Certain equity market factors have generated long-term outperformance versus the broader market.

This article describes a quantitative approach to thinking through how to combine these factor tilts into a portfolio that further improves performance.

While yesterdays article described qualitatively which parts of the business cycle see outperformance for various factor tilts, this article takes a mathematical approach to portfolio construction.

As I promised in yesterdaysqualitativeversion of this article on combining factor tilts, this article looks at a quantitative approach to portfolio construction. I have recently published extensive work on Seeking Alpha regarding the long-term outperformance generated by factor tilts -SizeValueLow VolatilityDividend GrowthEqual-WeightingMomentum, andQuality.

For each of the factor tilts described in my 7 Ways to Beat the Market series, I have full year total returns dating back to 1996. Longer datasets for these factor tilts are available, but the particular return series for the factor tilts that I am using in this article are replicated by low-cost exchange traded funds, giving readers a ready opportunity to explore these strategies in a cost-effective manner.

All seven of these factor tilts have generated both absolute and risk-adjusted outperformance versus the S&P 500 (SPY) as depicted below:

Notice that all seven strategies produced a higher absolute and risk-adjusted return than the S&P 500. The question I wanted to answer for readers was how could these seven strategies could be combined to produce the highest risk-adjusted return. To answer that question, I used a mean-variance optimization framework to solve for the weights that produced the highest Sharpe ratio.

Nobel Prize winner Harry Markowitz introduced Modern Portfolio Theory in a 1952 essay. The mean-variance framework he described assembled a portfolio of assets such that theexpectedreturn is maximized for a given level of risk. For expected return, variance, and my covariance matrix, I used the realized data over the past 22 years. Forward-looking expected returns would make portfolio construction much simpler!

In my first examination, I used the Solver function in Excel to solve for the portfolio weights that produced the highest risk-adjusted returns (without shorting). While I allowed the optimizer to pick any of the eight strategies – the seven factor tilts and the S&P 500 – I ended up with a 65.0% weight in the Low Volatility Factor (SPLV), a 26.5% weight in the Momentum (MTUM) factor, and an 8.5% weight in the Dividend Growth (NOBL) factor.

This portfolio produced a 10.8% total return with an 12.8% standard deviation of returns and a Sharpe ratio of 0.537. By comparison, the S&P 500 returned 8.3% per year over this sample period with a standard deviation of annualized returns of 17.9% for a Sharpe ratio of 0.247. The factor tilt optimization produced a return that was 2.5% higher per year with realized volatility that was around 70% of the broad market.

Despite factoring in the imperfect correlation between the different asset sleeves, small allocations to Size (IJR), Value (RPV), Equal-Weighting (RSP), and Quality (SPHQ) did not boost risk-adjusted returns. That should not come as a big surprise since Low Volatility and Dividend Growth produced the best risk-adjusted returns and Momentum produced the best absolute returns.

Some might counter that they do not fear volatility. They want to generate the highest absolute return, and believe that an effort to lower volatility could increase shortfall risk to their stated return objective. I do not agree with that method. As long-time readers know, I would prefer to add low cost leverage to an alpha-generative low volatility strategy to boost returns rather than buying riskier strategies that have higher realized volatility and drawdowns.

This is a learning exercise though, so in my second examination, I solved for the portfolio optimization that maximized absolute return. Interestingly, the strategy allocated all of its dollars to a combination of Momentum (91%) and Quality (9%) – the two strategies most recently introduced to this series. They are the strategies that had the highest absolute returns over this sample period. This combination produced a 12.0% annualized return, but would lead to a 20.3% annualized standard deviation of returns, a realized volatility that would be roughly 13% higher than the broad market over the sample period.

Of course, as the common finance axiom goes, past performance may not be indicative of future results. Not all of us are blessed with another 22-year sample period to revisit this analysis to shape our asset allocation decisions. We need to build the portfolio best suited to meet our investment objectives today.

I have looked at this type of optimization on longer time series datasets. I did not use those datasets here because they are not readily replicable through low cost index funds. Those longer datasets are also broader, and would introduce the Size element I tried to isolate into each of the standalone factor tilts. Those longer-run time series optimizations had larger allocations in Value. While that longer time series did have a weight to Low Volatility, its was smaller than in the 1996-2018 dataset, a period that featured steadily lower rates that could be viewed as providing outsized support to the more rate-sensitive Low Volatility and Dividend Growth strategies.

In the qualitative companion piece to this article, I showed how these different strategies perform over the course of a business cycle. Combining Momentum, which outperforms in the mid-cycle part of a bull market, and Low Volatility, which outperforms as the business cycle turns, could be a logical combination to producing market-beating performance over future business cycles as this combination outperformed over past markets.

I hope this article helps present a quantitative picture about portfolio construction from factor tilts. Expect to see future articles that focus on the intersections of these factor tilts packaged into low cost exchange traded funds.

Disclaimer:My articles may contain statements and projections that are forward-looking in nature, and therefore inherently subject to numerous risks, uncertainties and assumptions. While my articles focus on generating long-term risk-adjusted returns, investment decisions necessarily involve the risk of loss of principal. Individual investor circumstances vary significantly, and information gleaned from my articles should be applied to your own unique investment situation, objectives, risk tolerance, and investment horizon.

Disclosure:I am/we are long IJR,RPV,SPLV,NOBL,RSP,MTUM,QUAL,SPY.I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.