# Quantitatively Combining '7 Ways To Beat The Market'

Feb. 27, 2020 9:30 AM ETSPY17 Comments
Ploutos
21.14K Followers

## Summary

• 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 yesterday's 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 Monday's "qualitative" version 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 - Size, Value, Low Volatility, Dividend Growth, Equal-Weighting, Momentum, and Quality.

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 in the summary statistics rows at the bottom of the table that all seven strategies produced a higher absolute and risk-adjusted return than the S&P 500 over this period. The question I wanted to answer for readers was how 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 the expected return is maximized for a given level of risk. For expected return, variance, and my covariance matrix, I used the realized data over the past 24 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