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My majors are physics and math. I like to trade options for fun.
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  • Option Statistics For Dummies 0 comments
    Jan 8, 2013 8:35 AM | about stocks: MA, SPY, SLV, FFIV, CMG, NFLX, GLD, AAPL, AKAM, V, AMZN, GOOG, BIDU, PCLN

    Introduction

    Option price is affected by underlying security's volatility and it tends to change all the time. So we need a good yardstick to measure the option price. I did a little math for stock options I am particularly in love with. Here at my blog I will describe the results. I used simple option pricing model to see the return one can generate by buying call option and holding it till expiration. The result was averaged over one year and 5-year periods. So if you don't like to do math by yourself find the results below.

    I used some fundamentals for the sake of choice of the stocks. I will describe the procedure later. Few different option strategies will be compared.

    Long Calls

    Let us take for example call option for AAPL. The current implied volatility for near the money calls is 31% (according to http://www.morningstar.com/ ) . I am using historic data for AAPL to see if current IV makes long call option cheap enough to make a positive return. It turns out to be the trades will have positive result only 44% of times during last year (12 months period) but still results in $8 976 totals. Average price for calls is $1 712 for call with 1 month before expiration, so return is about 5 times the price.

    Table below shows the results of model for long call options on last 12 months base. It includes implied volatility for option (as at time of writing). The return for long calls is in second column and it shows ratio of the sum over 12 months to average price for buy to open. The data were organized in the descending order of the return on 100 bucks used to by long calls (3-rd column). The probability of positive result of trade was estimated on the base of 1-year period (4-th column). Average option price was also estimated over 12 month's period (5-th column). Sum over 12 months period includes as positive and negative trades as well. Last column shows the ratio of average return to the average risk.

    Ticker symbol IV Return for long calls Probability of positive result Average price for call Sum over period Return to risk
    V 16% 936% 58% 3.99 37.34 81%
    PCLN 29% 713% 56% 18.84 134.40 35%
    GOOG 19% 597% 42% 16.52 98.56 31%
    MA 26% 537% 56% 14.58 78.23 36%
    AAPL 31% 524% 44% 17.12 89.76 21%
    AMZN 27% 497% 50% 7.71 38.27 31%
    CMG 31% 143% 58% 15.16 21.76 11%
    NFLX 51% 133% 50% 9.16 12.21 11%
    BIDU 40% -187% 53% 7.61 -14.26 -14%
    GLD 13% -231% 47% 3.14 -7.23 -13%
    FFIV 36% -470% 50% 5.48 -25.72 -45%
    SLV 24% -474% 39% 1.57 -7.43 -33%
    SPY 12% -652% 47% 2.44 -15.93 -71%
    AKAM 28% -1114% 39% 1.99 -22.19 -546%

    One can see for example long calls for V provide amazing 9.4 times average option price over 1 year period. Apparently it was just excellent year for V. PCLN is the second in our table with "modest" return of 7.1 times the call prices. SPY calls show negative -652% annual return, so they are very expensive at current IV level.

    Let us see how it turns out to be for 5 years in row for annualized return.

    Ticker symbol IV Return for long calls Probability of positive result Average price for call Sum over period Return to risk
    GOOG 19% 607% 42% 16.52 100.27 27%
    PCLN 29% 565% 56% 18.84 106.48 34%
    AMZN 27% 473% 50% 7.71 36.48 26%
    V 16% 458% 58% 3.99 18.28 42%
    SPY 12% 416% 47% 2.44 10.15 27%
    GLD 13% 361% 47% 3.14 11.32 20%
    CMG 31% 311% 58% 15.16 47.12 26%
    FFIV 36% 274% 50% 5.48 14.98 20%
    MA 26% 255% 56% 14.58 37.20 26%
    AAPL 31% 232% 44% 17.12 39.78 17%
    NFLX 51% 229% 50% 9.16 21.01 16%
    BIDU 40% 153% 53% 7.61 11.64 13%
    AKAM 28% 90% 39% 1.99 1.80 6%
    SLV 24% 28% 39% 1.57 0.44 2%

    Again we can see very good picture for our champions, although a little more modest for AAPL. Still 6 times price paid for GOOG's calls is a very good, particularly taking into account a pour stock market performance during 2008 and part of 2009. Even for SPY one can see 4.2 times call's price as return at current IV level as well.

    One can easy do the same statistics based on historic data for every option of interest to see if it cheap enough before buying to open. I am going to do the same math for long puts and some other option strategies as well.

    Disclosure: I am long AAPL, PCLN, MA, AMZN.

    Stocks: MA, SPY, SLV, FFIV, CMG, NFLX, GLD, AAPL, AKAM, V, AMZN, GOOG, BIDU, PCLN
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