How do options traders look at their portfolios? Professional managers have numerous option strategies and techniques they use when managing a portfolio of options and cash positions. This article outlines some of these techniques and strategies.
Option Strategies
There are a number of option strategies that a professional trader can use, including using the options “Greeks” to manage a portfolio of options and cash positions. Here we will examine one method commonly employed in the foreign exchange (Forex) options markets. Naturally, different traders use different techniques according to their various management styles.
Options Strategies: Greeks, Forwards, and Risk
Risk Assessment
In this case, we will focus upon the options “Stepladder” report, generated by most option risk management systems. When managing a portfolio of options, it is inconvenient and inefficient to think of them on an individual basis. Indeed, a commercial bank’s Forex options trader may have hundreds or thousands of options positions with different maturities in his portfolio at any given time. In addition to his options position, the options trader will have cash positions as well. Therefore, there is a definitive need for a mechanism for describing the risk in the position at any given point in time and for a given underlying or spot rate.
With most option strategies, at a basic level, there are three kinds of risk to which the options portfolio is exposed: movements in the spot rate, convexity, and implied volatility. Delta-hedging can help insure against the exposure of an individual option to small changes in the spot rate. We also know that the delta value for an individual option will change as the spot rate changes, mostly because of the way the option’s price reacts to changes in the underlying spot rate. This is represented in the option’s “gamma” value. We also know that the option’s value will vary with changes in the implied volatility, which the market assigns to a particular maturity and strike.
Foreign Exchange Options
For option strategies involving a Forex option, we are talking about options on a forward. A forward obligates the buyer to exchange one currency for another at a pre-set rate for a particular delivery date. For example, a large consulting firm might enter into a contract on January 5 that pays it $10 million US dollars for delivery into its US dollar account for whatever value the currency is worth on February 2. If the market is working in their favor, they may want to lock in the current rate of exchange being used for February 2. If the spot rate is 1.50, this might imply a rate for February 2 of 1.5010. The difference, 0.0010, is called the “forward premium.” The forward premium is determined by interest rate arbitrage and is sensitive to the difference in interest rates between Canada and the United States. The consulting firm sells US dollars to ABC Bank for their February 2 value at 1.5010. Then, on February 2, it must deliver $10 million US dollars into ABC Bank’s US dollar account, in exchange for which ABC Bank will deliver $15,010,000 Canadian dollars into the consulting firm’s Canadian dollar account for their February 2 value, regardless of the prevailing Canadian dollar spot exchange rate.
A Forex option is an option on a forward because it gives the holder the right, but not the obligation, to exchange, in this case, $10 million US dollars for their February 2 value at a rate (or strike price) of 1.5010. If on February 1, the Canadian dollar is weaker than 1.5010 (i.e. the exchange rate is greater than 1.5010), the consulting firm can let the option lapse and exchange its US dollars at the prevailing spot rate for the February 2 value. (Note that the Canadian dollar has one day of settlement between the transaction and delivery). In this case, February 1 is the option’s maturity date.
Forex Stepladder
Because a foreign exchange option is an option on a forward, it is also sensitive to changes in the interest rate differential. The options dealer will generate a Stepladder report to characterize his portfolio’s exposure to changes in the spot rate, assuming that the interest rate differential for all maturities stays the same and that implied volatilities stay the same. Spot is at 1.50. The report is generated over a horizon of one day. Profit and Loss (P/L), Delta, Gamma and Vega are all denominated in US dollars.
|
Spot |
P/L |
Delta |
Gamma |
Vega |
|
1.5200 |
$67,256 |
$9,257,650 |
$3,240,445 |
$49,010 |
|
1.5150 |
$41,995 |
$7,111,889 |
$2,145,761 |
$46,789 |
|
1.5100 |
$18,554 |
$6,325,789 |
$786,100 |
$44,258 |
|
1.5050 |
$1,401 |
$4,976,111 |
$1,349,678 |
$37,337 |
|
1.5000 |
($11,256) |
$3,120,556 |
$1,855,555 |
$36,112 |
|
1.4950 |
($18,752) |
$125,778 |
$2,994,778 |
$32,145 |
|
1.4900 |
($17,895) |
($10,156,123) |
$10,281,901 |
$31,247 |
|
1.4850 |
($15,443) |
$556,741 |
($10,712,864) |
$34,125 |
|
1.4800 |
($16,742) |
($3,214,748) |
$3,771,489 |
$36,544 |
How do we interpret this Stepladder report? First, let’s consider the fact that this report is generated over a horizon of one day. We know right away that if spot stays at 1.50 without moving at all over the next trading day, we will have lost $11,256. This number is the “time decay” for the options portfolio. The time decay includes the total change in value of all of the options in the portfolio attributable to their maturities being shorter by one day. It also includes the cost of funding our positions. (If we borrow money to buy options, we must pay interest on these balances). All of these considerations inform the option strategies.
The position has a delta of $3,120,556 at a spot rate of 1.50. If spot trades higher (say up to 1.5100 over the trading day) the portfolio will get longer US dollars. We could dynamically rebalance the delta hedge of the portfolio at 1.51 by selling $6,325,789, making us delta neutral at 1.5100. Should spot subsequently dip back down to 1.5000, the portfolio will now be short $3,205,233 (the difference between $6,325,789 and $3,120,556). Buying back $3,205,233 makes us delta neutral again.
At the end of the day, we compare the P/L number implied by the closing spot rate (e.g. ($16,742) at a spot rate of 1.4800) to the spot trading P/L we have earned by dynamically rebalancing the hedge. Hopefully, the net number is positive.
Greeks
There are different ways of reporting the gamma based on option strategies. In this Stepladder report, the reported gamma is the difference between the current spot position and the portfolio’s spot position for a spot rate that is 0.0050 higher. It appears as if we are long an option expiring tomorrow with a strike somewhere between 1.4950 and 1.4900. We can infer this because of the discrete jump in the spot position by more than $10,000,000 between those two spot levels. It is offset by our short position in another option expiring tomorrow with a strike between 1.4900 and 1.4850, suggested by the discrete jump in the spot position of more than $10,000,000 between those two spot levels. This phenomenon is referred to as “strike risk” or “pin risk.” When we have two options expiring on the same day with similar, but not identical, strikes, it can be very challenging to manage the total delta position at expiry if spot is near either of the two strikes.
Finally, there is the “vega” value. At 1.5000, if the Canadian dollar’s implied volatility curve shifted up in a parallel fashion by 1 vol (i.e. by 1 annualized standard deviation), then the portfolio would make $36,112, even if spot did not move. Of course, if spot is not moving, then we are more likely to see implied volatility move lower, which compounds the portfolio’s time decay problem.
Option Strategies Conclusion
Professional options traders use a variety of management techniques in combination with option strategies to dynamically manage and hedge risk, forecast and evaluate volatility, and outline exposure to changes in spot rates.
– Article by Chand Sooran, Point Frederick Capital Management, LLC
Twitter: @csooran
