OmniVest Forum : User-Created Portfolios : Deleting Thread Portfolio Switching

Steve Mayo

Legend

Posts: 414

Joined: 10/11/2012
Location: Austin, TX

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Subject : RE: Portfolio Switching
Posted : 3/30/2014 8:24 PM
Post #29634 - In reply to #29631

According to a Feb 2010 article in the Morningstar Advisor, between January 1926 and April 2009, the S&P-500 had a monthly mean return of 0.91% and a monthly standard deviation ("sigma") of 5.55%. If the market follows a Gaussian or “normal” distribution, there should only be a 0.1% probability of the index exceeding a 3-sigma event. In other words, the index should only have dropped by more than 15.74% (0.91 - [5.55 x 3 standard deviations]) once between these dates. Yet over those 83 years, there have been 10 losses of three sigma or higher in that market index. That equates to about a 1% probability of a 3-sigma event. Thus, it seems that the S&P-500 is 10x risker than we all thought because of its fatter tails (the parts of the bell curve approaching zero).

But the fact remains that a 3-sigma event is still very rare in stock returns. So, three-sigma was the high goal that Mark and I set for ourselves. We want to be 99% confident that our switching algorithm is better than random chance. Can we do it?

The attached graph shows a 1000-iteration Monte Carlo experiment where we randomly chose between our two source portfolios. The error bars are three standard deviations above and below the mean Monte Carlo equity (dotted line). The red line is the return from our algorithm-switched portfolio. Note that the return on the switched portfolio is showing a better than three-sigma improvement over random chance for most of the 7-year period!! (P-value=0.01 using one-tailed paired t-test for means of Switched vs. Monte Carlo).

Yes! We can now say our portfolio switching approach is statistically valid,. And over the last 7 years, as simulated in OV, it generates a 20% higher average monthly return (5.97 vs. 5.0) with a 1% reduction (8.8 vs. 8.9) in risk (standard deviation) compared to our selected benchmark (Nirvana Club’s ARM-4 Margin). In the accompanying distributions, notice how the return has been shifted to the right.

Granted, we don’t have 83 years of data to compare against the S&P500, but both of these portfolios outperform the market, by 2.8 and 2.2 points respectively on a risk-adjusted basis. Ed and the Nirvana staff deserve all the kudos for that one!

[Edited by Steve Mayo on 3/30/2014 8:42 PM]

Attached file : SD Chart.jpg (103KB - 747 downloads)

Attached file : PastedGraphic-15.png (50KB - 746 downloads)

Attached file : Monte Carlo To 3 Sigma.jpg (116KB - 764 downloads)

Attached file : PastedGraphic-14.png (74KB - 728 downloads)