Monday, June 15, 2009

The Psychology of Leverage

One reason I wrote the recent posts on capitalization was because I've encountered an unusual number of small, developing traders who have experienced very significant drawdowns in their attempts to make a living from a small capital base.

A very worthwhile exercise is for a trader to take his/her average daily or weekly profit/loss and the variability (standard deviation) of his/her average weekly results and calculate different possible paths toward annual P/L returns. A process for doing this is called Monte Carlo simulation. If you run enough simulations, you'll find the statistical likelihood of your risk of ruin: i.e., the likelihood you'll blow up, given your edge (average profit/loss) and risk (average variability of returns).

What you'll find is that high leverage (which increases standard deviation/variability of returns) greatly increases risk of ruin--particularly if it occurs during a period of slump or market shift when edge decreases.

A nice tool to explore the relationship between edge and risk is Henry Carstens' P/L forecaster. You can run many simulations of two-year returns, given a particular pattern of weekly average profits and weekly standard deviation of returns.

In the simulations above, I assume a portfolio size of $100,000. The top chart shows a simulation of a trader with a solid edge (averaging $500 per week of profit or about 25% return per year) and reasonable risk (about 2/3 of all weeks will fall within a move of 2.5% or less). Note that meaningful drawdowns from peak P/L can occur in even this favorable scenario (other possible paths show little peak-to-trough drawdown), but the two-year return of $51,202.70 is quite nice and the trader never went red.

In the second scenario, we have the same edge of $500 per week, but now double the average volatility/risk. This could be the result of trading a market that is twice as volatile or trading the same market with twice the size/leverage. In this situation, the trader is again nicely profitable, making a two-year return of 50,636.10, but went through meaningful drawdowns--including a loss of about 16% of capital at one point. The increased leverage created increased P/L volatility, which is difficult to weather psychologically.

Our third scenario takes a trader with moderate risk (as in the first situation), but now the edge has dwindled to zero. This could be the result of a slump or a market shift. The trader loses $1445.60 over the two-year period--not a traumatic loss--but went through wild swings to get to that point: from 14% up to 20% down and back up to almost 15% to near unchanged. Here, even with no negative edge, the moderate volatility becomes challenging for the trader.

Finally, in the bottom chart, we see what happens to a trader whose edge dwindles to zero and who is running relatively high risk. The trader loses $3185.90 over two years, which by itself is not so horrendous. But the path toward those returns is enough to make the most calm, focused, and disciplined trader nervous. The trader loses about 24% of capital before making nearly 34% returns and then losing all of those. In other scenarios, the risky trader without an edge loses half of his/her capital.

It doesn't matter what you're trading: leveraging your positions magnifies the paths toward P/L endpoints. At some point, enough leverage combines with a period of diminished edge to create P/L volatility that either courts risk of psychological ruin, risk of actual financial ruin, or both. Note that I did not run crazy risk scenarios or situations in which the edge actually turns negative; those inevitably generate ruinous outcomes.

Note also that, if one predicated a starting portfolio of much less than $100,000, several of the above scenarios would indeed have come much closer to courting ruin. Losing over $20,000 on a $100,000 portfolio is far different than losing it on a $30,000 base.

You don't need to take my word for it; calculate your historical edge and P/L variability and run your own simulations in Excel or even with Henry's quick and dirty tool. You'll see what reasonable assumptions for upside and downside look like based on actual data and realistic probabilities. Judge your potential drawdowns versus your portfolio size and make sure you can weather expectable storms financially and psychologically. Your business plan as a trader deserves nothing less.