Flirting with Models™ | The Blog of Newfound Research

The Luck of the Rebalance Timing

On August 7, 2013

One of the biggest hurdles in executing tactical models is when to rebalance. When a signal changes? Weekly? Monthly? The choices can have a dramatic effect upon strategy results: the more timely the rebalance to the signal, the more of the movement that tends to be captured — but the more whipsaw and trading costs that are generally incurred.

While we believe our model of dynamic, volatility-adjusted momentum is a more efficient method of capturing momentum opportunities, rebalance and timing discussions are still relevant in overall portfolio composition.

I wanted to dig in to this issue and show how the decision of when to rebalance can make an incredible difference in long-term performance.

To examine the effects, I chose to play with one of the more famous tactical risk management models: Mebane Faber’s 10-month simple moving average timing model, popularized in his 2006 paper “A Quantitative Approach to Tactical Asset Management“. In the paper, Faber utilizes a simple methodology for determining whether an asset was eligible for inclusion in the portfolio based on whether it is above or below its 10-month moving average.

One of the issues is that in using the 10-month moving average, Faber’s model implicitly trades on the first day of each month. But what happens if we rebalance the 2nd day, or the 3rd? The 15th? Did choosing the 1st day end up materially changing the results?

In the interest of simplicity, I decided to model months as 21-day periods, and compared 21 different strategies using 1-day offsets, running the model on the S&P 500 ETF “SPY”. Each strategy rebalanced every 21 days; the 21st strategy rebalanced 20 days after (or, 1 day before, depending on your perspective) the 1st strategy. Signals occurred after close and trading occurred at the next opens. No trading costs or slippage effects were estimated.

The results are interesting to say the least. Strategies for days 19 and 20 highlight the difference a single day can make:A single day changed the max drawdown from 19.03% to a 30.22%; annualized returns drops from 11.33% to 10.51%. The full performance results for each strategy can be seen below:

While overall volatility levels remain fairly consistent, there is a 25,425bp spread between the total return for the best and worst returning strategies (717.14% and 462.89% respectively).

Obviously, when you chose to rebalance can have a huge impact on the whipsaw you incur.

So how can we fix this? Well, one of the ways is to put 1/21st of our portfolio in each of these strategies — rebalancing 1/21st of our portfolio every day — and rebalancing back to equal-weight at the beginning of every year. The results?

A total return of 625% (an annualized return of 10.98%)
Annualized volatility of 13.37%
A max drawdown of -19.03%

Now this analysis doesn’t take into account trading costs — but since we are rebalancing only 1/21st of our portfolio every day, the total turn-over ends up nearly identical to the turn-over from the original strategy. It’s certainly a bit more work — but it also helps limit the impact of choosing the wrong date to rebalance.

By being smart about when we choose to rebalance, and how we choose to rebalance, we can remove the “luck of the timing” — be it good or bad — from our strategy and capture the pure quantitative effects.

As January goes, so goes the year?

By Justin Sibears

On February 4, 2013

In Uncategorized

At Newfound, we are strong proponents of rules-based investing. However, rules-based investing in and of itself is not a panacea. The best rules will be defensible both in theory and in practice and be robust to dynamic market environments.

The following chart shows for each month the percentage of times that the sign of that month’s S&P 500 return matched the sign of the return for the period starting in the beginning of that month and ending one year later.

For example, the January figure means that starting in 1950, 69.8% of the time the sign of the return from January 1st to February 1st of that year matched the sign of the return from January 1st of that year to January 1st of the next year.

Month	Percent
January	69.8%
February	63.5%
March	73.0%
April	58.7%
May	65.1%
June	61.9%
July	54.0%
August	55.6%
September	52.4%
October	65.1%
November	65.1%
December	76.2%

What can we learn from this data? March and December returns seem to have done a better job than January of predicting the return for the following one year period. However, we need to dig deeper to see if these statistics are meaningful both in theory and in practice.

From a theoretical perspective, if we make some simplifying assumptions about the distribution of S&P 500 returns then we can explicitly compute the values in the above table. For the following discussion, we assume:

Returns are normally distributed
Monthly returns are i.i.d. (the distribution of each monthly return is identical and then return in one month does not affect the returns of subsequent months)
Annual S&P return has mean of 7% and volatility of 15%

If January’s return is very slightly positive, the probability of a positive annual return is 67.2%. If January’s return is 2.0%, the probability of a positive annual return increases to 72.1%. If January’s return is 5.0%, the probability of a positive annual return increases further to 78.7%.

The chart below shows the probability of a positive annual return given various January returns.

This illustrates that the historical data backing the heuristic that as goes January, so goes the year is an expected statistical artifact and provides no basis for generating value as an investment strategy. Strong market performance in January does not cause strong market performance in the following eleven months. Instead, strong market performance in January simply makes it more likely that the full twelve month return is positive in the same way that the team winning a football game at the end of the third quarter has a better chance of winning the game. Strong January returns give the full year return a head start, providing no forward looking information that can be used to trade profitably.

We can go a step further to evaluate the practical value of the heuristic by examining the performance of a related trading strategy. Consider the following strategies:

Strategy A: Hold a 100% long position in the S&P 500
Strategy B: Go long the S&P 500 in January every month. If the return is positive, go long the S&P 500 for the remainder of the year, otherwise go short.

Strategy B, based on the January heuristic, underperformed both on an absolute return basis and a risk-adjusted return basis.

Metric	Strategy A	Strategy B
Return	7.1%	5.2%
Volatility	15.4%	16.5%
Return/Vol	0.46	0.32

1) Is there economic/financial rationale for why the heuristic holds?When evaluating a potential trading heuristic, it is always useful to ask these questions:

2) Can the supporting data be explained statistically or is it truly an outperformance opportunity?

3) How would a trading strategy based on the heuristic have performed historically? If it has performed well, what are future market scenarios that could pose risks to its continued success and what are the magnitudes of these risks?

For another take on the January effect using conditional probabilities, see our weekly commentary.