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Math Help - how to statistically compare random investment returns to actual returns

  1. #1
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    how to statistically compare random investment returns to actual returns

    I have a string of (344) investment returns from an investment strategy. I compared these daily returns (my actual picks) to returns from random investment picks from the same stock universe. My returns won 60% of the days. A friend claims this is not that good as you would expect the random returns to win 50% of the time, so I really only won 10% of the time. How do I dispute this?

    Here' my thinking: I understand that normal distributions (the distribution I presume for investment returns allowing both long and short positions) are 50/50 around the mean. To presume a random sample would beat mine 50% of the time implies consistent distributions, i.e., same mean/variance structure.

    I think one answer is to perform a paired t-test with null hypothesis of no difference in means. A high enough t would prove random should not beat mine 50/50. 1. Does that make sense? 2. Is there something better?

    Any help/thoughts would be appreciated. Thanks
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  2. #2
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    Quote Originally Posted by MichelleM View Post
    I have a string of (344) investment returns from an investment strategy. I compared these daily returns (my actual picks) to returns from random investment picks from the same stock universe. My returns won 60% of the days. A friend claims this is not that good as you would expect the random returns to win 50% of the time, so I really only won 10% of the time. How do I dispute this?

    Here' my thinking: I understand that normal distributions (the distribution I presume for investment returns allowing both long and short positions) are 50/50 around the mean. To presume a random sample would beat mine 50% of the time implies consistent distributions, i.e., same mean/variance structure.

    I think one answer is to perform a paired t-test with null hypothesis of no difference in means. A high enough t would prove random should not beat mine 50/50. 1. Does that make sense? 2. Is there something better?

    Any help/thoughts would be appreciated. Thanks
    Sounds OK. n is large enough that the difference is probably significant at the 0.05 level. But I'll bet you dollars to doughnuts that you'll not change you friends mind.
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  3. #3
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    When you say "344 investment returns" do you mean 344 separate investment positions with one return each, or one investment positions with 344 consecutive returns, or what? These are fundamentally different situations. Not that it will change the answer, but that level of ambiguity tells me that you don't know what you're going on about.

    It is provably impossible to consistently outperform random investment in a fair market without insider knowledge. The market is inherently unpredictable, and no investment strategy that has ever existed has ever consistently outperformed the market itself, which a random portfolio will tend to track. Anyone claiming that they can do better than this for the same level of risk is quite simply selling snake oil. There is a certain trend towards numerology in some investment circles, and it is quite simply all malarkey. For example, most of a stock's "Greeks" are not reliable indicators of investment quality. Alpha is particularly meaningless since it is calculated relative to an arbitrary benchmark, which itself represents nothing at all.

    Furthermore normal distribution doesn't apply to a series investment returns. There is no arithmetic mean payoff that investment opportunities will tend to regress to. You cannot reduce securities investment to mathematical formalism, since the market is not a mathematical abstraction. It is a psychological abstraction of human action, which is not possible to realistically model today or in the foreseeable future.

    Either you have been misled by whoever sold you your "investment strategy" or you are ultimately seeking to mislead others for the same purpose. Either way, your thought process on this subject is completely wrong.
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