The idea of having a true benchmark for Trend Following (a.k.a. Managed Futures/CTAs), independent from the performance of the existing funds, could shake up the industry and have serious implications (increased competition and fees reduction resulting from commoditization of Trend Following).
The Beta of Managed Futures paper (PDF) by Conquest Group and their claim to an independent, mechanical Trend Following benchmark got me going. I decided to use it as a benchmark for the Trend Following Wizards we track here every month. The comparison calculations (using innovative metrics) can be found at the end of this article.
If CTAs mostly produce beta and a bit of alpha, they should really charge their fees accordingly, i.e. a flat management fee for the beta and a performance fee based on the alpha they produce – instead of a performance fee on the overall performance of the fund. But how do you calculate alpha?
Information Ratio: misinformation?
There are several ways to measure alpa and the Information ratio is a popular one. The concept behind the Information Ratio (IR) is interesting as it aims to measure the alpha (excess return) provided by the fund compared to the benchmark. It also takes into account the tracking error of the fund (volatility of the excess return).
As such the IR can be expressed as follows:
However, there is a (common to many CAPM models/tools) flaw in this ratio calculation: it uses the arithmetic mean return rather than the geometric one. This difference could give a positive IR to a fund producing negative alpha and viceversa. To convince yourself, consider a hypothetic manager producing +15% alpha followed by 14% alpha at regular intervals. Calculate both average returns: the arithmetic one, +0.5% and the geometric one, 1.1%. How is this for painting a different alpha picture!
Another way to calculate Alpha
Alpha is the true value added by a manager, regardless of the underlying market/benchmark.
If investors simply want to get exposure to the alpha from a specific manager, they could simply “buy the manager” and short the benchmark (with constant rebalancing). Once taking into account the manager’s beta to the benchmark (to derive respective long and short positions), all that is left to the investor is the alpha produced by the manager (with zero market/beta risk).
Taking this logic into account, below is an alternative way of calculating a (modified) Information Ratio to give a more accurate picture of the true alpha as per the logic mentioned just above:
 Calculate the manager’s beta to the benchmark:
 Normalise both sets of monthly returns using beta as a multiplier
 Calculate monthly alphas as the difference between normalised returns:
 Compound alpha and calculate its geometric mean (i.e. compounded growth rate):
 Calculate the geometric standard deviation of the monthly alpha (variability of alpha, i.e. omega):
 Divide alpha by omega to obtain this new Information Ratio (let’s call it Geometric IR)
Trend Following Wizards ranking
Below is the calculation of the standard and modified/geometric Information Ratios for the Trend Following Wizards, for which we could find historical performance – as well as other information such as alpha, beta and correlation (using Pearson productmoment coefficient) to the benchmark. To give some background, total performance and standard deviation of returns over the full period have been added as well.
For this exercise, the Conquest Group Managed Futures Select fund was used as a Trend Following benchmark (as this is what it aims to produce), with the period covered being Jun04 to Mar10 (full history of the benchmark). All fund performances below are considered net of fees.
Fund  Rtn.^{a}  SD^{b}  IR^{c}  Beta^{d}  Corr.^{e}  Alpha (yr)^{f}  GIR^{g} 

Abraham Trading^{1} 
53.86%

5.01%

0.00

0.53

0.47

3.12%

0.06

Chesapeake Capital^{2} 
44.60%

5.34%

0.01

0.66

0.55

0.99%

0.02

Clarke Capital^{3} 
48.55%

7.90%

0.01

0.30

0.17

4.34%

0.05

Dunn Capital^{4} 
59.38%

9.01%

0.04

1.21

0.60

1.07%

0.01

Eckhardt Trading^{5} 
61.34%

3.53%

0.00

0.35

0.43

5.43%

0.14

EMC Capital^{6} 
76.00%

5.18%

0.05

0.83

0.71

3.20%

0.07

Hawksbill Capital^{7} 
88.80%

9.47%

0.08

1.21

0.57

1.76%

0.02

Hyman Beck & Co.^{8} 
82.06%

4.92%

0.06

0.71

0.64

4.66%

0.10

JWH & Co.^{9} 
1.34%

8.03%

0.07

1.21

0.67

8.51%

0.12

Man AHL Diversified^{10} 
65.85%

3.71%

0.02

0.59

0.71

3.91%

0.12

Millburn Ridgefield^{11} 
60.85%

3.95%

0.01

0.53

0.60

3.84%

0.10

Rabar Market Research^{12} 
55.87%

4.20%

0.00

0.51

0.54

3.49%

0.08

Saxon Investment^{13} 
57.15%

3.12%

0.01

0.32

0.45

5.20%

0.15

Superfund^{14} 
21.84%

6.53%

0.05

0.83

0.57

3.17%

0.05

Transtrend^{15} 
57.89%

2.27%

0.02

0.30

0.58

5.47%

0.24

Winton Capital^{16} 
116.63%

3.70%

0.12

0.48

0.58

9.72%

0.25

Notes:
^{a. Total Compounded Return since 2004
b. Standard Deviation of monthly returns since 2004
c. Classic Information Ratio
d. Beta of the manager to the benchmark
e. Correlation (Pearson)
f. Annualized Alpha
g. Modified/Geometric Information Ratio
1. Abraham Trading was founded by Salem Abraham, after he was introduced to Managed Futures and Trend Following by Jerry Parker. He is considered as a “secondgeneration” Turtle.
2. Chesapeake Capital was founded by Jerry Parker, a former Turtle.
3. Clarke Capital was founded by Michael Clarke in 1993.
4. Dunn Capital was founded by Bill Dunn.
5. Eckhardt Trading is the firm managed by William Eckhardt, who coled the Turtle experiment with Richard Dennis
6. EMC Capital was founded by Liz Cheval, a former Turtle.
7. Hawksbill Capital was founded by Tom Shanks, a former Turtle.
8. Hyman Beck & Co. main principals are Alexander Hyman and Carl Beck.
9. JWH & Co. was founded by John W. Henry, Owner of the Boston Red Sox.
10. Originally ED & F Man. Became a succesful CTA under Larry Hite and went on to form part of The Man Group plc, which subsequently bought AHL to form the Man AHL: the systematic trading division of the Man group.
11. Millburn Ridgefield have been trading Trend Following models since the early 1970′s. As they report performance figures one month later, last month performance is not reported in this report and their YTD, AUM stats are from the month before.
12. Rabar Market Research is the company of Paul Rabar, a former Turtle.
13. Saxon Investment was founded by Howard Seidler, a former Turtle.
14. Superfund founder and CEO: Christian Baha.
15. Transtrend is a Trend follower CTA based in Netherlands
16. Winton Capital is a Londonbased CTA founded by Dave Harding (also cofounder of AHL).}
Note that the negative values of Information Ratio are usually not really relevant.
The Pearson coefficient measures gravitate around 0.60, which shows some degree of correlation to the benchmark – maybe not as strong as initially hinted by the Conquest paper. Obviously, the higher the correlation numbers, the more support for the thesis of a possible Trend Following benchmark.
Interestingly, the two versions of the Information Ratio show some discrepancies (expected as per earlier explanations) with a few funds switching from negative IR to positive geometric IR (and viceversa). Most notable is the case of Transtrend, which goes from negative IR (0.02) to the secondbest geometric IR (0.24). Comparing all individual results, it seems that the geometric Information Ratio is a much better measure of alpha.
It can appear strange that some funds underperforming the benchmark still appear to produce alpha (example of Chesapeake Capital: return of 44.60% vs 56.95% for the benchmark). This is due to the methodology of the calculation, which assumes constant rebalancing between the benchmark and the fund to capture and compound each period’s alpha.
Finally, it is worth noting that despite (much) higher fees for the Trend Following Wizards (compared to Conquest Group MFS fund acting as the benchmark), most of them still exhibit alpha/excess return.
Below are the numbers for the benchmark and its corresponding leveraged version (3x) from Conquest:
Fund  Return  StdDev  IR  Beta  Correl.  Alpha (yr)  GIR 

Conquest Group MFS 
56.95%

4.44%

0.17^{*}

1

1

0%

0

Conquest Group MFS 3x 
85.14%

13.93%

0.10

3.12

0.996

7.04%

0.46

Some of these numbers are selfevident (ie correlation, beta of the benchmark to itself); but of interest is the fact that the 3x option produces negative alpha at the rate of over 7% per year while keeping a very strong correlation to the standard fund/benchmark (not so surprising given the previous discussion on leverage). Meanwhile, the classic IR still indicates positive alpha…
^{*} Note another aberration from the classic IR calculation. It is theoritically not possible to calculate the IR of a benchmark with itself (results in a 0 into 0 division). However, the IR of ALL straight beta multiplications of the benchmark (with correlation = 1) are identical (just a byproduct of the linearity of mean and standard deviation). Constructing a virtual benchmark with a beta very close to 1 (ie 1.00001) and a correlation of 1 to the real benchmark allows for calculating both IR (standard and geometric), while, for all intents and purposes, the virtual benchmark can be considered equal to the real benchmark. It would result, from the classic IR calculation, that the benchmark actually produces alpha to itself (IR>0)! The geometric IR correctly computes to 0.
Another Tool in the Box
We can see that the Trend Following Wizards ranking using the Geometric Information Ratio gives a different insight to their raw performance numbers.
Hopefully, you find this Geometric Information Ratio useful to compare several funds, instruments or even your own strategies relative to a common benchmark. In any case, it is worth noting the importance of understanding how any performance metrics work. Following blindly the results from the classic Information Ratio might result in incorrect conclusions.
Stephane // Apr 23, 2010 at 10:33 am
Hi Jez,
First, I’d like to congratulate you for the quality of your posts, they are very valuable. Could you please provide an excel file that generates the Geometric Information Ratio calculation?
kind regards,
Stephane
Jez // Apr 23, 2010 at 2:00 pm
Hi Stephane.
Thanks for your comment – it’s nice to hear!
I was thinking uloading the spreadsheet would be a good idea but I still need to tidy up the various spreadsheets I worked with this week. Probably a weekend job and a followup post with a full formula and Excel spreadsheet examples.
Stephane // Apr 24, 2010 at 3:42 am
Great Jez!!
keep up the good job!!
felicity // Apr 27, 2010 at 2:10 pm
I think what really makes the difference is how you calcualte the excess return or alpha. As long as you “beta” normalize the return, or (Rb*Rb), geometric and arithmetic IR out of it are not far from each other.
Jez // Apr 27, 2010 at 3:28 pm
@felicity, you’re right, the betanormalization is probably the most important factor in improving the IR. However you could argue that there is still the theoritical possibility for a positive arithmetic alpha and a negative geometric one.
I computed the betaadjusted arithmetic return based IR :
ABRAHAM 0.080
CHESAPEAKE 0.041
CLARKE CAP 0.082
DUNN 0.024
ECKHARDT 0.155
EMC 0.090
HAWKSBILL 0.057
HYMANBECK 0.120
JWH 0.093
MAN 0.136
MILLBURN 0.115
RABAR 0.098
SAXON 0.166
SUPERFUND 0.023
TRANSTREND 0.250
WINTON 0.273
The results are very much in line with the GIR results in the post
Stan Cramer // Apr 30, 2010 at 7:46 am
There is a far simpler way to look at this situation, namely, as a humble scatterplot.
For each time period, plot a dot whose xcoordinate is (the benchmark’s return in that period) and whose ycoordinate is (the money manager’s return in that period). I uploaded an example of this kind of scatterplot at this URL, feel free to link to it however you wish: http://img511.imageshack.us/img511/3697/alphabeta.png
“Beta” is the slope of the linear regression line, and “Alpha” is the yintercept of the linear regression. Leave the covariance and other fancy formulae & computations to your regression software, and instead focus on the intuition provided by a simple picture.
It’s as plain as the nose on your face: Beta (slope) shows the amount of comovement, Alpha (yintercept) shows how much the manager outperforms the benchmark. The third output from regression, Rsquared, shows how well or how poorly the benchmark matches the manager.
Your “innovation” in this article, is to suggest that instead of plotting (returns), it is preferable to plot (the logarithm of returns). Otherwise it’s identical.
Jez // Apr 30, 2010 at 8:42 am
Hi Stan,
Thanks for suggesting an alternative solution to this problem. Unfortunately your approach, yet simpler, fails to capture some of the information contained in the GIR, such as the compounding effect, which appears when using geometric average of returns (or alternatively continuously compounded returns).
The approach suggested in the post is quite different from simply plotting the logarithm of returns. Indeed, using regression analysis and its intercept to calculate alpha does result in different rankings for the CTAs observed, both also different from the ranking based on the GIR value.
To illustrate one of the differences, I plotted a scatterplot using Dunn and the benchmark as per your suggestion. Note that the alpha that would be derived from that method is positive (similarly to the standard IR calculation), while the geometric Information Ratio calculation is negative.
jack // Sep 27, 2010 at 1:58 am
In my opinion there is only one way to calculate Alpha and that is to compare system output with broker statements to generate the Beta result. Anything above/below Beta generated will be +/ Alpha.
An Beta/Alpha ratio would be welcome but it requires transparency from the CTA´s.
Jez Liberty // Sep 27, 2010 at 4:51 am
jack – you might be referring to the manager’s execution alpha (ie real executed price vs. system price), however this post was more related to the manager’s overall alpha compared to simple beta exposure to “generic” Trend Following returns (from a transparent benchmark)
jack // Sep 27, 2010 at 4:54 am
Jez – What do we really know about the underlying managers in any (benchmark) systematic trend following index. Did they always lived to the system, or was there a directional overlay at times. How much alpha do we need to account for if any?
The only way of finding out is to compare system output with broker statements going back over the reported time and create another measure ratio called Systematic(Beta)/Alpha. However, that would require full transparency from the CTA´s.
Jez Liberty // Sep 27, 2010 at 5:21 am
this is why the benchmark for Trend Following is independent from the performance of the existing funds, but instead implements basic mechanical strategies – you can read the Beta of Managed Futures paper (link above in post) for more info.
Moreover, the manager’s alpha might and is probably already included in the system itself (ie CTA alpha rarely comes from diverging from the system but mostly from innovative research methods that feed into the system rules). Well, at least for 100% systematic CTAs.
jack // Sep 27, 2010 at 8:09 am
That doesn´t make much sense to me at all. What are those basic mechanical strategies and how do they work compared to what we use for example? Is it one strategy, or multiple strategies?? Which markets, leverage, etc….to many variables here to even try to compare apples with bananas. In my opinion this whole exercise is not painting a clear picture and never will.
Merely to point out that real life is always, but always messier than that!
One of our trading rules is: ignore the clients and focus on the job of making money, and that has been a key element what has ensured our success.
Jennifer @ emanaged futures // Aug 4, 2011 at 6:58 pm
Very interesting mathematical approach. I think Stan’s method, while simpler, would produce less reliable results. Betanormalization is really the key which makes this meaningful information. Very good summary.