By Justin Sibears, Newfound Research

We often compare portfolio construction to cooking. There are two equally important elements: the ingredients and the recipe. The ingredients are the signals that are used to select investments. The recipe is the set of rules used to transform those signals into portfolio allocations.

When it comes to factor investing, it seems that the signals oftentimes get all the attention. Investors struggle with whether incorporating factor-based strategies is worth it, argue over which are the premier factors, debate whether factors can be timed or not, and fret about premiums being driven towards zero as acceptance of factor-based strategies increases.

In all of this (admittedly an interesting debate), the importance of the recipe – i.e. how we move from a factor score to an actual strategy – is often lost.

Let’s use the momentum factor as an example.  What decisions do we need to make to build a momentum portfolio?

First, we need to decide how to measure momentum. The simplest and most traditional approach would just be to use trailing total return. However, there are many other ways to measure momentum. We could use risk-adjusted momentum (i.e. looking at trailing Sharpe Ratios instead of trailing returns). We could use idiosyncratic momentum (i.e. measuring trailing returns after stripping out the stock’s exposure to the broad market).  We could use a regression on past prices to estimate the stock’s trend. We could smooth prices using various moving averages. We could diversify by blending multiple signals together.

We also need to decide over how long of a period we want to measure momentum. Do we want to use 12 months? 9 months? 6 months? Do we want to skip to the most recent month to account for mean reversion as is common in the academic literature or include it?

Do want to rebalance weekly, monthly, quarterly, or at some other interval?

How concentrated do we want the portfolio to be? Do we choose the 30 stocks with the highest momentum? 50 stocks? 100 stocks?

How will the stocks be weighted? We could market-cap weight the holdings. We could equal-weight the holdings.  We could allocate in proportion to each stock’s momentum by giving the highest allocation to the stocks with the most momentum.

If we wanted to get really fancy we could run some type of optimization like equal-risk contribution, mean-variance optimization, or minimum volatility.

If we go this route, then we really open Pandora’s box. We now need to decide how to estimate our parameters (means, volatility, and correlations). Do we use historical data?  If so, how much? What measures do we use?  How do we account for estimation risk?

Do we care about controlling for other risk factors, like sector risk?  If not, we may let the portfolio be sector unconstrained and therefore let the sector exposures just fall out of the stock selection. If yes, we need to decide how to control it. Do we force the portfolio to be sector neutral (i.e. have the same sector weights as the market)? Are we comfortable with a middle ground, where sector weights are allowed to drift from market-cap sector weights, but only by some pre-specified amount?  If we want to go this route, how loose or tight do we set those thresholds?

We could go on and on and on. The degree of potential customization of the recipe is largely limitless. In the ramblings above, we mentioned at least six dimensions of customization for a momentum strategy:

• Momentum measure
• Lookback period
• Rebalance frequency
• Concentration
• Weighting Scheme
• Sector Constraints

If these were the only six dimensions and there were only ten choices per dimension, there would be a whopping 1,000,000 potential variations of the momentum strategy!

Illustrating the Impact of the Portfolio Construction Recipe

To illustrate the impact that these choices can have on returns, we conducted a simple experiment. Our investment universe consists of the 200 largest holdings in the SPDR S&P 500 ETF (ticker: SPY)[1]. Using this universe, we create 1,080 different momentum portfolios by varying the construction rules (5 momentum measures x 4 lookback periods x 3 rebalance frequencies x 3 levels of portfolio concentration x 3 weighting schemes x 2 methods of dealing with sector risk[2]).

As a quick note, since we are only interested in exploring dispersion across strategies, all performance statistics presented are normalized by subtracting the median for that metric across all 1,080 strategies.  For example, an annualized return of +5.0% means that a strategy outperformed the median by 5.0% per year.  Similarly, a Sharpe Ratio of -0.10 simply says that the strategy’s Sharpe Ratio was 0.10 lower than the median Sharpe Ratio across all 1,080 strategies.

The dispersion of full period performance statistics is quite large. On a raw return basis, the worst performing strategy underperformed the median by 12.0% annualized while the best performing strategy outperformed the median by 18.0% annualized.  A difference of more than 30% per year between the best and worst strategy is certainly nothing to sneeze at.  Even if we ignore the tails of the return distribution, the dispersion remains very evident.  The 95% confidence interval is -5.5% to +11.5%.  The standard deviation of annualized returns across the strategies tested is 5.3%.

The results are very similar if we change focus to risk-adjusted returns using the Sharpe Ratio.  The worst strategy on a risk-adjusted basis has a Sharpe Ratio 0.57 below the median, while the best strategy’s Sharpe Ratio is 0.27 above the median.  The 95% confidence interval is -0.18 to +0.14 and the standard deviation of Sharpe Ratio relative to the median is 0.10.

Data Source: CSI and SPDR. Calculations by Newfound Research. Data analysis starts in May 1995 as that is when all portfolios could calibrate given available price data. Returns are hypothetical and backtested and do not reflect any strategy managed by Newfound Research. Returns include the reinvestment of dividends. The strategies all were constructed with explicit hindsight bias as the universe consists of the 200 largest stocks in the SPDR S&P 500 ETF (ticker: SPY) as of May 2018. Past performance does not guarantee future results.

While the dispersion of full period results is interesting, what we really want to focus on is the dispersion in returns over shorter time horizons because these are the differences that fuel many behavioral biases.  To do so, we calculate rolling one-year returns for each of the strategies.  We then rank these returns across all strategies at each point in time and then plot the 95% confidence interval.  Again, all returns are normalized by subtracting the median return at each point in time.