There are two simple options that can be used to leverage a strategy:
- position sizing
- notional funding
These were discussed more in detail in a “how to apply leverage?“.
Today, I just want to revisit this concept with a classic system: the Donchian Channel.
As Ralph Vince’s Optimal f tells us: there is an optimal “bet size” (our fraction of capital risked on every trade) to achieve maximum “Terminal Wealth” (i.e. maximum CAGR).
This can be better illustrated with this chart generated by stepping through different position sizes for the Donchian system:
One can see that past a certain point (2% position size), the extra leverage is detrimental to the actual return. On the other hand the Max Drawdown figure keeps on rising.
To apply leverage, we are free to slide along the curves to reach a desired level, but there is no point going past the optimal f. A 0.50% position-sized system will have less return and less volatility than a 1.50% one, but a 3.5% one will have less return and more volatility.
I went into more detail comparing the notional funding leverage to the position sizing one in that post mentioned at the start. A couple of problems with notional funding (which can be thought of as trading an account with part-real funds, part-imaginary funds to reach a desired notional account size) are:
- its impact dilutes over time (unless some re-balancing occurs)
- its results are dependent on the equity curve path
The second point is easily illustrated by this example: consider a system with a CAGR of 30% and MaxDD of 50%.
If the notional funded account (trading a 100K notional account with real funds of 50K) reaches its MaxDD immediately, the loss would be 50% of 100K = -50K, which wipes out the real funds.
On the other hand, if the account gets the opportunity to grow sufficiently before hitting the MaxDD, it will have built a “cushion” allowing it to better withstand the MaxDD.
With this in mind, I still wanted to check the impact that notional-funding leverage would have on the performance figures from the system.
I chose to leverage the system(s) tested under different position sizes with a 100% notional-funding levered one and a 50% de-levered one (think notional funding in reverse: trading a 200K account as if it was 100K):
The chart above shows the impact that both types of leverage have on CAGR and MaxDD (note that position size is not charted, but as we saw in the first chart, it increases with MaxDD).
Why Notional Funding does not affect Max Drawdown
The CAGR figures (for a given position size) increase with the leverage provided by notional funding. However, the MaxDD figures seem little changed by this type of leverage.
The track record used for testing was fairly long (15 years) and this is one of the reasons why MaxDD figures seem barely affected:
If the MaxDD occurs after years of compounding at high double-digit rates, the account will have grown by a large factor compared to the initial account and the effect of notional funding will be diluted to next to zero.
Let’s imagine an extreme scenario for illustration purposes:
The strategy returns 100% a year for 10 years (no volatility, drawdown: just smooth straight line), then it drops by 50% (MaxDD) in the next year.
- If you start trading with 100, you end up with 100 x 2^10 = 102,400 after 10 years and 51,200 (102400 x 0.5) after the eleventh year: CAGR = (51200/100)^(1/11) – 1 = 76.32%, MaxDD = 50%.
- If you start trading with notional account size of 100 but real funds of 50, you end up with 100 x 2^10 – 50 = 102,350 after 10 years and 51,175 after the eleventh year: CAGR = (51175/50)^(1/11) – 1 = 87.78%, MaxDD = 50%.
- If you start trading with notional account size of 100 but real funds of 200, you end up with 100 x 2^10 +100 = 102,500 after 10 years and 51,250 after the eleventh year: CAGR = (51250/200)^(1/11) – 1 = 65.57%, MaxDD = 50%.
If one rebalances regularly (ever year, every 5 years, every x% increase) to keep the level of leverage significant, we would expect to keep a similar impact on CAGR but a stronger impact on MaxDD.
In the chart above, we would expect the 100% leverage curve to move towards the right (i.e. higher drawdowns) and the -50% one to move towards the left.
A Couple of Points
- It does not make sense to leverage a strategy using position size past its “optimal bet size” (how to evaluate it is probably the topic for
another posta book like Vince’s)
- It does not make sense to de-lever using notional funding as it will mainly reduce CAGR but not the drawdown
- If using notional funding, re-balancing would affect MaxDD
This is just an intro point on how money management is an essential part of any system…
Note: that the figures are dependent on the number of portfolio instruments, length of track record, length of breakout, etc. so do not attach too much importance on the actual figures. The main point is how these figures are relative to each other.