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# The Greeks: Theta

Martin Noël
March 28, 2017
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This week, we will look at another Greek variable: theta. Theta measures the change in the price of an option following a change in the time remaining to its expiration. You will recall that an option’s premium has two components: intrinsic value and time value. But since an option that has reached expiration has run out of time, its value has become equal to its intrinsic value. This means that whoever buys such an option can expect to lose 100% of its time value. If the investor is to make a profit on such an option, this loss will therefore need to be offset by a corresponding increase in its intrinsic value, which will need to reach the option’s breakeven price. So time value decays, to the detriment of the option holder, and this decay is favourable to the writer of the option. Investors can use theta to estimate the amount of decay in an option’s time value from one day to the next.

For example, consider an investor who is bullish about the prospects for shares of George Weston Limited (WN) and who decided to buy ten call contracts, WN 20170421 C 110, at \$3.75 on Friday, March 17, 2017 when WN was trading for \$112.43 at market closing. The intrinsic value of this option was \$2.43 (\$112.43 – \$110.00), and its time value was \$1.32 (\$3.75 – \$2.43). The investor is therefore certain to lose \$1.32 per share, or \$1,320 for 10 contracts, over the course of the 35 days left until expiration on April 21, 2017. To make up for this loss, the price of WN will need to increase to the breakeven price of \$113.75 (\$110.00 + \$3.75), i.e. by an amount equal to the option’s intrinsic value of \$1.32.

As we can see in the above table, the call WN 20170421 C 110 has a theta of -0.0391. This means that this option will lose close to \$0.04 per share every day until expiration on April 21, or close to \$3.90 for each contract held (\$39 per day for all 10 contracts). Let us assume that the investor considers this loss of time value to be too great, and wants to reduce it as quickly as possible. One of the possibilities is to go short on another call to benefit from its decaying time value.

Therefore, as we can see in the above table, the investor can transform the held position into a bull call spread by writing 10 calls, WN 20170421 C 115 at \$0.90. This will reduce the negative impact of theta by \$0.0261 per share, or by close to \$26 per day. This brings the total negative impact of decaying time value to only \$13 per day (\$39 – \$26), or \$420 in total, from now until expiration on April 27, 2017, compared to an initial impact of \$1,320.

However, since in finance there is no such thing as a free lunch, this reduction in the risk posed by decaying time value also comes with a smaller potential profit should the price of WN rise. We began by going long on 10 calls, WN 20170421 C 110 at \$3.75, which would allow us to profit from any increase in the stock price above the breakeven price of \$113.75, but then we wrote 10 calls, WN 20170421 C 115 at \$0.90, creating a bull call spread with a lower breakeven price of \$112.85 (\$113.75 – \$0.90). On the other hand, we also limited our maximum profit to only \$2.15 per share (\$115 – \$112.95), for a total maximum profit of \$2,150 on the 10 contracts.

Investing involves making choices, and options give us more choices by allowing us to fine-tune our risks based on several variables. This is clearly a benefit, since it lets us adjust our risk-return profile to suit our objectives. The use of theta allows us to better contain the risk incurred as a result of decaying time value. We need to keep in mind that each adjustment that helps us in one way will work against us in some other way. Such compromises must be made in order to attain our goals.

Note that there are several other strategies that allow us not only to limit or reduce the adverse effect of decaying time value, but also to profit from such decay. These are called neutral or non-directional strategies, and we will be looking at some of them over the next few weeks.

The strategies presented in this blog are for information and training purposes only, and should not be interpreted as recommendations to buy or sell any security. As always, you should ensure that you are comfortable with the proposed scenarios and ready to assume all the risks before implementing an option strategy

Martin Noël http://lesoptions.com/

President

Monetis Financial Corporation

Martin Noël earned an MBA in Financial Services from UQÀM in 2003. That same year, he was awarded the Fellow of the Institute of Canadian Bankers and a Silver Medal for his remarkable efforts in the Professional Banking Program. Martin began his career in the derivatives field in 1983 as an options market maker for options, on the floor at the Montréal Exchange and for various brokerage firms. He later worked as an options specialist and then went on to become an independent trader. In 1996, Mr. Noël joined the Montréal Exchange as the options market manager, a role that saw him contributing to the development of the Canadian options market. In 2001, he helped found the Montréal Exchange’s Derivatives Institute, where he acted as an educational advisor. Since 2005, Martin has been an instructor at UQÀM, teaching a graduate course on derivatives. Since May 2009, he has dedicated himself full-time to his position as the president of CORPORATION FINANCIÈRE MONÉTIS, a professional trading and financial communications firm. Martin regularly assists with issues related to options at the Montréal Exchange.

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