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Greek Lessons: Theta Explained

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Theta & the Nature of Time Decay in Options Contracts

There is a com­mon the phrase, ‘some things in life are all about tim­ing’. In regards to options con­tracts, tim­ing is an extreme­ly impor­tant vari­able in deter­min­ing price or val­ue of the con­tracts.

Theta, in options ver­nac­u­lar, refers to degen­er­a­tive impact of time on the price of an option con­tract. An option con­tract offers the buy­er the right, but not the oblig­a­tion, to buy (call) or sell (put) a secu­ri­ty or oth­er finan­cial asset at an agreed-upon price (the strike price) dur­ing a cer­tain peri­od of time or on a spe­cif­ic date (exer­cise date).

How does one val­ue such an instru­ment? The answer involves the con­cept of time decay.

Fis­ch­er Black, Myron Scholes, and Robert Mer­ton answered this ques­tion in the ear­ly 1970’s with the famous Black-Scholes option pric­ing mod­el. With­out going into the gory details, the mod­el says sev­er­al inputs are nec­es­sary to val­ue an option, includ­ing the cur­rent price of the asset, the volatil­i­ty of the asset’s price, the agreed upon price that the asset can be bought or sold, and the time frame over which the option is valid.

Expiration and Time Decay

That last vari­able, the time val­ue of the option, is worth explor­ing in more detail. The clos­er the expi­ra­tion date, the low­er the time val­ue is of the option. This is known as “time decay” or “theta decay”. An impor­tant fea­ture of time decay is that it does not hap­pen in a straight line. Time decay starts off slow and then accel­er­ates as the expi­ra­tion date draws near. The graph below illus­trates the notion of time decay.



Source: Swan Glob­al Invest­ments

Any­one who ever bought a tick­et from a scalper to a sport­ing event should be famil­iar with this phe­nom­e­non. The tick­et is like an option; it is an option to attend the event. How­ev­er, as soon as the game is over the tick­et is worth­less. If the big game is a month or two away the scalper’s price will fluc­tu­ate a bit depend­ing upon the demand for tick­ets. But if the demand for seats isn’t there, the price of that tick­et starts to drop in the days and hours lead­ing up to kick-off. The scalper doesn’t want to be left hold­ing a bunch of unsold tick­ets (i.e., expired options), so a tick­et sell­ing for $200 a month ago might be had for $10 just before the game starts. This is an exam­ple of time decay.

A key com­po­nent of Swan’s Defined Risk Strat­e­gy (DRS) is to active­ly man­age time decay. Swan pur­chas­es long-term two-year put options to help pro­tect its mar­ket hold­ings against down­turns. Hence the name, defined risk strat­e­gy.

How it Works  -

  1. Dur­ing the first year, the mar­ket posi­tion has pro­tec­tion while the put option is exposed to a small amount of time decay. The DRS then avoids the sec­ond half of the above chart by sell­ing off the option in the sec­ondary mar­ket about a year before expi­ra­tion.
  2. Then, the hedge is re-estab­lished by pur­chas­ing a new two-year LEAP. By engag­ing in this “rolling hedge” strat­e­gy, the DRS is not left hold­ing a bunch of worth­less, expired put con­tracts at the end of the year.

This is a much more effi­cient, cost-effec­tive way of Pro­tect­ing a Port­fo­lio Against Sys­tem­at­ic Risk and is rather unique to Swan’s DRS.


Impor­tant Dis­clo­sures: Swan offers and man­ages the pro­pri­etary Defined Risk Strat­e­gy (“DRS”) for its clients includ­ing indi­vid­u­als, insti­tu­tions and oth­er invest­ment advi­sor firms. Swan’s DRS per­for­mance results here­in are of the DRS Select Com­pos­ite which includes all non-qual­i­fied accounts. Addi­tion­al infor­ma­tion regard­ing Swan’s com­pos­ite poli­cies and pro­ce­dures for cal­cu­lat­ing and report­ing per­for­mance returns is avail­able upon request. All Swan per­for­mance results have been com­piled sole­ly by Swan Glob­al Invest­ments and are unau­dit­ed. Oth­er per­for­mance return fig­ures indi­cat­ed in this mate­r­i­al are derived from what Swan believes to be reli­able sources (i.e., S&P 500 index, oth­er index­es and bench­marks), but Swan does not guar­an­tee its reli­a­bil­i­ty. This analy­sis is not a guar­an­tee or indi­ca­tion of future per­for­mance. Invest­ments in for­eign secu­ri­ties involve addi­tion­al risks includ­ing cur­ren­cy risk. Ref­er­ences to the S&P 500 and oth­er indices and bench­marks are for infor­ma­tion­al and gen­er­al com­par­a­tive pur­pos­es only. Index­es are unman­aged and have no fees or expens­es. An invest­ment can­not be made direct­ly in an index. The adviser’s depen­dence on its DRS process and judg­ments about the attrac­tive­ness, val­ue and poten­tial appre­ci­a­tion of par­tic­u­lar invest­ments, ETFs and options in which Swan invests or writes may prove to be incor­rect and may not pro­duce the desired results. Swan Glob­al Invest­ments, LLC, Swan Cap­i­tal Man­age­ment, LLC, Swan Glob­al Man­age­ment, LLC and Swan Wealth Man­age­ment, LLC are affil­i­at­ed enti­ties. Fur­ther infor­ma­tion is avail­able upon request by con­tact­ing the com­pa­ny direct­ly at 970–382-8901 or 021-SGI-052815

By |2018-10-02T15:08:21+00:00June 16th, 2015|Blog|Comments Off on Greek Lessons: Theta Explained