Reducing Uncertainty by Tranching
In the first 4 parts of this study we have focused on the optimization and robustness of the primary parameters necessary to apply the ITA Wealth Momentum Strategy – the appropriate look-back periods to measure momentum (Rate Of Change – ROC) and Volatility and the appropriate weights to apply to these factors. In the process of generating this data we have used a form of Monte Carlo analysis to randomly select check dates on which portfolios might be reviewed and to “average” the data to generate the heat maps used in the earlier parts of the study. However, we have not directly addressed the issue of “luck” associated with the random selection of review dates as first reported in Ernie Stokely’s post on January 12, 2015 (https://itawealth.com/2015/01/12/back-testing-issues-remain-skeptical-results/). In this Part 5 we directly address this issue and look at possible variations of the “tranching” concept to reduce or minimize the uncertainty associated with this effect.
Sticking with the Rutherford Portfolio as our benchmark portfolio we can run a standard back-test using the “robust” parameters identified in earlier parts of the study i.e. ROC1 = 60 trading days (87 calendar days), ROC2 = 100 trading days (145 calendar days) and Volatility = 13 trading day mean variance. These parameters are weighted 30%/50%/20% respectively to determine the Overall Rank as calculated in the Kipling 8.0 and Tranche 1.6 spreadsheets. When we introduce “check date noise” into the model by randomly choosing a minus 2 (-2) to plus 5 (+5) trading day variation from a standard 23 trading day (33 calendar day) review cycle we get a series of performance curves as shown below:
In the above figure we see that the average total return (heavy black line) based on 50 tests using random check/review dates (33 Calendar days -2/+5 trading days), over the ~9 year test period, is 287.3% (15.98% CAGR). However, it can be seen visually in the figure (lighter grey lines) that there is significant variation in this total return from a low of ~150% ($250k final value) to a high of ~400% ($500k final value). The Standard Deviation of the returns is 58.7%, therefore, assuming a normal (bell curve) distribution the 95% confidence limit is calculated as 287.3% -/+ 117.4% (2 SD) or ~170% to ~405%.
This uncertainty, due to the “luck” factor of the portfolio review date, makes many investors uncomfortable. We therefore look at variations of the tranching model , as suggested by the folks at Newfound Research, (http://www.thinknewfound.com/wp-content/uploads/2014/11/Minimizing-Timing-Luck-with-Portfolio-Tranching.pdf) to see if we can minimize this uncertainty.
In order to test the tranching model we varied the two additional parameters required by this model:
- The number of Tranches
- The number of days between tranches
Since the portfolio review period is ~23 trading days (33 calendar days) combinations of number of tranches and days between tranches resulting in a maximum look-back period of up to ~21 trading days was chosen for the tests.
At each tranche date, the standard “Kipling” momentum model (using the parameters identified above) is used to select the top 2 assets (and ties) ranked higher than SHY. The final portfolio allocation is then calculated as a weighted average of the individual tranche selections as in the Tranche 1.6 spreadsheet.
The results of the tests are summarized in the figure below:
In this figure, returns are plotted against the maximum look-back period reflected in the various tranche/separation combinations – e.g a 21 day look-back period can be covered using either a 21 tranche series with 1-day separation, an 11 tranche series with 2-day separation, a six tranche series with 4-day separation or a 5 tranche series with 5-day separation.
Average total returns (left hand axis) are plotted as solid lines for tranche separation values from 1 to 5. From these plots we note that there is a general reduction in total return as we increase the look-back period. This is probably not unexpected since we are introducing lag into the evaluation signals.
It is a little difficult to compare the separation curves directly since certain look-back periods cannot be achieved directly using a combination of number of tranches and separation between tranches – there is therefore some level of interpolation between data points except for the 1-day separation curve. However, we can note that there appears to be a small peak in performance (using small separation values) in the region of 4 look-back days. Due to the need for interpolation, as noted above, the 2-day separation curve does not show an obvious maximum at the 4-day look-back period, but there could be a maximum there – we only have data at the 3-day and 5-day points. Perhaps more significantly, returns do not drop off dramatically until we get to look-back periods in excess of 10 days.
Using calculated data of the Standard Deviation of average total returns we can calculate a value where there is a 90% probability of achieving a value, P(0.9), greater than a certain minimum level. These P(0.9) values (right hand axis) are also plotted, as dashed lines, against look-back period in the above figure. Obviously, since these values are at the low end of the range of returns in plots similar to the top figure they are less than the total return numbers, hence the reason for the 2 scales on the left and right hand axes. However, we can note from the above figure that P(0.9) values are relatively constant for all tranche lookback periods from 3 to 15 days, after which they drop off quickly – this in conjunction with the drop-off of average total returns.
As an illustration of what this implies, let’s look at the results of a 50 iteration test (50 different random 23 -2/+5 review date sequences) with a 9 day look-back period using 9 tranches with 1-day separation (red curves at 9-day look-back in above figure):
Comparing this with the top figure we note that we have an average total return of 287.7%, essentially the same as the basic “Kipling” return without tranching. However, note the significant reduction in variance (44.9% SD) between the minimum and maximum returns due to check date noise – “luck”. This results in an improvement in the P(0.9) return from 212% to 230%. Maybe an 18% difference over 9 years isn’t huge – but it is 2% annually – and, at least in this case, the average expected total return hasn’t been compromised.
- Tranching significantly reduces the Standard Deviation (variance) of total returns;
- Total returns may be reduced significantly at longer (tranching) look-back periods;
- There is a trade-off between reducing the variance in total returns and the expected total average return;
- Based on data from the current study a tranching look-back period of 3-15 days would appear to be beneficial and to offer a “robust” range for adjusting the tranche parameters (number of tranches and separation between tranches). Shorter tranche separation periods (1-4 days) are preferable. Possible combinations might be:
Note: The number of assets included in the portfolio increases (more diversification) with the number of tranches included in the analysis.
Although I prefer to avoid optimization, and hence offer a range of “robust” parameters that might be used, the results of these tests are still an optimization of the Rutherford portfolio assets over a relatively short (9yr) period of time that may not be typical of future market conditions. Members are advised to absorb this information and to use it carefully. Future tests using different portfolios and covering different time periods may offer further insight into the best way to use the tranching methodology.
We await your comments and requests for clarifications since we recognize that there is a lot of information contained in the above figures and it may be difficult for members to follow.
David and Ernie