Single Fund Analysis Performance (Peter Urbani via Infiniti Capital vs. RAPM's)
- Peter Urbani
- Aug 20, 2009
- 6 min read
On the out-of-sample Performance of the Infiniti SFA score versus traditional Risk Adjusted Performance Measures (RAPM’s).
As published in the Alternative Intelligence Quotient Magazine by Peter Urbani
Peter Urbani is Chief Investment Officer of Infiniti Capital, a Hong-Kong-based hedge fund of funds group.
Ever since the seminal work on Portfolio Theory by Harry Markowitz (1959) and the subsequent work of William Sharpe the measurement of portfolio returns has been inextricably linked to level of risk associated with achieving those returns.
This has led to the introduction of a number of Risk Adjusted Performance Measures (RAPM’s) most famously the reward-to-variability or Sharpe-Ratio.
Typically calculated as the portfolio returns in excess of those of the risk free rate over the standard deviation of portfolio returns, the Sharpe Ratio embeds the concept of the variance squared, standard deviation, or volatility as the appropriate measure of ‘risk’ to use.
Over time practitioners and academics alike have realized that this poses a number of problems for the accurate measurement of ‘risk’. In fact the use of variance was largely an act of convenience to simplify the math in the days before computers. Markowitz himself has said that for some investor’s semi-variance might be a more appropriate measure to use.
The reason for this is simply that variance or standard deviation as is more commonly used ( square root of the variance ) is not a measure of ‘risk’ at all but rather a measure of uncertainty. Standard Deviation suffers from a number of well known deficiencies most particularly the fact that it does not differentiate between good ( upside ) ‘risk’ and bad ( downside ) ‘risk’. Moreover, it is a symmetric measure that assumes both upside- and downside-variance are the same.
In recognition of these deficiencies a number of other RAPM’s have been developed to better address these issues. Probably the best know of these is the Sortino Ratio which replaces the standard deviation with the downside deviation or second lower partial moment (LPM2) as the denominator in the Sharpe Ratio.
Still others include the modified Sharpe Ratio where the denominator of risk is represented by the Cornish Fisher expanded or ‘modified’ Value at Risk (VaR).
More recently Shadwick and Keating pioneered the use of the Omega Function sometimes also used as Omega Ratio. In this formula the area under the probability curve in excess of some threshold return is taken over the area under the curve of the downside part of the distribution. This can be calculated in both discrete- form using empirical data or continuous form by fitting a distribution.
From a practitioners perspective what we care most about is how well these measures predict the relative ranking from one period to the next and whether or not using one particular method produces superior returns to another. Although these RAPM’s are typically used for calculating the relative ranking of funds they can also be- and often are- used as the objective function in direct portfolio optimisations. For instance maximizing the value of your Portfolio’s Sharpe Ratio is the same as minimizing its variance and gives the same set of weights as the classical Markowitz mean variance optimisation formulation. Minimising your ‘normal’ Value at Risk will give the same solution. However, as mentioned previously measures based on standard deviation such as Sharpe and the normal Value at Risk calculation do not consider the asymmetry of returns
Infiniti too has its own proprietary measure called the Infiniti Single Fund Analysis (SFA) score. This measure is a weighted average of a number of underlying statistics that has also been standardized to a reference data set making it both a relative and conditional measure. The SFA score can further be decomposed into Risk, Return and Persistence sub-scores.
In the study referenced below we compare the out-of-sample performance of a portfolio built using the Infiniti SFA score as its objective function versus the performance of portfolios built from the same data set using the Sharpe, Sortino and Omega measures. For reference we also include a naive benchmark made up of an equally weighted continuously re-balanced portfolio of all of the 36 underlying hedge funds in the selection universe. The portfolio’s are re-optimised to the objective function and rebalanced on a quarterly basis.
The results of the study suggest that the SFA score is capable of generating annualised rates of returns (CAGR) of around 15% versus those of around 11.5% for the Sharpe Ratio, 13% for the Omega Ratio and just 10% for the Sortino Ratio.
More importantly, although the Sharpe ratio of the resultant time series remains better for both the Sharpe and Omega portfolio’s, the ratio of the annualised return to the absolute drawdown over the period, which is arguably a better measure of realized risk to return, remains highest for the SFA score portfolio.
Infiniti CIO, Peter Urbani says, “The reason for the superior performance of the SFA scores is due to it not being a simple point estimate but being calibrated relative to a reference data set of other hedge funds. This improves the predictive power of the method because it responds dynamically to market conditions. In order to ensure the availability of data for the SFA reference scores the portfolio are also optimized with a one-month data lag. This means that January SFA scores which only become available in February are used to obtain the March opening portfolio weights.”
Unlike traditional performance measures, the SFA score is both conditional on the time period being used and relative to a large reference data set of other hedge funds. Where other methods typically standardize everything back to a normal or Gaussian distribution, the IAS uses the best fitting distributions throughout. This has the effect of calibrating the range of scores more closely to real-world data.
Urbani stresses that the method is not perfect. “The SFA scores will not provide the best returns over each and every single time period, however, over any meaningful length of time they will tend to out-perform.”
“We were somewhat surprised by the poor performance of the Sortino ratio portfolio relative to that of the Sharpe ratio portfolio”, says Urbani. “We believe this may have been due to the fact that the quality of the 36 underlying hedge funds used was very good. This enabled the computer to select portfolio weights that gave a portfolio with zero downside deviation in the in-sample optimisation periods. The low variance of these portfolios did not persist out-of-sample in the subsequent periods causing this portfolio to underperform.”
“This is a classical problem of over-fitting your data which results in there being little relationship between the in-sample period and the performance in the next period. The Sharpe Ratio suffers from a similar problem but more because it is capturing only the linear effects of the portfolio whereas we know there are significant non-linear effects present in Hedge Funds. ”
The SFA score is able to capture some of these non-linear artifacts because of the statistics used in its calculation and the best-fitting non-normal distributions it uses. These have the effect both of improving the predictive power of the method and ensuring the resultant pay-off is positively skewed or as close to positively skewed as possible. This translates into more upside risk than downside risk.
Urbani says, “Subsequent studies where we have used less well performing hedge Fund indices have confirmed our beliefs and the intuitive expectation that the Sortino ratio should out-perform the Sharpe ratio.”
The SFA score has been developed by Infiniti over the past several years and has been used internally for the past two years. It is included as a ranking method and objective function in the recently launched Infiniti Analytics Suite (IAS).
He says, “We do not force people to use the SFA scores. This is a key point of differentiation between the IAS and other software packages. Just because we have a good idea doesn’t mean everyone should use it. That’s why this is an option in the IAS along with the ability to use just about any other known RAPM for optimisation purposes or to build your own.”
Below is a Powerpoint presentation which illustrates the superiority of the compound SFA score against traditional scoring methods like Sharpe, Sortino and Omega.
References:
The Infiniti SFA score as a RAPM – Peter Urbani (2009) https://www.academia.edu/7822710/SFA_Score_as_a_Risk_Adjusted_Performance_Measure
Portfolio Selection: Efficient Diversification of Investments – Harry Markowitz (1959) http://cowles.econ.yale.edu/P/cm/m16/index.htm
Sharpe Ratio – William Sharpe http://en.wikipedia.org/wiki/Sharpe_ratio
Sortino Ratio – Frank Sortino http://en.wikipedia.org/wiki/Sortino_ratio
Omega Ratio - A Universal Performance Measure – Keating and Shadwick (2002) http://www.performance-measurement.org/KeatingShadwick2002a.pdf
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