Decay and Investing: When Time Keeps On Slippin’ Into the Future

With the end of year approaching, the market pace tends to slow down. Between Thanksgiving and New Year's Day we are in holiday mode – wrapping up the year that was and preparing for the year that shall be.  For the lucky among us, that will mean spending time enjoying a warm fire, opening presents and re-watching Trading Places with those we love (I’ve heard some people watch It’s a Wonderful Life, too).

Let’s revisit the amazing ending of Trading Places whereby the heroes, Winthorpe and Valentine, use illegal insider information to enrich themselves at the expense of the Duke brothers.  (It sounds bad in 2016, but in 1983, it was considered okay). How do they do it?  With orange concentrate futures!

Had they been trading equities, they could have chosen to trade either equities themselves or options on those equities. Since they were trading in commodities, however, they couldn’t trade commodities themselves but instead needed to trade futures. Why? 

Oranges are perishable. If you believe the price of oranges will go up over time – perhaps your thesis is that oranges are about to become the next fad diet– you would not simply purchase and store oranges as those oranges will shortly rot. What you can do, however, is purchase the future price of an orange at some distinct point in time – that is, commit to pay a price of "X" (the “futures” price) for a future transaction, instead of doing the transaction today and paying "Y" ("Y" is the current, “spot” price), since you have no means of storing oranges today. 

For all you wannabe commodity traders out there, note that generally X>Y (known as “Contango”).  Thus, if the market price of whatever commodity you are trading in (“Y”) doesn’t appreciate to at least X, the futures investor will lose the value of X-Y when the futures contract expires. 

This means the commodities investor is generally playing at a slight disadvantage – he must invest in futures, and time is generally against him as the value of his future “decays” every day as the contract approaches expiration. (As many underperforming commodity ETFs have demonstrated)

This general concept of “decay” plays out in many financial contracts and investments, and a good understanding of how decay works is instrumental in managing certain investments.

Any product that has a limited lifespan will result in some loss of value as it approaches the expiry date. A simple example is an insurance policy on your house. If you buy a policy for $1,200 that covers fire damage for a one year period, that policy will decline in value by roughly $100 for every month that passes. At the end of the year, the policy is worthless and it is no longer enforceable – it is past its expiration date. Ultimately, the policy holder paid a “premium” in order to protect an investment, in this case, their house.

Options work in similar ways to that insurance policy. A premium must be paid for the right, but not the obligation, to be able to purchase or sell a stock at a specified price at some future point.   

Let’s compare a put option to an insurance policy - the put option can protect the current value of a stock against decline, just like an insurance policy protects the value of your home from decline due to fire damage.  As the option ages, it gets “used up” and its value decays.  

Let’s use a concrete options example: an investor has a particular concern about a short-term market decline hurting his portfolio. On November 1, 2016, he decides to purchase protection for his portfolio with a “deductible” of 7.5% - he eats the first 7.5% of losses and none thereafter. He purchases a put on the S&P 500 that is 7.5% out of the money (meaning 7.5% below the current level of the market) that expires on January 15, 2017, providing him with 2.5 months of insurance.

At the timeI wrote this article on Nov. 1, the price of this option is $2.24, which translates to a cost of 1.05%. If the market stays constant or appreciates through January 20, 2017, then 100% of this cost is lost – like paying for fire insurance and not having a fire. 

Note the rate of decay to expiration is not linear but rather geometric. 

Following is a graph of the expected daily decay of this 7.5% out of the money put option:

Expected Daily Decay As can be seen, the cost of decay is higher initially but as the probability of actually piercing the put level declines, the decay tails off. An interesting outcome of this geometric decline, is that a much longer term put (e.g., a 12-month put) would decline in value less between now and January 20th than a 2.5 month put. 

Thus, our crafty friend could buy the 12-month put and simply sell out of it on January 20, giving himself the same protection at less cost (approximately 20% less cost), since the decay of the 12-month put over 2.5 months would be less than the decay of the 2.5 month-put over 2.5 months. 

Here’s some numbers behind the analysis: the price of a 7.5% out-of-the-money October 31, 2017 put is $9.84 (4.63%) (assuming current market characteristics). Between November 1 and January 20th, given market levels and characteristics remain the same, the put would expect to decline $1.84, materially less than the short term put cost of $2.24 mentioned earlier.

Below is a graph illustrating relative decay over the time period:

Relative DecayThis may seem like a no-brainer situation (or even an arbitrage play), but it’s more complex than we are able to describe here due to differing characteristics that will affect it, including, among other items, the sensitivity to changing market prices and volatility. 

Let’s introduce one more wrinkle in time – season. Traders recognize that some days are slower than others, and the entire month of December is typically slow. Thus, option market makers may price in a lower cost to purchase downside protection during these times of year – e.g., when I was a trader on the exchange floor, I would move my machine’s date forward to see how the options in the particular securities I was trading would price five days later, and at times I would start moving the pricing forward early, speeding up decay. 

This may appear to be a meaningful change to outsiders (e.g., volatility is super low!), but all it demonstrates is that the odds of anything occurring have been artificially reduced by the calendar.

In conclusion, the increased use of options and forwards (e.g., VIX-based products and commodity-based products) by both individuals and funds make an understanding of decay a useful tool to investors. Conversely, not understanding decay has repeatedly hurt investors (e.g., not understanding contango and what impact it has on commodity funds), so it behooves market players to have at least some familiarity. 

So this holiday season as you watch the morally ambiguous Winthorpe and Valentine trade in futures, recognize the role decay plays in your investment outcomes. 



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