r = Three-Factor model + (ß4 * UMD) + ε

where

**“Buy small, cheap stocks, which are on the rise.”**

##### The Five-Factor Model

Fama and French improved their three-factor model by adding two additional quality factors. They used profitability and investment aggressiveness. Interestingly, they did not include momentum in their revised model.

r – Three-Factor model + ß4 * RMW + ß5 * CMA + ε

where

RMW – (Robust minus Weak) – The historic excess returns of assets with high operating profitability over ones with ones with low operating profitability.

CMA – (Conservative minus Aggressive) – The differences between firms that invest conservatively vs those who invest aggressively.

**“Buy small, cheap stocks, with high profitability, which reinvest earnings.”**

Many investors question the exclusion of momentum in the Fama-French models, since its impact on return was widely accepted. Cliff Asness, founder of AQR and former student of Fama, argued for a six-factor model which also included momentum.

##### The Factor Model for the Future

Additional factors include the dividend and growth factors, but the majority of the variance in return is explained by the ones outlined above. We have incorporated this research into our investment process. We have 6 high level factors for you to base your investments on – value, quality, health, dividend, volatility, and technical. Apply a data-driven approach to your investing and use our outperforming multi-factor models at Aikido.

## Quantitative Investing – A Brief History

Quantitative investing is the search for above average returns using data. Factor investing, which is one example of quant investing, attempts to break down the investing process into quantifiable characteristics. We can then use the data to build an outperforming portfolio. But where did this data-driven approach come from? See our previous post to learn more about the types of quantitative investing.

Systematic trading dates back as far as 17th century Holland, where Dutch traders used telescopes to gain an informational advantage. They watched for ships arriving at ports, and traded commodities depending on their understanding of the ships contents. Factor investing originated in mid 20th century.

## Capital Asset Pricing Model (CAPM)

In the 1960s, CAPM was introduced as the first factor model. It tries to explain the variance between the performance of different stocks. It contains a single factor; risk. CAPM says that an investment should return the risk free rate (US Treasury Bills) plus a risk premium, measured by the volatility (standard deviation) of returns. As a result, investors who want to achieve high returns should invest in more volatile stocks, according to this model. The volatility of a stock, relative to the market is known as beta (ß).

r = Rf + ß(E(Rm)-Rf)

where

If you remember any linear algebra, it should look familiar. The intercept is (Rf), the risk free rate while the slope is (ß) beta.

The higher the risk, the higher the expected return.## The Three-Factor Model

Quantitative investing progressed in 1981, where the three-factor model was introduced. It investigates the effect of size on the returns of equities. In essence, it suggests that smaller stocks outperform larger stocks over long periods. Some investors propose that the increased volatility and decreased liquidity of smaller stocks, drive its outperformance. In 1992, Kenneth French and Eugene Fama found that a simple three-factor model, containing size, market risk and value accounted for over 90% of a stocks returns. The value factor used was the price-to-book factor (P/B). This valuation multiple compares a companies market price to its book-value. In short, we should buy stocks which are on sale or discounted, it seems intuitive.

r = CAPM + (ß2 * SMB) + (ß3 * HML) + ε

where

There are other value-factors which can be substituted in, instead of P/B. These include the price-to-earnings and price-to-sales ratios.

“Buy small, cheap stocks.”## The Four-Factor Model

Meanwhile, the effects of momentum on asset prices was also being investigated. Momentum is the difference in price from one period to the next. 3, 6 & 12 months are the time periods by which most momentum strategies focus on. It was accepted as an additional factor in 1997, and the three factor model was expanded to the ‘Carhart’ four-factor model. Momentum makes use of human behaviour patterns such as herding and confirmation bias. Consequently, at market peaks the top performing stocks can often have the biggest drawdown, as experienced in the Great Financial Crises and Dot-com bubble.

r = Three-Factor model + (ß4 * UMD) + ε

where

UMD – (Up minus Down) The historic excess return of high momentum stocks over low momentum stocks.

“Buy small, cheap stocks, which are on the rise.”## The Five-Factor Model

Fama and French improved their three-factor model by adding two additional quality factors. They used profitability and investment aggressiveness. Interestingly, they did not include momentum in their revised model.

r – Three-Factor model + ß4 * RMW + ß5 * CMA + ε

where

RMW – (Robust minus Weak) – The historic excess returns of assets with high operating profitability over ones with ones with low operating profitability.

CMA – (Conservative minus Aggressive) – The differences between firms that invest conservatively vs those who invest aggressively.

“Buy small, cheap stocks, with high profitability, which reinvest earnings.”Many investors question the exclusion of momentum in the Fama-French models, since its impact on return was widely accepted. Cliff Asness, founder of AQR and former student of Fama, argued for a six-factor model which also included momentum.

## The Factor Model for the Future

Additional factors include the dividend and growth factors, but the majority of the variance in return is explained by the ones outlined above. We have incorporated this research into our investment process. We have 6 high level factors for you to base your investments on – value, quality, health, dividend, volatility, and technical. Apply a data-driven approach to your investing and use our outperforming multi-factor models at Aikido.