*Using Tranching to Mitigate “Timing Luck”*

7/6/2015

Ernie Stokely

ITA Wealth members are hopefully now all aware of the effect over time of the choice of the rebalancing (checkup) date on portfolio return. Some check dates give better results than others, and there is no way to know *a priori* what “good” dates will be. The chart below illustrates the problem. This chart is a Monte Carlo back test of the Rutherford portfolio from 7/9/2007 to 6/15/2015. The calculated checkup date every 33 (calendar) days was randomly modified over a -2 to +5 (trading) date range. The gray lines represent each individual back test. Note the very large possible outcomes, where the dark line represents the average of all back tests and the red line is the return for VTTVX, a Vanguard 2025 Retirement Investor fund that was chosen as an index. The Kipling 8.0 workbook momentum management technique was used to guide the selection and allocation of assets at each checkup date. A maximum of two assets with equal portfolio asset allocation were chosen for the selected portfolio at each checkup date. If no assets had better performance than SHY, the entire portfolio was invested in SHY. If only one asset had better performance, the portfolio value was split between SHY and the qualifying asset.

Fig. 1 Monte Carlo Test of Rutherford Portfolio with Two Assets

There is little doubt that this unknown variation in portfolio return is one of the most troubling aspects of the 33-date checkup scheme using the momentum method. It has been deemed to be the “elephant in the room” by one astute ITA member. We have played with a number of schemes for reducing the effect, but so far none has been satisfactory.

The effect shown in Fig. 1 is addressed in a paper by Newfound Research entitled, “Minimizing Timing Luck with Portfolio Tranching: The Difference Between Hired and Fired.” The URL for this interesting paper can be found at this link:

Minimizing Timing Luck with Portfolio Tranching

The first part of the paper develops a statistical model for the effects of what they coin “timing luck” and the last part of the paper has a suggested method for reducing the effects of timing luck using tranching. Basically, the idea is to analyze the market several times during the checkup cycle and record the momentum results at each analysis point, thereby developing potential momentum tranches. Then, using some averaging method, at the checkup date compute a portfolio and its allocations from the results of the inter-period portfolio momentum analyses. I asked HedgeHunter to read this paper and help me understand the method they proposed for implementing this method.

He presented an excellent suggestion for testing. Suppose we are at some checkup date. We can form a set of “tranche portfolios” by running the momentum engine four times: once using the checkup date, another, say, 6 trading days prior, another 12 trading days prior, and the last 17 days prior. At each of those days we fully analyze the market and we calculate using the Kipling 8.0 momentum engine. A selected portfolio is allocated according to the specified rules (in this case, equal allocation for all assets as explained above). We then compute a combined portfolio by selecting every asset that was chosen at any one of the 4 inter-period checkup points, and we allocate the select portfolio assets according to the number of times a particular asset was chosen. A chart provided by HedgeHunter gives a clearer explanation.

In Table I we are running the momentum engine with 2 assets maximum in the portfolio. On the checkup date assets D and A are chosen (equally weighted). Eight calendar days earlier assets B and D are chosen. Sixteen calendar days earlier assets B and C are chosen, and so on. If we move to the right-hand side of the table, we see a list of all of the assets that were chosen and their allocation in percent. For a 2-asset select portfolio situation, there will be 2 assets/tranche date times 4 tranche dates, or 8 assets chosen (some the same asset) with a weight of 0.5 each (total of 4.0 when added together). In this illustration each of the assets, A-D, will be in the final select portfolio. They will be allocated in the final portfolio allocation by adding the total contribution in percent over the four periods for each and dividing by 400%, as shown in the bottom row of Table I. This is the algorithm I implemented, except my inter-period checkup dates were slightly different.

Calendar Day | Asset 1 | Asset 2 | A | B | C | D | |

9 | A | B | 50% | 50% | |||

17 | B | C | 50% | 50% | |||

25 | B | D | 50% | 50% | |||

33 | D | A | 50% | 50% | |||

Weighted Portfolio | 25% | 37.5% | 12.5% | 25% |

Table I: HedgeHunter’s Suggested Tranching Method

Before presenting results, it is enlightening to take a look at a real table from just two 33-day periods of the back test. Here are the actual number that were obtained during a small part of the back test.

TLT | PCY | SHY | VTI | TIP | VNQ | VWO | RWX | VEA | DBC | GLD | |

1 | 50% | 50% | |||||||||

2 | 50% | 50% | |||||||||

3 | 50% | 50% | |||||||||

4 | 50% | 50% | |||||||||

Wgts | 12.5% | 50% | 12.5% | 25% |

TLT | PCY | SHY | VTI | TIP | VNQ | VWO | RWX | VEA | DBC | GLD | |

1 | 50% | 50% | |||||||||

2 | 50% | 50% | |||||||||

3 | 50% | 50% | |||||||||

4 | 50% | 50% | |||||||||

Wgts | 50% | 50% |

An additional fabricated example is included to illustrate the method.

TLT | PCY | SHY | VTI | TIP | VNQ | VWO | RWX | VEA | DBC | GLD | |

1 | 50% | 50% | |||||||||

2 | 50% | 50% | |||||||||

3 | 50% | 50% | |||||||||

4 | 50% | 50% | |||||||||

Wgts | 12.5% | 25% | 12.5% | 12.5% | 25% | 12.5% |

Table II – Actual Momentum-Select Portfolio Results from Back Test

We start with all the assets in the portfolio. Each subset of data starting with the portfolio ticker list and ending with the two or three assets that were funded for the next 33-day cycle represent the calculations for a single 33-day cycle. Rows 2-4 represent the momentum and allocation results at each inter-period checkup point.

**Just look at how much the select portfolio would have changed in the first data set if one had picked any one of the four different dates for rebalancing for the next 33 days!** This is a great example of the problem we face with timing luck.

The Rutherford portfolio was run with the same conditions using the tranche calculations as just described (Fig. 2). There is an obvious reduction in the variation among the individual 8-year runs.

Fig. 2 Rutherford Portfolio (2 assets) Using Tranche Techniques

One calculation that was run during the tranche study was the average number of assets that were funded over all of the runs (one could have up to 8 maximum, even though we specify that we only want a maximum of two at each inter-period check point). The average number of selected portfolio assets was 2.96.

Now we know that if we increase the number of assets in the portfolio, the effects of timing luck is reduced as reflected in the standard deviation of the total returns. So, this raises the question of how the tranche method would stack up with the results from just specifying three assets instead of two and only doing the checkup every 33 days as before. These results are shown in Fig. 3.

Fig. 3 Monte Carlo Test of Rutherford Portfolio with Three Assets

Another idea proposed by Lowell was to see what happens if we use the tranche technique but only specify a single asset in the select portfolio. Here is that chart.

Fig. 4 Rutherford Portfolio (1 asset) Using Tranche Techniques

Finally, an ITA Wealth member, Herb Haynes, proposed weighting the tranches so that the more distant tranches got less weight and the more recent ones got more weight. To test this idea, the 2-asset portfolio was rerun with weightings 0.5, 0.25, 0.15, and 0.1 applied to the inter-period allocations as the tranche timing moved from the checkup date into the past 33 days. In other words, referring to Table II, Row 4 33-day allocations would have a 0.5 multiplier, the Row 3 allocations would be multiplied by 0.25, and so forth. The results are shown in the chart presented below as Fig. 5.

Fig 5. Rutherford Portfolio Using a Weighted Tranche

Now, let’s get to the numbers. Here is a table comparing the salient results of the three back tests.

Method | AverageReturn | Std.Dev. | Ave.CAGR | Ave.Volatility | Max. DD* | Ave. DD |

Tranche – 1 asset | 234.2% | 36% | 17.1% | 17.2% | 20.9% | 12.2% |

Tranche – 2 assets | 230% | 26.1% | 16.9% | 13.8% | 18.7% | 9.6% |

Tranche – 2 assets/wtg | 242.8% | 33.6% | 17.5% | 13.8% | 18% | 9.4% |

Two assets (no T.) | 258.6% | 60% | 18% | 14.3% | 18.8% | 9.5% |

Three assets (no T.) | 192.4% | 30.5% | 15% | 11.8% | 19.2% | 8.9% |

VTTVX | 51.7% | ——- | 38.4% | 38.4% |

*DD = draw down

Suppose we calculate the coefficient of variation (SD/mean) for the methods.

Tranche – 1 asset: 0.15

Tranche – 2 assets: 0.11

Tranche – 2 assets/weighting: 0.13

Two assets (no. t): 0.23

Three assets (no t.): 0.159.

Seen in this light where lower numbers suggest less variation, the tranche method clearly gives the best reduction to timing noise when return is also considered.

Of special interest are the tranche results that used temporal weighting to calculate the final allocations. This result had the second lowest coefficient of variation but the highest CAGR and second highest average return.

__Conclusion__

Like everything in life, the tranche method seems to have much to offer but is not perfect. It clearly give the biggest bang for the buck when the coefficient of variation is considered. It also has good volatility, CAGR, and DD numbers. The tranche/weighted result is worthy of special consideration. Just adding a third asset to the portfolio to reduce the timing luck effect seems to cost too much in reduced returns in light of the amount of timing luck that is reduced.

Keep in mind that this implementation of the tranche method just uses 4 tranche inter-period calculations. The referenced paper even mentions daily tranche calculations, but I do not believe daily attention to a portfolio would be of interest to ITA Wealth members.

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