Quick MATHturbational Note

Maximizing the compounding rate of equity is only equivalent to minimizing the risk of ruin under the following two conditions:

(1) certain MATHturbational assumptions about the distributions of returns hold true, and

(2) “ruin” is defined strictly as losing 100% or more of the equity.

I haven’t done a proof since taking topology and real analysis in the mid-1990s, so I’ll let the intelligentsia debate the “assumptions” in (1), above.

It is good to note, however, that “ruin” is most definitely NOT strictly defined as losing 100% or more of equity. Yes, that would be ruinous, but that definition is only a subset of the events which make up the broader class of “ruin.”

For a retail trader, “ruin” means any drawdown large enough to stop them from trading or discourage them from continuing to trade a proven system. If they’re trading for a living, they may well hit a drawdown sufficient to make them either change their lifestyle, or go back to work for “the man.” That is truly an onerous amount of ruinage.

For a hedge fund manager, “ruin” could be any drawdown, volatility from month to month, or even insufficient returns over time, which is marked enough to encourage investors to seek redemption from the fund.

In real life, maximizing the compounding rate of equity often results in an INCREASED risk of ruin.

Party Like It’s 1991

In January 1991, the S&P 500 had a Price/Earnings ratio in the mid-teens. The yield differential on corporate bonds, compared to long-term Ts, was about average, and had been rising to that point.

Meanwhile, the yield curve (long-term T’s to 3moTs) was pretty steep, and had been steepening.

Finally, CPI was rising at an uncomfortably high rate, year over year.

The NBER eventually called that period a “recession” beginning in July of 1990, but they didn’t “call it” until April of 1991.

Sounds a lot like now. Hmm.

Using data available from AAII, one could do a regression analysis with the S&P 500 index’s PE, the corporate bond spread and its year over year change, the long-term-to-short-term T spread and its year over year change, and the year over year change in headline CPI as independent variables.

I suggest the subsequent year’s change in the S&P 500 index be the dependent variable.

I’ve already done that work. I may (or may not) post it later. Any nerd could do it. Some of y’all probably should do it, as well.

The adjusted R-square for the regression, along with the t-Stats and P-values for each coefficient, could be provided as proof you did your “homework.” Alternately, submissions detailing the variable whose coefficient had the highest (least significant) P-value might be accepted as proof of work.

Discussion points could include macro reasons why each variable type’s (valuation of the index, yield curve, corp spreads, and CPI change) coefficient has the sign that it does, or illumination of the differences between P-value of a coefficient, additional predictive value of an added coefficient, and relative formula weight of said coefficients in a regression.

Rotational System Drawdown Continues

Rotational is a trend-following system that believes there’s always a bull market somewhere, and in previous downturns this year, the portfolio has been able to ride it out OK because it was in “what was working.” Not this time. Good in the straightaways, not so good in the turns.

This is the largest drawdown the system has generated in test or tracking. It’s important to remember that, no matter how long any system’s backtest, that its worst drawdown is always in front of it, just as its best performance is always in front of it. A backtest (or an actual trading return stream) is only a small sample from a larger heteroscedastic distribution, and as long as the recent results are within the same rough order of magnitude as the sample (they are), there’s no evidence of “brokenness.” In backtest, the system had a half-dozen drawdowns in the teens, and the current drawdown is 23.3% from peak equity, which is comparable to its backtested compounding rate and average annual return. It’s potentially unnerving, yes, but not outside of the expected range of results. The system doesn’t change, however. It just executes, regardless of circumstance, and while it does tend to to suck wind at turning points, it makes up for it in the straightaways - because there’s almost always something trending. We’ll see if the current leaders, stay leaders.

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To view my actual trades and model portfolios for the different systems I track, visit The Rempel Report. If you’d like to become of member of The Rempel Report, you can register here. At The Rempel Report, I track model portfolios for four different mechanical trading systems, disclosing all results (good and bad) at regular intervals. I also track my personal portfolio, and disclose all trades before I make them. Members receive email notification of new posts and can contribute to the site through comments. Registration is still free!

The 10Q Detective Has A New Site!

The 10Q Detective has a new site!

All The Backtests Are Now Posted

I track a variety of different trading systems, and post my own trades - before I take them! - as I personally trade my own systems. It’s called accountability, and it’s called “eating your own cooking.”

One thing I’ve been meaning to do for some time is take the backtest results that I used to determine these systems, and post them for your reading pleasure. Life being what it is, that job stayed on the list but below the line; something I wanted to do but always had something else on the list above it. Well, no longer.

All the backtests are now posted. The Timing program test was posted a while back, but this week I’ve posted the other three.

Timing explanation and backtest.
Current posts and results for the Timing model portfolio.

Fundamental explanation and backtest.
Current posts and results for the Fundamental model portfolio.

Rotational explanation and backtest.
Current posts and results for the Rotational model portfolio.

Aggressive explanation and backtest.
Current posts and results for the Aggressive model portfolio.

To view my actual trades and model portfolios for the different systems I track, visit The Rempel Report. If you’d like to become of member of The Rempel Report, you can register here. At The Rempel Report, I track model portfolios for four different mechanical trading systems, disclosing all results (good and bad) at regular intervals. I also track my personal portfolio, and disclose all trades before I make them. Members receive email notification of new posts and can contribute to the site through comments. Registration is still free!