -10% on RF and a +10% on the RC. You can eliminate any price changes. It’s all revolves around portfolio theory.

You need to look at the variance of the position. You need to look at the variance of the cash position and future position. Depending on how they move together

Refer to the variance chart attached

The idea putting together a portfolio of futures and cash. Trying to minimize risk on the return. You’re trying to minimize risk to get a given return. You minimize the top equation but taking the first order condition to choose H. This is to find the optimal hedge. To Minimize the variance we take the first or condition differentiated with respect to H define h*. Depends on the covariance between cash and futures in the variance of futures. This is the regression coefficient

Look at next variance image chart attached

You rewrite the optimal hedge to put it into a more intuitive framework. There is an equation of the co relation coefficient used from statistics.

If you choose has the same or higher price volatility in the cash,h* has no greater then correlation coefficient between them which is less than 1.0 at absolute value.

Normally h* is less than 1.0

You substitute the correlation coefficient into the optimal heads rate. This is equal to the correlation coefficient,

if there’s no basis risk to correlation coefficient is equal to one. If cash and futures move exactly parallel to each other, Sigma c and Sigma F will equal each other. Rho The correlation coefficient and optimal hedge ratio should equal one. This is not typical.

Optimal hedge assumptions

A risk averse hedger

Fix long cash position

Short futures position combined with cash

Each portfolio of cash and features can be evaluated on the merits of its expected return and variance

Long cash position earns a higher put risk your expected return going to combine cash and futures has position

Hedges are not speculating on price expectation

If you have different optimal hedge ratios you will have different portfolios. You then need to evaluate each portfolio based on its expected risk and return.

You put an E in front of the RC because you don’t know what the expected return will be. Going into the head you will expect there will be a return on the cash position. If you set H equals one that is perfectly correlated so the expected return of hedge is equal to zero.

A return to an unhedged position return on the cash position will be greater than zero but will carry a high variance. This makes it much riskier.

See risk and return photo attached

Risk first hedgers are interested in the expected return of the hedge position which is combined with futures i and cash. X axis is the variance of the hedge position which is the riskiness of it. You could go 100% health versus zero percent hedged. This will affect the portfolio for where you are 100% unhedge were just holding cash. There is expected High return with high risk. This point u on the curve. The point H with 100% hedged, you have low return with low risk.if h is equal to .5 it would be halfway between point h and point u. Fronttier which is a risk return of all the alternative portfolios. Shape of the frontier depends on the variance on the future and and the covariance term.

So if we involve optimal hedge which revolves around risk aversion. We choose a point where where this new curve is tangent with the risk return frontier. The risk aversion is an upward sloping indifference curve. If you have the indifference curve I , Frontier provides risk and return of different portfolios, you can find the optimal hedge at point h*. This gives us the minimal risk at the expected return.

If the shape of the H U curve underlying variances and covariances Will get a different h*. You can use historical data to get your expected variance.

Options

Options on future contracts have many counterparts in our economy. For instance US Air Force buys options to access C-17 cargo aircraft. Private air cargo companies like FedEx sell the option. Each aircraft is worth about $300 million in the Air Force reports that save billions of dollars under this arrangement.

This is not options on stock but only options on futures. Options contract is written on a futures contract. For example if you look at futures oil contract there is an option pit next to the oil futures. The option gives you the right as a buyer to a future position but not the obligation. The risks are much different for options by her versus the future buyer. The futures contract you’re obligated to take delivery or accept the settlement price during expiry if it is a non-deliverable contract. An option you have right to obtain the futures contract but you’re not obligated to it. Each option will have a strike price, premium set in the pit, and it will be attached to certain futures month.

For example December crude oil will have a futures price set in the pit. If the price is $30, where The options pit where you can buy call or put options. Call option is the right to to go along in the futures. Production is the right to go short. That option would have a strike price. This is the price you would go long or short. Exchange will set range of strike prices. For oil there may be a strike price ranging from $25-$35. This is when you enter to get that strike price range which is attached to a certain month. There will be a pit that will trade call options with a right to go long. If you strike prices thirty dollars if you’re interested in. If the futures price is $30, you say the option is at the money. This is because the strike price the same as the future price. If you expect the future price of oil to rise in the next few weeks.

Also buy call option but this gives you the right. To obtain a futures contract at the strike price if the strike price is $30. You’re buying the right to long at 30 in December.. If the oil price dropped from $30-$20, you long 30 you will be losing a lot of money since you long at 30. If you buy the call option then you’re buying the right

If you buy the call option your find the right option when the future dropped from 30 to 20, option becomes worthless. In order to obtain the right to go long at $30 you had to pay the premium at that time. If you buy the option to weeks before December the premium on the option will be let’s say a dollar, you can buy it for a dollar per barrel which results in $1000 per contract for the right to go along at $30 per barrel.

Delivery month is December. Strike price is $30 per barrel it is A 1000 barrel contract. The premium could be one dollar Per barrel. The premium is determined in the trading pit. All the other factors are set by the exchange. Strike is determined by supply and demand. In order to buy the option you have to pay for what the market is asking for the premium.

When you buy premium of one dollar a few weeks before the expiry, you can exercise which would give you a $30 per barrel. Or you can sell the option if the premium rises to two dollars per barrel if the price of oil goes up. If the price of oil falls the value Falls below a dollar. As we approach expiry if the price per barrel falls below $30 the value will be worthless.

Options are preferred by speculators because if you know you buy December futures, you worry about the price. If you buy an option to pay a one time upfront premium which is the most you can lose. The risks for the seller a much different as a seller I am obligated to provide the long position if you exercise the option. If you Oil price jumps up the 40, you will exercise the option. The seller will get a call from the clearinghouse telling you the option has been exercised, you need to provide the position to The buyer of the option. The option seller or hedger so it will then get a short position. So if oil rises to 40, the seller of the option will be exposed to more risk. The sellers of options are professionals who expect the value the option to go up. They use probability to calculate the direction of the pricing.

If the trader buys the option, but the option becomes worthless how does the clearinghouse close it off. The buyer can either exercise the option or resell it. The clearinghouse worry about the seller of the option as if the price starts to rise, they know if you shorted or sold a call option at $30. There can be a margin call protect the trader. The margin call is equal to the value loss to protect the buyers of the option. When the trader wants to exercisethey will acquire the long position that $30.

If a trader buys a strike price of $25, if today’s price is $30.The trader buys a position to go long at $25. It will cost more and options pit will sell minimum of five dollars, the premium will go up from five dollars to six or seven dollars.

Most options will expire before the the futures contract. This could be usually 7 to 10 days before.

Will the premium change before the settlement date?

For crude oil December contract which expires in June. Futures price is $30 in December while the price in June is $30. Strike price in December is $25 while June has a $25 strike price. Premium for December 6 dollars. On December the difference between the future and strike price is 30-25 equaling five dollars which is the intrinsic value. So if the trader wants to buy a call option in June, The strike price might be eight dollars. Since there’s more time between now and June, there’s more uncertainty. The more time to maturity the higher the premium will be with everything else constant. This becomes time value. There is no free lunch if you buy futures contracts, you don’t pay premium. All you pay is a small brokerage fee where you get more leverage in a futures contract. If you buy an option you pay a premium. So if you pay a premium of six dollars and the futures price goes up. The trader still breaking even so it needs to go to at least 31 to get a profit. If you buy a futures contract where the price goes from $30-$31, you would’ve made $1000. For options trader you were down $1000 when you start when you choose an option. The premiums can vary depending on supply and demand. Options on futures has less history than futures.

Options: positions and components

Options convey a buyers right but not an obligation to buy [call] or sell [Put] a commodity or asset at a specific price [Strike price] within a specific time.

Buyer pays a premium for this right

Call option is the right to go long in underlying futures contract

Put option is the right to go short and underlying futures contract

PThe writer is the seller of an option does he go short the option

Volatility in the oil market you will pay a higher premium. The maximum loss is what you pay for the premium. Price needs to rise by certain factor in order to return of the premium before you start to make a profit.

If you buy an option with premium of a dollar in the previous oil example. See attached image. So the premium was at the money but the price goes down. The premium will a erode quickly. If this is a case of premium goes out of the money.

The buyer you’re buying the right to go long want to call option. You can exercise it or not. The buyer of a put, you’re buying the right to go short. So if you think prices are going down in a put option, can exercise or sell the option. If you don’t but the price rises, the option becomes worthless

Writer of the options exposed to severe risk unlike the buyer. They do receive the premium upfront so the premium is the most you can make as a writer of the option. If the option becomes worthless for the buyer this is the best scenario for the writer of the option.

The Black scholes Will calculate a fair premium. You can statistically calculate the probability of a commodity price direction.

Options: positions of components

Referr to options positions image

You can buy a call or sell a put. Every buyer there is a seller.

Option components

Buyer

Seller

Underlying futures contract

Strike price

Expiration date

Premium

What can happen to an option?

Option will expire on unknown date so she does do nothing

Exerciser will assume if you choose position at the auction strike price so exercise option

You must buy [sell] an option identical to the one previously sold [bought] so which will offset the option

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