Advancing the option idea

Continuing our series of tutorials on risk management tools, here, in the first of a two-part article, we look at the workings of advanced option strategies.

In the previous article in this series of tutorials, we introduced the basics of options (see EPRM December 2001, pages 32–34). Here, in the first of a two-part discussion, we turn our attention to advanced option strategies.

Calls and puts – which are described in the last month’s article – can be used for price speculation, but are also very useful as hedging instruments.

Someone who has purchased a product – that is, who is long that product – and is concerned about downward price movement can buy a put, giving the right to sell that product as described last month.

And someone who has sold a product – that is, who is short that product – could buy a call, giving the right to buy the product at a predetermined price, and therefore giving protection against unwanted upward price movement.

This price protection feature, and the availability of numerous strike prices, greatly expands the number of ways we can speculate or hedge. And it is possible to tailor our position even further by using a combination of options rather than simply buying a call or a put.

How to put these combinations together in order to best match our price expectations or exposures is the topic of this two-part article.

AT-EXPIRATION ANALYSIS

The building blocks of these more advanced option strategies are the at-expiration profit-and-loss (P&L) profile graphs printed in the introductory options article (see figures 1 and 2).

Using options on crude oil futures as our example, a $20.00 call – an option giving the right to buy crude oil at $20.00 a barrel (bbl) – that costs $0.60/bbl to buy would have a P&L profile at expiration, as shown in figure 1.

At futures prices below $20.00, the option is not worth anything, since we can buy the crude oil cheaper in the futures market than through exercise of the option. A loss would then be realised on that option, equalling the amount of premium we paid for the option. In our example, the loss would be $0.60/bbl.

But at futures prices above $20.00, the option would be exercised. At $20.60, we would recoup the investment in the option, and for every cent above $20.60 we would make another cent in profit on the call. The seller of that option, of course, would have a profit at those futures prices for which the buyer shows a loss, and a loss at those futures prices for which the buyer has a profit – it’s a zero-sum transaction. A $20.00 put would have a P&L profile that is the mirror image of that for the call – as it gives the right to sell, it would profit if futures prices fall below the strike price. Its profile is shown in figure 2.

Since there are many available strike prices, two types of options, and the ability to both buy and sell these options, there are many possible combinations. Over time, a number of strategies have been developed that have proved useful in certain circumstances.

The ultimate aim is to put together a P&L profile for the combination that shows a profit in the price range we most expect to see if we are speculating, or in the price range we have the most exposure to if we are hedging. Building these P&L profile charts when multiple options are involved is simple – for each futures price, just add up the gains and losses for each option.

Since the lines on the P&L profile charts are either horizontal at the underlying prices at which the options are not exercised, or rise or fall at a 45° angle at the underlying prices at which the options are exercised, this can be done easily using a piece of graph paper.

STRADDLE STRATEGY

The simplest combinations involve the purchase or sale, not of a call or a put, but of a call and a put at the same time. These are generally speculative positions, since we would not usually need to hedge against both falling and rising prices.

If we were to buy our $20.00 call for $0.60/bbl, and our $20.00 put for $0.60/bbl, we would pay a total of $1.20/bbl. But at futures prices above $20.00 our call would start making money, and at prices below $20.00 our put would start making money. The P&L profile of this strategy, called a straddle, is shown in figure 3.

This is a strategy we would use when we expect to see a very volatile market but are unsure of which direction the market will move. An example in the crude oil market would be the situation just before a meeting of the Organisation of the Petroleum Exporting Countries (Opec). In equity markets, it would be just before an earnings announcement or a press conference at which important news will be announced, while in foreign exchange markets it would be at a time of great political instability in a country.

As discussed in the previous options article, greater market volatility boosts the value of both calls and puts, so this strategy, being long both, should profit handsomely. If, on the other hand, we expect the market to be tranquil, with no significant price changes in either direction, we would be tempted to sell the straddle and collect that $1.20/bbl in premium.

If we are correct, and the futures market stays around $20.00/bbl, then there would not be a large enough futures price gain or fall to offset the premium we collected, and we would then show a profit on the strategy. If, however, we are wrong, and there is a significant price move in either direction, we would lose out. The P&L profile for selling the straddle would be the same as for buying it, but upside-down (see figure 4).

STRANGLES AND BUTTERFLIES

What if we were still expecting to see a significant price move, but were unwilling to pay $1.20/bbl for the straddle? Is there a way to cut down the cost of this strategy? There are in fact two possible approaches, each of which has advantages over the other in certain circumstances – one is called a strangle and the other a butterfly.

The strangle is the simpler of the two. Instead of buying a $20.00 call and a $20.00 put, we could buy a $21.00 call and a $19.00 put. This could reduce the cost considerably, depending on volatility levels and the time left until the options expire. Of course, with reduced cost comes reduced rewards – a greater price move would be needed before this strategy would pay out.

If, for example, the strangle cost $0.75/bbl, we would have to see a move above $21.75 before the profit from the call would offset the premium cost of the options, or a move below $18.25 before the profit from the put would do so. For the seller of a strangle, the wider profit range would come at the cost of lower premium collection, and, therefore, lower potential profit.

In the case of the butterfly strategy, we would still buy the $20.00 straddle, but then would sell a strangle to reduce the cost. Say we sell the $18.00/$22.00 strangle – the $18.00 put and the $22.00 call – for $0.50/bbl. The net cost of the strategy is then reduced to $0.70/bbl. The $20.00 call still starts making money as the futures price moves above $20.00, and the $20.00 put still starts making money as the futures price falls below $20.00, but the call and put we sold limit the amount of profit we could make.

At a futures price of $22.00, the $20.00 call has made a full $2.00/bbl, easily making up for the net $0.70/bbl cost of the strategy. But at futures prices above $22.00, the further gains from the $20.00 call we bought are offset by losses on the $22.00 call we sold. Profit is capped at $1.30 – the $2.00 profit less the $0.70 premium cost.

The same principal holds for prices below $18.00. Profits from the $20.00 put we bought are offset by losses on the $18.00 put we sold, and profits are again capped at $1.30. If these strategies prove too expensive, we can reduce costs even further by combining them. In this case, we could buy the $19.00/$21.00 strangle, and sell a $17.00/$23.00 strangle.

This is similar to the butterfly, where we bought a straddle and sold a strangle against it – in this case, we are buying a strangle and selling a wider strangle against it. This is called a condor.

The P&L profiles of the three strategies just described are shown in figures 5, 6 and 7.

Straddles and strangles are often bought or sold at-the-money, meaning that the strike prices of the calls and puts that make up the straddle are roughly equal to the then-current futures price, and the strike prices of the calls and puts in the strangle are roughly equidistant from the then-current futures price.

One strategy used by option sellers who have a particular expectation of where futures prices will be when option expiration occurs is to sell a straddle or strangle centred on that expected price.

If, for example, futures prices are now at $20.00 but we expect prices to rise to $21.00 by expiration, then we would sell the $21.00 straddle. Since the $21.00 put is in-the-money, we would collect more in premium for this straddle than for a $20.00 straddle, and if we are correct in our expectations the payout would therefore be much higher.

LOOKING TO HEDGING

The strategies we have examined in this article are admittedly of little use in hedging. When hedging a price exposure, we are usually looking for an instrument that will show a profit when prices go in one direction or another, in order to offset losses incurred by the position which we want to hedge.

In the next issue of EPRM, we will look at some directional strategies, which can be used both for speculation and hedging.

Doug Coyne is an energy consultant and faculty at The Oxford Princeton Programme headquartered in Princeton, New Jersey. He is based in Woodbury, Minnesota.
e-mail: dcoyne@oxfordprinceton.com

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