In many situations good quick action beats slow brilliant action.   This is especially true when the “best” answer arrives too late.  The perfect pass is irrelevant after the QB is sacked, just as the perfect diagnosis is useless after the patient is dead.  Lets call this principle the temporal dominance threshold, or beat the buzzer.

Now imagine taking a multiple-choice test such as the SAT or GMAT.   Let’s say you got every question right, but somehow managed to skip question 7.   In the line for question #7 you put the answer to question #8, etc.   When you answer the last question, #50, you finally realize your mistake when you see one empty space left on the answer sheet… just as the proctor announces “Time’s up!”   Even thought you’ve answered every question right (except for question #7), you fail dramatically.   I’ll call this principle query displacement, or right answer/wrong question.

The first scenario is similar to the problems of high-frequency trading (HFT).  Good trades executed swiftly are much better than “great” trades executed (or not executed!) after the market has already moved.   The second scenario is somewhat analogous to the problems of asset allocation and portfolio theory.  For example, if a poor or “incomplete” set of assets is supplied to any portfolio optimizer, results will be mediocre at best.  Just one example of right answer (portfolio optimization), wrong question (how to turn lead into gold).

I propose that the degree of fluctuation, or variance (or mean-return variance) is another partially-wrong question.  Perhaps incomplete is a better term.  Either way, not quite the right question.

Particularly if your portfolio is leveraged, what matters is portfolio semivariance.  If you believe that “markets can remain irrational longer than you can remain solvent”, leverage is involved.  Leverage via margin, or leverage via derivatives matters not.  Leverage is leverage.  At market close, “basic” 4X leverage means complete liquidation at a underlying loss of only 25%.  Downside matters.

Supposing a long-only position with leverage, modified semivariance is of key importance.  Modified, in my notation, means using zero rather than μ.  For one reason, solvency does not care about μ, mean return over an interval greater than insolvency.

The question at hand is what is the best predictor of future semivariance — past variance or past semivariance?  These papers make the case for semivariance:  “Good Volatility, Bad Volatility: Signed Jumps and the Persistence of Volatility” and “Mean-Semivariance Optimization: A Heuristic Approach“.

At the extreme, semivariance is most important factor for solvency… far more important than basic variance.  In terms of client risk-tolerance, actual semi-variance is arguably more important than variance — especially when financial utility is factored in.

Now, finally, to the crux of the issue.   It is far better to predict future semivariance than to predict future variance.  If it turns out that past (modified) semivariance is more predictive of future semivariance than is past variance, then I’d favor a near-optimal optimization of expected return versus semivariance than an perfectly-optimal expected return versus variance asset allocation.

It turns out that respectively optimizing semivariance is computationally many orders of magnitude more difficult that optimizing for variance.  It also turns out that Sigma1’s HAL0 software provides a near-optimal solution to the right question: least semivariance for a given expected return.

At the end of the day, at market close, I favor near-perfect semivariance optimization over “perfect” variance optimization.  Period.  Can your software do that?  Sigma1 financial software, code-named HAL0, can.  And that is just the beginning of what it can do.  HALo answers the right questions, with near-perfect precision.  And more precisely each day.







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