COMMENTAR Y
e) Fifth, even if the above mistakes may seem obvious to most people, there is yet another mistake you can make when trying to figure out which CTA fund to pick. Most people believe that they should pick the CTA manager with the highest stand-alone Sharpe ratio. When doing it in this way, you are making the assumption (probably unconsciously) that you would invest all of your money into a CTA fund. In reality, however, most clients prefer to keep some of their existing investments, e.g., equities/equity funds, bonds/bond funds, other hedge funds and so on, so that they get an overall diversified portfolio with a number of different exposures.
In such situations, investors should instead try to find the CTA fund that delivers the greatest value to the client’s total portfolio. By calculating the Sharpe ratio (and other statistics you may be interested in) of the overall client portfolio (when including the respective CTA funds one at a time), you will be able to identify which CTA fund has the best fit to your specific portfolio. When doing these portfolio simulations, it is of course important to assure a like-for-like comparison, such that the volatility of the different CTA funds is normalised (put on an equal level). Since excess return is a function of the volatility in the fund, one can scale the excess return of different funds with the relative level of volatility.2
It should be noted that the goal of a CTA fund is to be a good ‘Sharpe-booster’ and ‘tail-risk hedge’ in the context of a client portfolio. Because of this goal, you should not expect CTA funds to have particularly high stand-alone Sharpe ratios (but you can probably expect the attractive combination of a positive skew and excess kurtosis). In fact, an abnormally high stand-alone Sharpe ratio should instead raise questions. Has the fund drifted away from the pure CTA strategy? If that is the case, the fund may not be able to protect the client portfolio in a bear market in the same way as it might have done in the past. Notice also that funds that may have boosted the client portfolio Sharpe ratio over a period of time, during which no bear markets developed, may look like a great CTA for a while. However, in years such as 2008 (equity bear market) and 2013 (bond bear market), it becomes pretty clear which funds actually possess the attractive tail-risk hedge and longer- term Sharpe-boosting features.
“CTA funds” come in many different flavours today:
i. CTA funds that have stayed true to the classical medium-term trend-following style, i.e., the strategy that seeks to boost client portfolio Sharpe ratios and protect client portfolios
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during bear markets by being a statistical – not a perfect – tail-risk hedge;
ii. Funds that are on their way to becoming multi-strategy hedge funds (probably doing so to maximise their stand-alone Sharpe ratio and to be able to handle larger assets under management);
iii. The ones that have chosen to become longer-term trend-followers or who have complemented their CTA strategy with long- only exposures to bonds and/or equities (a style drift prompted by large AUM and/or a desire to maximise stand-alone Sharpe ratio);
iv. Funds that have chosen to trade the futures markets on a higher frequency, i.e., high- frequency traders or short-term traders (who strive to be a complement to the medium- term trend followers and/or to protect client portfolios from shorter-term market corrections – these funds tend to have a fairly limited capacity, though).
In other words, investors who are searching for a classical CTA investment are advised to take a closer look at the different funds before making their decisions.
f) The sixth thing to keep in mind when comparing track records of CTA funds is the following: a like- for-like comparison also requires you to use the same data frequency for all funds. Theoretically, it should not matter if you calculate the annualised volatility on the basis of daily data, weekly data or monthly data. However, because CTA returns are not normally distributed and because they are not independent of each other, your estimates of the annualised volatility may differ quite considerably depending on whether you use e.g., daily or monthly data in your calculation. In other words, be sure to use the same data frequency for all CTA funds to get a fair comparison, even if some of them offer more frequent valuations than just monthly or weekly data.
g) Finally, when it comes to making forecasts about the future returns of CTA funds (as well as other hedge funds), some people just use the historical average return of the respective CTA fund as their forecast. Such forecasts may unfortunately be quite unrealistic. The reason is simple. Recall the fact that the net return of a CTA fund comes from two different sources, the risk-free rate on the base portfolio and the excess returns generated in the futures overlay.
Since the risk-free rate used to be clearly higher prior to 2008 than it has been thereafter, you
need to deduct the historical risk-free rate from the net return numbers and instead add the current risk-free rate (a much lower rate) in order to get a more sensible return forecast in today’s interest environment. THFJ
NOTES
1. In his article “The Sharpe Ratio” (1994) William Sharpe is first calculating the excess returns between the fund and the risk-free rate for each year (or another data frequency). Then he calculates a simple arithmetic average of the annual excess return numbers. The average return per annum is then put in relation to the standard deviation of the annual excess returns. This ratio is called the Sharpe ratio. William Sharpe is assuming a 1-period situation and is therefore using the arithmetic average for calculating returns per annum rather than the geometric average. Considering that investing is a multi-period phenomenon and that returns are ‘base-dependent’, we prefer to use the geometric methodology for calculating average returns per annum. A return of -50% in year 1 and +100% in year 2 would yield an arithmetic average return of (-50% +100%)/2 = +25% per annum. With the same assumptions, the geometric average return will be ((1-0.50)*(1+1.00))^(1/2)-1 = 0% per annum. Also, whereas William Sharpe first calculates the excess returns and then the average, we choose to calculate the geometric annualised returns for the fund and the risk-free rate first and then take the difference between the two annualised numbers. When it comes to the standard deviation of the excess returns, we approximate the volatility of the risk-free rate to be zero and just use the volatility of the funds to calculate our risk-adjusted return ratio. Rather than inventing a new name for our way of defining risk-adjusted return (which under normal situations will be quite similar to the original Sharpe ratio), we have chosen to refer to it as the Sharpe ratio.
2. This is only true as an approximation. The mathematics of scaling risk and excess returns are not so obvious. When you increase or reduce the size of the futures positions in a CTA fund to create a product with a different risk target, the excess return for a single day (i.e., the return beyond the risk-free rate or the return attributable to the base portfolio) will be directly proportionate to the excess return on a product that is run with another risk target. However, in a multi-period context, the effects of compounding start to distort the direct relationship between volatility and excess returns. Thus, in a multi-period context, scaling excess returns with the level of volatility should only be done as an approximation.
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