The Time Decay of Options

December 1998

 

Options are instruments which give the holder the right to buy or sell a fixed quantity of a specific asset (the 'underlying asset') at a specific price (the 'strike price' or 'exercise price') prior to a specific date (the 'maturity date' or 'expiration date'). The underlying assets can be equities, indices, commodities, fixed income securities, currencies or futures contracts. Call options give the holder the right to buy the underlying asset at the strike price, while put options give the holder the right to sell the underlying asset at the strike price. In either case, holders are not obliged to exercise their right to buy or sell if it would be less costly to buy or sell at the prevailing market price -- in such instances, the option simply expires unexercised with no penalty to the holder.

People buy options for different reasons. Call options allow investors to lock in a purchase price if they wish to buy a stock at a later date, while put options are often purchased as a form of insurance against an unanticipated drop in the price of an asset or assets held in a portfolio. Because option values are primarily derived from price movements in the underlying asset (hence the term 'derivative'), options allow investors to benefit from the upside potential of the underlying asset without having to make the full cash outlay or margin payments. While many investors purchase options as part of their broader portfolio strategy, options can be actively traded in their own right.

One factor that option investors must bear in mind is that options are a depreciating asset: all else being equal, an option's value declines over time, and may in fact be worthless at maturity. This is known as 'time decay', and should be understood by investors before they start trading options. Option valuation is based on a number of factors: the underlying asset price, the strike price, interest rates, time to maturity, and volatility in the underlying asset price. Holding all other factors constant, call prices are positively related to the underlying asset price and interest rates, while put prices are positively related to the strike price. Both calls and puts are positively related to volatility (more volatility is always good for options), and negatively related to time to maturity.

 

Option Value

Option prices are made up of two components. The first is the option's 'intrinsic value', which is the value of the option if exercised today. For calls, the intrinsic value is the asset price less the exercise price (or zero if the exercise price exceeds the asset price), and for puts, the intrinsic value is the exercise price less the asset price (or zero if the asset price exceeds the exercise price). The second component is the option's 'time value', which represents the value associated with being able to exercise the option at a later date. Since there is always some probability — no matter how remote — that an option will have a positive payoff at expiration, time value will always be positive, even if intrinsic value is zero. In short, the time value reflects the probability of receiving a payoff above and beyond the option's intrinsic value at some point prior to expiration. The premium paid for this time value is a function of market conditions (interest rates and volatility) and the length of time left before the option expires. As the option gets closer to expiration, time value is worth less and less, since the distribution of possible option payoffs gradually converges to the option's intrinsic value. At the expiration date, time value shrinks to zero and the option value is equal to its intrinsic value.

Time value isn't a linear function. In other words, while time value shrinks to zero over the life of the option, this process starts out slowly and accelerates closer to the maturity date. Figure 1 shows the time decay of an at-the-money option (an option whose strike price equals the underlying asset price). As can be seen from the diagram, half of the time decay of this six month option occurs within the last 60 days of the option's life. Most options traded have fewer than three months to maturity. In other words, the most trading volume in the options market relates to options subject to the rapid time decay at the far right of the diagram in Figure 1.

Figures 2 and 3 show the time decay for an in-the-money option (an option whose intrinsic value is positive) and an out-of-the-money option (an option whose intrinsic value is zero), respectively. Initially, these options tend to lose their time value at a faster rate than at-the-money options: a six month option that is either in-the-money or out-of-the-money by 10% will have lost almost 60% of its time value within two months of expiration, while at at-the-money option will have lost less than half of its time value. As the option reaches maturity, however, time value decreases at a much higher rate for at-the-money options.

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In-the-money options will always afford a higher value than either at-the-money options or out-of-the-money options by virtue of their intrinsic value. While Figure 2 and Figure 3 demonstrate that in-the-money and out-of-the-money options are subject to similar time decay, the vertical axis measures time value only. The y-intercept on Figures 1, 2 and 3 does not include intrinsic value. For an in-the-money option with an underlying price of $110 and an exercise price of $100, the value to which a call option will ultimately converge is $10. Another point worth mentioning is that while the diagrams depict the time decay for call options only, put options follow essentially the same pattern. A put's payoff schedule mirrors that of a call option (puts are out-of-the-money when calls are in-the-money, and vice versa), but the time decay features are identical between the two in most instances. The only times for which put options behave different from call options is when they are deep in-the-money — i.e. when the strike price is significantly higher than the underlying price such that there is very little chance of the stock rising enough to render the put worthless. In such cases, puts tend to lose all of their time premium faster than deep in-the-money calls.

 

Option Strategies

Time decay has implications for investors wishing to trade options. Time erodes the total value of an option, all else being equal, which favours sellers. Consider the purchase of a three-month out-of-the-money call option on a stock the investor believes is poised for a significant increase. If the stock remains flat over the first 30 days, the option holder has just lost about 40% of the initial investment through time decay alone (and even more if the stock price falls). The investor may even lose money if the stock increases, if the increase isn't large enough to offset the time decay. It is possible to be correct in predicting a stock price movement yet still lose money buying options — for instance, if the increase isn't large enough to make up for time decay or if the movement fails to manifest itself prior to the option's expiration date.

When buying options, investors should buy value, just as they do for stocks. Options that are at-the-money or slightly in-the-money offer two advantages over out-of-the-money options. First, if the underlying asset price moves less quickly or less dramatically than expected, the loss on investment will be smaller than it would be for out-of-the-money options due to the slower time decay. Second, as the underlying asset price increases, at-the-money and in-the-money options appreciate by a greater dollar value than out-of-the-money options due to the fact that their intrinsic value increases, while the intrinsic value of an out-of-the-money option remains zero (at least until the underlying price increases enough to equal the strike price). There is, however, a caveat to buying these options: at-the-money and slightly in-the-money options are more expensive than out-of-the-money options due to their intrinsic value and higher probability of earning a positive return, and therefore offer less leverage than out-of-the-money options which tend to be fairly inexpensive. For a given percentage increase in the underlying asset price, the percentage change in an out-of-the-money option is higher than for the other two options. Due to their higher price, these options increase an investor's total risk — the premiums on these options are much higher than out-of-the-money options, yet there is still a non-trivial chance that they will expire worthless, particularly in volatile markets.

Option buyers are best advised to establish a dollar amount that they are willing to risk for one trade, and purchase at- or in-the-money options with these funds. They should also select options with five or six months to maturity rather than 30 to 90 days, since options in the latter group are subject to a sharp drop in time value as expiration approaches.

For option sellers, the objective is to capture the premium without having to fulfill their obligation when an option is exercised against them: if an investor owns a stock valued at $50 and sells a three-month call option with a strike price of $50, the investor keeps the option premium today and hopes that in three months, the stock will be worth more than $50 such that the option holder won't exercise his right to buy it. For sellers, time decay works in their favour. At-the-money options offer the greatest premium per unit of time due to their time decay profile — they lose the most value in the last two months prior to expiration.

A 'covered call' is an option strategy in which an investor sells a call option on an asset that he or she already owns. Investors selling at-the-money options as part of a covered call strategy will maximize their returns with options that have 75 to 135 days until expiration. Investors selling out-of-the-money calls should look for options with slightly longer terms to maturity, in the range of 120 to 150 days. When an investor sells out-of-the-money calls and the stock remains unchanged, one strategy is to buy the calls back one month prior to expiration when they trade at a very low premium. This locks in a profit equal to the change in the call price from the date it was sold to the date it is repurchased (equal to the time decay, all else being equal), and ensures that the option will not be exercised if there is a sudden change in the stock price.

An 'uncovered call' is an option strategy in which an investor sells a call option on an asset that he or she doesn't already own. This is riskier than a covered call strategy, since the writer (seller) would be obliged to purchase the asset at the (higher) market price and immediately sell it at the (lower) strike price if the option was exercised. Since there is no upper bound to stock prices, the potential loss from this strategy is unlimited. Uncovered option sellers should select a much shorter time frame than covered option sellers. Out-of-the-money options should be sold 4 to 5 weeks prior to expiration, and sometimes even sooner. At-the-money options can be sold as late as a few days prior to expiration.

 

Choose Strategies Carefully

Options are conceptually very easy to understand, yet their pricing dynamics are fairly complex. Time decay is one feature of options that must be taken into consideration when considering the purchase of sale of options as part of a broader investment strategy. Understanding how time decay affects options at-, in-, or out-of-the-money will help investors make informed decisions about how to maximize returns from their option strategies.