Several CTAs or fund managers offer a standard version of their fund, along with a leveraged version (called enhanced risk, 2x or 3x fund, etc.). However a simple performance comparison of the leveraged option against the standard option usually makes it obvious that the former does not offer a simple performance multiplier of latter.
I was looking at Conquest Capital Group and their MFS fund (based on the Trend Following benchmark used in their paper discussed here), which offers two such options: their standard fund and a 3x option.
The main fund, since inception (2004), returns 56% (net of fees) with a max drawdown of 14%. Their 3x leveraged option, over the same period, returns 85% with a max drawdown of 47%. The risk is indeed tripled, but the reward falls fairly short of it. When removing the fees on both funds (1% for the standard fund and 3% on the leveraged fund), the performances are 66% vs. 120%. This is just an example. Most CTAs are similar in that respect and it highlights some effects of leverage.
A similar concept has become more mainstream with the recent apparition of leveraged ETFs and the realisation by some investors of the large volatility decay that they incur (when they are held on a long term-basis, i.e. anything longer than intra-day). Check the long-term charts of FAS and FAZ (3x leveraged bullish and bearish financial ETFs): the only long-term profitable trade would be to short both, to cash in on the volatility decay while being hedged (since Nov 08 they are down respectively 58% and 98%).
This is simply due to the design of these instruments, which aim to replicate and triple the daily returns of the tracked benchmark. This highlights a fact about leverage: multiplying the arithmetic returns will not result in the same multiplication of the geometric returns.
A typical way of leveraging a trading strategy is to increase the position size, and the resulting risk and return for each trade.
Assuming a fractional betting strategy for position sizing, the leverage dictated by the value of the fraction of capital risked on each trade will impact the overall average geometric return. Theories describing this phenomenon are the Kelly criterion and Ralph Vince’s Optimal f.
One of the main implications of this type of Money Management is that, for every strategy, there is an optimal fractional position size to maximize the (past) geometric return (and future if you assume that the past is a good representation of the future). Any fractional position size higher than this optimal value would result in a lower return.
Any strategy (with its resulting stream of returns) has an embedded maximum leverage, which can be defined with the optimal f.
Notional funding can be compared to trading with imaginary money. Typically, CTAs also offer notional funding: they trade your account based on an agreed notional amount, which is different from the actual funds in the account. For example, you could send 100k to your CTA and instruct them to trade it as if it were a 300k account. Or you could do the same thing with your own trading system.
One could intuitively think that this is exactly the same thing as tripling the position size but there is a difference.
Let’s consider this simple example with a strategy producing two consecutive trades of +10% and -5%:
The notional-funded account would close at 300 x 1.10 x 0.95 = 313.50. This would result in a gain of 13.50 on actual funds of 100: +13.50%, which is exactly triple the return one would get on a fully-funded, unleveraged account (100 x 1.10 x 0.95 = 104.50 for a 4.5% return)
Leveraging by tripling the position size on an account of 100 would result in two consecutive trades of +30% and -15%. Final balance would be: 100 x 1.30 x 0.85 = 110.50 – or a +10.50% return.
Initially, notional funding appears a better solution to the leverage issue as it does not suffer from the volatility decay or erosion of returns introduced by increasing position size.
But funding always comes at a cost, pretty much in the same way as an overdraft gets charged by your bank. Another way to look at notional funding is to compare it to borrowing trading capital. The higher ratio of your notional account you borrow (higher leverage), the more the cost of borrowing will impede your trading returns.
In practice, you do not really borrow any funds (only by the power of imagination) but this practice still ends up impacting your return when you start taking into consideration the return on margin.
This paper from EDHEC Risk (PDF) looks at Trend Following/Managed Futures performance and presents an interesting breakdown of the overall return of such strategy. Assuming interest being paid at T-bill rates on the margin used for trading, it represents the bulk of the returns compared to actual Trend Following gains and rebalancing gains.
This is one of the reasons for the hidden cost of notional funding: a notional-funded account would enjoy the same Trend Following and rebalancing gains as a fully-funded account of the same size, but only a fraction of the return on margin (which is based on the actual account size).
To illustrate that point, below is a chart showing the impact of fees and margin interest on an arbitrary performance curve:
Notice the fairly sizable difference between taking return on margin into account or not (red v. blue curves). The green curve adds fees at 1% annually. The return on margin was assumed to be the T-bill rate for that month.
Another issue of Notional funding used as leverage are the constraints imposed by the underlying strategy.
Any strategy requires a minimum margin commitment to support the positions. Effectively the Margin-to-Equity ratio will dictate the maximum leverage one can use to trade a strategy.
The Drawdown is also a leverage-limiting factor: the more risk the strategy generates (higher drawdowns), the less leverage can be applied. If a strategy regularly exhibits drawdowns at the 40% level, there is a always the possibility that such drawdown appears at the beginning of trading the strategy. Based on the level of leverage, a notional-funded account might not have the time to build enough equity cushion to withstand the drawdown, which would result in the actual account funds going to 0 or a margin call.
Note that in this case, the sequence of trade returns has an impact on the outcome: if the strategy produces gains of 100% followed by a drawdown of 40% a 3x leverage via notional funding would still result in a gain of 60% (300 x 2 x 0.6 = 360, or a profit of 60 with actual funds of 100). If the 40% drawdown appears first, the notional account would shrink to 180, which would result in a negative actual account balance (trading would have to be stopped before then).
With these considerations and the benefit of hindsight, here is a comparison between the same arbitrary strategy as above (fees and interest included) traded with:
The notional funding appears to be the better option. However the position sizing leverage is independent of the order in the sequence of returns – as opposed to the notional funding leverage. If that nasty current drawdown (which is the largest one historically) had appeared at the beginning of trading and carried on further to reach 17%, the notional-funded account would have been wiped out.
The next chart highlights the impact of leverage on the difference between the two types of leverage for that specific strategy:
The target curve represents a simple multiplier (equal to the leverage factor) of the unleveraged performance (which, as we have shown is not attainable). The position sizing leverage clearly exhibits the behaviour discussed in Optimal f theories with the return breaking down past the optimal value.
Hopefully, this gives you a few ideas about how to work leverage in your trading strategies or when sending funds to CTAs. Taking the time to look into it has cleared up a few points for me.