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.


Michelle B said...

Excellent post (comme d'habitude). And again there is nothing with which I can disagree.

See if I can yet describe what I am trying to explain. Risk to reward is the focus. If you are leveraged or not, if your stop gets you out with .05 loss versus a gain of .20, what is the problem? If your win rate is 60 to 70%, than why is the leveraged state dangerous?

Misuse of leverage is truly a common problem. But what I have found in my many years of trading, is that discipline via risk to reward via stops allows one to get the advantage of leverage. Whether if you have a large cash base or a sizable buying power based on leverage, the problem that prevents turning consistent profits is not having an consistent small edge and not having the disciple to stop your risk to reward (4/5 to 1 risk to reward). The market does not care if your capital is leveraged or not.

For an experienced trader to shy away from leverage, to me, troubles me as much as overusing leverage troubles you. After all, the young traders that work at prop firms, are using some one's else cash. Daytrading equity of 4x leverage has no cost attached to it if the position is closed within the day.

I may be dense and just not getting your finer points, and I am certainly not encouraging the use of leverage or large positions whether they are cash based or leveraged for beginners/intermediate daytraders. Your posts are very important and on target for developing traders. I am just defending the use of leverage for experienced traders. If daytrading leverage was terminated, then a cash base of around $100,000 would be necessary for me in order to continue to make a decent living.

Trader Kevin said...

We see one of the dangers of the use of leverage in the returns of leveraged ETFs. FAS and FAZ, which are ostensibly mirror images of each other, are both down more than 60% since Thanksgiving. The underlying index is basically unchanged over the same time frame.

Brett Steenbarger, Ph.D. said...

Hi Michelle B,

You make an excellent point; it is definitely possible for successful traders to be risk averse and make too little use of leverage. In general, when a portfolio manager is running a high Sharpe ratio and is trading liquid markets and scalable strategies, risk managers will encourage greater leverage/P&L variability.

So, yes indeed. If you're able to structure trades with a 4:1 reward/risk and a 60+% win rate, leverage is certainly your friend. And with that kind of edge, you shouldn't remain a small trader for very long!

Thanks for the feedback--


Brett Steenbarger, Ph.D. said...

Great point, Kevin; that's a startling statistic--


kris said...

Very nice post. However I think the analysis is not fair in this respect that for leveraged traders you just increase the volatility without changing the average profit. If you use say 2x leverage then increase your expected profit x2 and then compare the results.

E-Mini Player said...

If you guys haven't already, pick up a copy of "When Genius Failed: The Rise and Fall of Long-Term Capital Management" by Roger Lowenstein to see what Leverage can do.

Doc, any suggestion on how much leverage is prudent when trading the e-mini S&P500? I personally allocate a minimum of $5K per contract traded.

fortune8 said...

Anything when improperly used can be damaging! Leverage itself is not bad, how it is being mis-used is. Power is not bad, how it is being mis-used is. Think about when buying a house, aren't you using leverage? FAS and FAZ always get the mention. But did you take a look at YTD performance for DXO versus USO, 79% vs 16% for a 2x leverage ETF. For 2x leverage shouldn't the return be 32%? Hmm? Who's complaining?

There are always two sides to a coin.

Severino said...

Michael B

I am curious to what you are trading?
Using for example the ES mini and being able to get a 60% win rate on risking 1 point to get 4 is impressive indeed.

joachin said...

I think the Z value resumes all this information.

Z value is a grate teller because you compare the average return with the average volatility unit.

A Z>3 will say that your performance is 3 times better than your volatility.

A Sharpe ratio can't differentiate luck from skill like Z value does.


So we would be comparing average performance with average failure per unit measured. In that manner you take more into account the draw downs from time to time.

Do you use Z value? Why? or Why not?

JimRI said...

Two brief comments:

On FAS and FAZ, these derivitive leveraged issues really only work for intraday trading. Direxion, is clear about this and I recall reading there had been some legal action regards it. One should not expect to use them over multiday or longer terms. My broker will not allow shorts or margin on any of this class of derivitive and they go so far as to advise clients to not use them for longer term plays.

On leverage, it is interesting that Jesse Livermore, the "all time greatest trader" who made a billion in the 1929 crash, and millions in the 1906 era crash could not resist despite his own admonitions, and finally filed bankruptcy in 1934, and committed suicide in 1940.