Relationship of leverage and drawdown

Let's say there is a trading system that produces an average annual compounded return of 35% with a max drawdown of 13% at 2x leverage.

If that leverage were to be increased to 4x, would everything also double? For example, should it be expected that the returns would increase to 70% and the drawdown would increase to 26%.

I understand however, that there is often a difference between theoretical concepts and what really happens.

Could someone explain this relationship?

Thanks,
Daryl

 

I've tested quite a lot of trend following systems using a fixed fraction of equity for position sizing. My impression is that as the amount risked per trade increases then so does the sharpe ratio (up to a point, anyway). However as risk increases the amount of time in a drawdown also increases.

If someone could give a more rigorous explanation of why this is, or is not the case I'd also be grateful.

 

I did some work in this area a couple of years ago. Here's what my sharpe looked like at different amounts of leverage.

Just because the sharpe ratio reaches a maximum at a certain point, does not mean that you should use that amount of leverage. I actually looked at 8 different risk measures back then (now I can probably come up with more). But there is no right answer as to which risk measure is best and how much leverage to use.

 

It depends quite a bit on the system itself. You need to analyze the distribution of trades and see how "normal" the distribution is. If your system has a large number of outliers - fat tails - (i.e. large winners and large losers), then the leverage to DD ratios will be exagerrated and possibly unstable. This comes from the fact that you will easily experience (n) large losses in a row and potentially have a very bad year that will affect your compunded annual return significantly. The reverse is also true with a good run of (n) large winning trades.

Attached is a basic analysis using a relatively normal system trade distribution. You can see a few things:

1. DD increases linearily with leverage (again because this system is fairly normal, this concept generally holds).

2. The compounded annual return starts to plateau (the concept of diminishing returns).

3. Perhaps most critical is the risk ratio; this line has a greater slope than the DD line. This means that you are taking on more risk for lesser return as you increase leverage (duh).

For a trend following system, I would suggest you do this analysis and see what happens. I personally do not leverage systems with large wins and large losses - that combination would be unstable IMO... the large losses or string of average losing trades (low win percentage) are what get you. Ideally, if you want to use leverage on a system, one would want a system that has normally distributed trades with a high win rate (>50%) and low max losing trade value.

Regards,
Mike

 

The answer depends on the implementation and if/how you capitalize p/l.

M

 

I think it is correct that if you double leverage then drawdowns are doubled. But as mentioned above drawdowns are longer when you are using more leverage compared to when you are not. At higher degrees of leverage it can take MUCH longer to get out of a drawdown assuming the same rate of return. In fact the time and % return required to get out of a drawdown seems to grow at an exponential rate as leverage increases (this is just my observation, I can't fully explain the math behind it so I don't know if this statement is completely accurate).

The best way to see what I am talking about is with a simple example. Lets look at 3 scenarios with different amounts of leverage:

1)
100k to start, no leverage
20% loss (drawdown of 20k)
80k in account
it would now take a 25% gain to get back to 100k

2)
100k to start, 2:1 leverage (200k buying power)
20% loss (.20 x 200k = 40k drawdown)
60k in account (now 120k buying power)
it would now take a 33.33% gain to get back to 100k
(40k drawdown/120k buying power = .3333)

3)
100k to start, 4:1 leverage
20% loss (.20 x 400k = 80k drawdown)
20k now in account (80k buying power)
it would not take a 100% gain to get back to 100k
(80k drawdown/80k buying power = 1)

This example is a bit over simplified and doesn't really take all variables into account but it should show that even though drawdowns increase at a linear rate the % returns required to get out of the drawdown (and therefore time) increases at a much faster rate.

 

If you double your leverage, drawdowns will double. But your return will increase by a lesser amount. This should be obvious from this example:

Lev X1
Ret: 100%
MD: 50%

Lev X2
Ret: 0%
MD: 100%

Your drawdowns will start to drag down your return and eventually your return will drop to 0.

 

If leverage is doubled then the return is doubled if the contracts/shares are doubled per position.

Drawdown is also doubled only if positions are doubled and the time it takes is the same, I do not understand why some other posters claim that the time in drawdown wil be affected. Everything is scalable except time.

Alex

 

This is wrong. You've misunderstood the premise - we're talking about a trading system with a series of trades producing an *annual* return, not an investment in a specific product.

 

Let's try to clarify things because I think you misunderstand and/or using words in a different context that everyone else uses them.

Let's say you have 100k cash and 10 stock trades in the year. You buy 1000 shares and you make $1 profit in each trade. You make $1000 on each trade and your return at the end of the year is 10%.

Now, should your broker increase your leverage from let's say 2x to 4x or 8x or 10x your return will not be affected UNLESS you increase the number of shares.

You should NOT calculate your return on the leveraged capital but only on the cash portion of the capital. The loan offered from the broker is NOT your capital, it's just that, a loan to increase your purchasing power.

Now, if 5 trades in a row in the above example lost $1 after you made 5 consecutive wins, your drawdown is 5K and this is not affected neither in magnitude not in duration UNLESS you increase the number of shares you buy long in each trade after you increase the leverage.

The same is true for futures and forex.

Annual return is calculated on the cash portion of the account and increased leverage does not affect return unless you also change your position size.


Do you think you can calculate your annual return based on someone else's money?

Alex