Finding the right "leverage" to use for maximum performance

Trading and Markets
1

Some traders strongly believe that “high” leverage is bad, and “low” leverage is good and less risky.

Although it is not the true definition of leverage according to Investopedia, I am going to use C2 definition of leverage (capital allocated to a trade divided by total trading capital available).

Now consider the following scenario, it will show that there is no such thing as “good” or “bad” leverage.

Take a coin, toss it in the air 100 times. The ratio of heads to tails landing up should be very close to 50/50. If you were to win $2.00 every time the coin landed heads up and lose $1 every time heads landed face down, you should have won approximately $50 by the end of 100 tosses. This is a positive expectation situation. The odds of you winning are heavily in your favor. We will further say you have $100 to bet with.

The question is, what percentage of your money should you risk on each flip of the coin?
What would you say is the best percentage (leverage) to reinvest on each flip?
10%, 25%, 40% or 51%?

This means that if you begin with $100 and choose to risk 10% of your capital on each flip, you begin by risking $10 on the first flip. If the coin lands heads up, you win $20. You would then risk $12 of the new $120 total on the next flip of the coin. If you lose, you lose $12 and if you win, you win $24 and so forth.

Would it make a difference which % (leverage) you used? If so, how much?

Remember, you make twice as much when you win than when you lose. The odds of you winning are 50% every time. The answer may surprise you!

By risking 10% of your money on each of the 100 flips (a $10 bet on the first flip) you will turn your $100 into $4,700! Higher leverage increases your return from 50% ($50) to a 4700% return!

Reinvesting 25% of your money (an even higher leverage) would have turned $100 into $36,100! An increase of just 15% per toss increases your total return from 4700% to 36,100%.

It looks like it gets better the more you invest, right ? So more leverage is good, right?

But wait. Increasing your risk another 15% every flip to a total of 40% being risked on each flip would turn your $100 into $4700. This time by increasing your risk (leverage), your return dropped drastically!

What if 51% of your money is invested? With this scenario, you actually lose money even though the odds are statistically in your favor. Your $100 decreases to $36. A loss of 64%!!

As you can see, there is no “good” or “bad” leverage, only optimal leverage.
And again, as previously mentioned, only a backtest can give us the optimal leverage to use.

The concept behind this simple head or tail game can of course be applied to any trading system with a positive mathematical expectancy (also called trading edge).

2

Optimal leverage is subject to change based on market conditions. Backtest are only history. History only repeats itself when conditions remain the same.

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3

Sure, you can also use a dynamic leverage value if you like, based on market volatility for example. If the backest reveals that it outperforms a fixed leverage then so be it.
But quite frankly, I seriously doubt that it will make any difference whatsoever in the long run.

4

The best way to consider “optimal leverage” is understanding what I believe the most important statistic to consider. Average Annual Return / Max Drawdown. Ideally, a very successful strategy or portfolio should be above a 2. For example if the average annual return is 10% then the maximum drawdown should be 5% or lower. Higher annual returns are great - as long as that ratio stays above 2. I’d be skeptical that a strategy was over-leveraged if it was returning 50% per year but had a maximum drawdown of 40%. That just isn’t sustainable and will blow up for good at some point.

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Hi D_Financial,

Yes, I also read a long time ago (I believe it was in the Stocks and Commodities Magazine) that the average annual return on investment should be at least twice the maximum drawdown of a trading system (2 to 1 ratio).

However, although this sounds like a good ratio, I NEVER take anything for granted. For example, what if trading systems with a 2 to 1 ratio tend to produce mediocre returns compared to systems with 1 to 1 ratio, or some other ratio, on a risk-adjusted basis ?

You also wrote and I quote : “I’d be skeptical that a strategy was over-leveraged if it was returning 50% per year but had a maximum drawdown of 40%”.

The whole problem has to do with the definition of leverage. Leverage is the amount of money that our broker loans us, compared to the capital we need to initiate the position. If I only need $1 000 (margin money) to control, say, $100 000 worth or currency then my leverage is 100 to 1.

Why?

Because my broker loaned me $99 000, that’s why.
That’s the true definition of leverage, period, case closed and end of story.

But that’s not even the point. The point I am trying to make is that it is mathematically IMPOSSIBLE to be “over”-leveraged if we maintain a fixed stop, like 2%.

If someone can prove otherwise I would love to hear from him/her.

Cordially.

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I assume you still leave room for nuance. For example, SPY had a max drawdown somewhere between 50-65% but average return of around 9% year it is not leveraged and has little chance of a true blow up.

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They say markets do not blow up, traders do (due to poor or no money management).
We must also keep in mind that during a “blow up” or black swan event, trend-followers make a killing.

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Yes, my point is that if you think you have a great strategy because you have a 30% annual return but that also comes with a 40% max drawdown, you might be overleveraged. 40% is dangerous and can accelerate quickly towards an account blowup. It might make more sense to use a smaller portion of your account for that strategy and hold onto more cash. If you deleveraged and had a 50% cash position, you would then be at a 15% annual return on the total account with a 20% maximum drawdown. That is a better return and drawdown ratio than holding the SPY and you are much less likely to blow up your account.

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Believe me I understand perfectly well what you are trying to say, so let’s examine your idea.

Consider the following scenario.

Trader A has $10 000 in his trading account. He has a trading system called BigBucks but after just 1 month of trading he experiences a 60% drawdown.

Would you say that the BigBucks system is risky?

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Risky is a very relative term. More information would be needed to answer your question. Risk tolerance, portfolio / strategy definition etc. For example, if the strategy was long SPY and the SPY was down 60% that month, it would be hard to define that strategy as risky since that style of portfolio is essentially what is prescribed to many retirement accounts. Even then, risky would be an opinion as it’s a relative term.

I’m talking more about the use of leverage and the risk of the account blowing up. In the above example, the likely outcome in a buy and hold strategy of SPY is that the account would not blow up (if it did, we would have much bigger issues). However an unhedged futures strategy that has a maximum drawdown of 60% is way too risky for me and likely 99% of investors here at C2. That sort of strategy could quickly accelerate from a 60% drawdown to 100% as there isn’t really a floor on valuation like there is with an index.

This is why max drawdown alone isn’t enough to draw a conclusion. However, when you add in annual return to get to a ARet/MDD ratio, that provides more information on the risk associated with the strategy or portfolio.

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11

Ok, so we both agree that the BigBucks system is risky compared to, say, a system with a 15% maximum drawdown (for simplicity we will assume both systems traded the same financial market during the same period of time).
To recap, the BigBucks system lost $6 000 after only 1 month of trading, a 60% drawdown (starting capital was $10 000).

Now, here is my point.

Another trader, let’s call him Joe, is also trading the BigBucks system and he started the same day. The size of his positions was also exactly the same. But in his case, his starting capital was $100 000 (10 times more than the first trader), so he “only” experiences a 6% drawdown.

So now, and according to your reasoning, the BigBucks system is an excellent system, because its maximum drawdown is a mere 6%.

So, simply by changing the size of the starting capital, the same exact system can be classified as very risky…or excellent!

See the problem when we introduce “leverage” (defined as trade capital divided by total capital) as a measure of risk?

12

@D_Financial that was very well put. I like your reasoning.

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13

In your example I would say the second trader may have been wise and saw the risk of a 60% drop causing them to use less leverage. Aka better money management.

*Could always just be luck though.

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No, because both traders are simply following the same exact signals from the BigBucks system, the only difference is the starting capital.

Make the starting capital bigger and you can transform any 100% drawdown into a 1% drawdown, thus creating the illusion that the trading system is extremely “safe”, even if it has zero trading edge to begin with.

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Drawdown is meaningless without understanding return. I never said a maximum drawdown of 6% = excellent system. If that means an annual return of 2% it’s probably not a good system. Does that make sense?

This is why I proposed using Annual Return / Max Drawdown ratio as a component of understanding if you are using the right leverage. Again, it’s not the only measure, but it can be very helpful.

So, are you overleveraged if your Max Drawdown is 20%? Well that really depends on your return. 1) If your annual return is 45%, you may not be. 2) If your annual return is 10% and you are trading futures (not just holding SPY), then I would argue you are overleveraged for those returns and you should revisit your strategy. In the first example you have a very respectable 2.25 Annual Return / Max Drawdown ratio. In the second example it’s 0.5 which is not attractive.

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But how do calculate your leverage, exactly?
What parameters do you use in your calculation?

PS: Yes I agree about the ratio maximum drawdown/ ROI, but that’s another subject.

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Annual Return / Max Drawdown was the entire subject of my original post :slight_smile:

I don’t calculate leverage although I know C2 uses a calculation. All brokers are really different in the way they use margin so a quantitative leverage calculation doesn’t really mean much as it’s apples to oranges across different brokers.

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Yes of course, and it was an excellent post, there is indeed a correlation between ROI and maximum drawdown, as far as the profitability and the safety of a trading system are concerned

So how do you know if a trader is “over” or “under” leveraged?

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IMO, you have to look at multiple inputs and then make a decision. There isn’t 1 metric or calculation. The first things I would look at are risk adjusted returns which includes max drawdown and what instruments are being traded. Additionally other metrics like length of drawdown, tail / max risk of trade, etc. should also be looked at. There isn’t a definitive answer to the question - I believe multiple inputs need to be considered.

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Of course there is.
Here is the official definition : “Leverage is an investment strategy of using borrowed money — specifically, the use of various financial instruments or borrowed capital — to increase the potential return of an investment.” (Investopedia).
This leverage is set by our broker (example : 50 to 1 in the Forex market)

And here is the C2 definition: “Leverage is the ratio of total notional value controlled by a strategy divided by its Model Account equity.”

For some reasons, the C2 definition is used by the vast majority of traders, or so it seems.

Anyway, thanks for your input and have a pleasant trading day.