Frequent readers of this blog know that I am somewhat obsessed with the concept of timing luck and portfolio tranching, with the ultimate goal of reducing the variance of active returns. For those less familiar with the topic, you can read our introductory white paper here.
I recently wrote a more in-depth research paper on the topic, covering how timing luck affects tactical portfolios, smart beta portfolios, and strategic portfolios alike.
Here the abstract:
While the choice of rebalance frequency is often well thought out, the choice of when to rebalance a portfolio is often an after-thought. Research papers, and even live strategies, typically use convenient calendar dates like the first or last trading days of the month.
In this paper, we introduce the concept of offset portfolios, the collection of portfolios running identical strategies with an identical rebalance frequency, but rebalancing on unique days. The variance in total return profile between these offset portfolios highlights the impact of timing luck: the deviation from the long-term expected strategy return due entirely to when a portfolio is rebalanced.
This variance can have a massive impact on both hypothetical back-tested research as well as live track records. We demonstrate that from the period of 1950-2014, the tactical trading methodology proposed by Faber (2013) may overstate its total return profile from the true expected strategy return by 1800 percentage points, simply due to its choice of end-of-month rebalancing.
Timing luck affects tactical, smart beta, and strategic portfolios alike. In this paper we provide examples of portfolios of each type, generate the offset portfolios, and build a model for the spread between the best and worst performing offset portfolios over time.
We then introduce the concept of portfolio tranching, proving that an equal-weight portfolio-of-offset-portfolios minimizes the impact of timing luck. We then demonstrate the impact tranching would have on each of the examples provided earlier in the paper.
Since they say a picture is worth 1000 words, I thought I'd just throw up some of the figures from the paper.
First. the equity curves and portfolio statistics of a tactical strategy based on a simple 200-day moving average timing model. These portfolios all have the same rules, but are rebalanced on different days.
Below are a point-in-time snapshot of the allocations for different target 6% volatility portfolios, all governed by the same rules but rebalanced on a different day. We can see that simply rebalancing on the last day of the month or somewhere in the middle can dramatically affect portfolio composition based on changing correlation and volatility levels.
We can look at, for a single one of these portfolios, the allocations over time versus the allocations of a tranched portfolio. We can see that while the individual portfolio has a jagged allocation profile, the tranched portfolio smooths the allocations over time, making it less sensitive to timing based allocation differences. It is not a stretch to say in the strategic case that tranching is related to resampling, if you consider each of your offset portfolios to have slightly perturbed variance-covariance statistics.
Below we plot the different equity curves of a value stock portfolio, with the same screening rules but rebalanced on different days. Highlighted is the tranched portfolio as well as the "average" of investing across all the portfolios. We can see how simply rebalancing at different days can lead to dramatically different portfolio results, but also that the tranched portfolio is an excellent proxy for the true average.
The full research paper is available for download here.