Discretionary trading

[grems8544]

Just my oppinion but I think it is best to initially take leveraged ETF's out of the equation when searching for the optimal use for a given amount of capital.
Otherwise the test will probably indicate it's best go with TNA/TZA only for maximum gain.

The problem I see with that is that this is based on historical data. The maximum drawdown of any system lies in the future and is unknown.
Risk of ruin is probably quite high going all in on TNA/TZA even tough historical tests show it maximizes profit.

Instead of trying to maximize gain it might be better to maximze the MAR ratio. (MAR = CAGR / Max DD) This way, risk is taken into account.
My guess is diversification in systems leads to a higher MAR ratio and to a smoother equity curve. I believe that it is safer to use leverage on a diverse portfolio of systems (either by margin or leveraged ETF's) than it is to do so on a single system, no matter how great historical backtest says that system is.

Completely concur with Ray's comment. If I may add some color ...

Risk adjusted positioning increases the work we must put into our trading activities. It basically throws out the concept of "I'll own a maximum of 10 positions and my portfolio is Y, so each position is Y/10". While this approach certainly works, it is far less than optimum as the number of positions gets less and less. As M&K, O'Neil, et al. advise, fewer positions is best. If you believe this, then the impact of MDD is crucial as the drawdown contains more of your capital. Unfortunately, most individuals who counsel a low number of holdings rarely address risk-adjusted position sizing, because it's not a Finance 101 concept.

The obvious question is how to correctly position size. The not-so-obvious answer is dependent upon:

1) the expected gain of the securities in the entire portfolio
2) the correlation of the securities in the entire portfolio
3) the variance of the individual securities in the entire portfolio
4) the standard deviation of the prices of the individual securities
5) the allocation of capital between the different components of the individual securities

A very good starting point on understanding these concepts can be found in the following PowerPoint presentation. I've zipped it because ".ppt" is not an available upload option.

mathematicsofDiversification-ch05.zip

The key concept here, which directly supports Ray's assertions, are that we start the optimization process by constructing a portfolio with a minimization of variance in mind. Here, variance is equated to drawdown. Hence, for a given set of equities with quantified gains as well as standard deviation of the price series, we can form a portfolio which reduces variance while increasing gain.

The PowerPoint shows how to do it for a two-security portfolio -- doing it for more (which obviously is practical) requires more work and further requires that you know how to use Excel. The outline of how to do this for N-portfolios is also in the PowerPoint, and relies heavily on the work of Simon Benninga. The book has a disk with macros and worksheets ready to go, but of course, you have to understand some of the basic concepts shown in the PowerPoint in order to get anything meaningful out of the book.

Further supporting Ray's assertion that we should not use leveraged instruments in our optimization process is this paper:

1st_Place_Tony_Cooper_abstract.pdf

This is a heavier read, but pay attention to Figures 1 and 2, which give you some framework around the "optimum" leverage levels for the general market over various periods in the past. This paper is relevant because leveraged instruments multiply BOTH volatility as well as gains, resulting in the same behavior as their non-leveraged counterparts during the optimization process (I ignore the impact of the daily rebalancing of leveraged daily ETFs, which is adverse over the longer term).

Finally, the approach in the book and the included paper above do not address in a concise manner that volatility changes with the time frame being measured; they use standard lookback periods and take the volatility as equal-weighted over the lookback period. This is not a good approach in real life, so this last paper is a (heavy) introduction on using a moving average concept to have a better volatility estimate:

TD4ePt_2-StatisticsOfFinancialMarketReturns.pdf

Riskmetrics pioneered research on risk management, and I've not found a better reference.

If you've made it this far and you have a basic understanding of the concepts of volatility, jump to chapter 5, specifically Table 5.7 onward, to get a view on how the exponentially weighted moving average (EWMA) model is used in the forecast of returns and variances.

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Disclaimer: This is all a work in progress, and I'm still learning, learning, learning. Portfolio/position sizing is HARD, which is why most people (including me) simply do the Y/10 per position and are done with it. The concept of minimal-variance portfolio construction is hard to achieve, yet maintain in a practical fashion, but this shouldn't make you throw your hands up and say "it's not worth it". It's clear it *is* worth it, especially if you are happy with your holdings and have the knowledge that you're closer to maximum efficiency in gains and reduction in drawdown than you'd ever be with a Y/10 approach.