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Snapshot on Money Management and Leverage – Corrected

October 8th, 2010 · 5 Comments · Money Management

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:

CAGR and MaxDD vs. Position Size

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.

Notional Funding

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):

CORRECTED Leverage by Position Sizing or Notional Funding

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 post a 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.

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5 Comments so far ↓

  • A reader

    In the 3 examples you are giving, imagine your drawdown hits first. all of them will draw down 50 units, which will be 50% for all accounts on the notional basis, but very different percentages if you look at your real funds. my thought is that notional funding is not a form of leverage, you are simply trading a 100% funded account but give the customer a line of credit. The customer should have the account as 100% funded on his books when he calculates return. The only benefit is that extra cash is freed up.

    However consider the 3 examples you have and use 1, 2 and .5 X leverage and rebalance every year (in actual trading your position size will rebalance for you), and you’ll see the true value of using X leverage. You can start with a smaller account size, assume the same (!) dollar risk (25% on a 100 account is the same unit risk as 50% on a 50 account) and make more money in terms of $ and % (after enough time). the key thing is that the initial $ risk remains the same. the drawback is that a leveraged account will reach the point of no return (where worst drawdown won’t make the account go below starting point) later. added benefit is that higher leverage will usually improve MAR for most trendfollowing systems

  • Jez Liberty

    Dear reader,
    Very good point. I suppose I am stretching it a bit when I talk of notional funding as a leverage tool. As we saw it can seem more efficient (in terms of increasing Reward-Volatility ratio) than position sizing because the overall MaxDD figure increases an order of magnitude slower than CAGR…
    However, the fact that it is path-dependent makes it more of a gamble…

    Notional funding used for freeing up extra cash is probably what it is mostly used for

  • Pretorian

    Hi Jez, if we consider the some of the Wizards, don’t you think that their level of leverage is already the optimal? They already have good CAGR and some have pretty large drawdowns. Although there are some examples like Cheasapeake and Abraham that reduced risk to appeal to institutioal investors. The point is: would really recomend using notional funding to increse returns? I am about to invest in some managed futures programs and I have been studying the topic for some time. Very enlighting article as usual. Thanks

  • Jez Liberty

    Pretorian,
    The angle I was looking at notional funding here was to compare its merits as money management/leverage tool in combination with changing position size on a self-traded strategy (where you have control over all parameters).

    I would suppose that the most classic approach with regards to investing with CTAs and using notional funding is to avoid committing all funds to the account or potentially for investors that cannot meet the minimum account size. In terns of leverage, most CTAs would probably offer you the option to apply different levels of leverage through a managed account – therefore notional funding for leverage might not be the ideal option.

  • KBF

    Pretorian:
    most CTA programs do not use optimum leverage, if by optimum you mean maximizing risk adjusted returns instead most CTA’s target a certain risk target (i.e. x% drawdown or y% annualized stand. dev). using notional funding gives very different results than increasing risk per trade.

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