What it means
For decades the standard tool was the capital asset pricing model, which said a share's expected return depended only on how much it moved with the overall market. Two researchers, Eugene Fama and Kenneth French, showed that small companies and cheap companies had historically earned more than that single factor predicted.
Their model adds a size factor and a value factor to close the gap. The size factor is usually written SMB, short for small minus big: the extra return of a portfolio of small companies over a portfolio of large ones.
The value factor is HML, high minus low, the extra return of shares with a high book-to-market ratio over those with a low one. Each share is assigned a sensitivity to these factors in the same way it is assigned a beta to the market.
This matters in ordinary business because the model often sits behind a company's cost of equity, which in turn drives the discount rate used to value projects and acquisitions. A small, asset-heavy business will usually come out with a higher required return under this model than under the capital asset pricing model, which makes its investments look less attractive.
Getting that number wrong by two percentage points can turn a yes into a no on a large capital project. In use, the sensitivities are estimated by regressing (statistically fitting) several years of the company's monthly excess returns against the three factor returns.
Analysts then combine those sensitivities with long-run estimates of each factor premium to produce a forward-looking expected return. The factor data is published and freely available, which is part of why the model became a standard reference.
The model has well-known limits and later extensions. The size and value premiums have been weak or negative for long stretches, and Fama and French themselves later added profitability and investment factors to create a five factor version.
Treat the output as a reasoned estimate with a wide margin of error, not a precise answer.
In practice
Real-world examples.
Example
A pension fund reviews an equity manager who claims consistent outperformance. Running the manager's returns through the three factor model shows that almost all of the excess return is explained by a persistent tilt towards small value shares, so the trustees renegotiate the fee down to something closer to an index rate.
Example
A privately held speciality retailer is preparing for sale and needs a defensible cost of equity. Its adviser uses the three factor model with the sensitivities of a basket of small listed retailers, arriving at 14.2% rather than the 11.0% a simple market beta would have produced.
Example
An asset manager designs a new fund with deliberate exposure to the size and value factors. The three factor model provides both the design rationale and the benchmark against which the fund's performance is later measured.
Formula
Calculation
Expected return = Risk-free rate + (Market beta x Market risk premium) + (Size sensitivity x SMB premium) + (Value sensitivity x HML premium)
Take a mid-sized industrial distributor. The risk-free rate is 4.0% and the market risk premium is 6.0%. The estimated sensitivities are a market beta of 1.1, a size sensitivity of 0.8 and a value sensitivity of 0.4, and the long-run premiums assumed are 2.5% for size and 3.0% for value.
Market component: 1.1 x 6.0% = 6.6%. Size component: 0.8 x 2.5% = 2.0%. Value component: 0.4 x 3.0% = 1.2%. Adding the risk-free rate gives 4.0% + 6.6% + 2.0% + 1.2% = 13.8%.
The capital asset pricing model alone would have given 4.0% + 6.6% = 10.6%, so the three factor version raises the required return by 3.2 percentage points. On a project generating a level $2,000,000 a year indefinitely, that is the difference between a value of $2,000,000 / 0.106 = $18,867,925 and $2,000,000 / 0.138 = $14,492,754, a gap of $4,375,171.Case study
Seen in the real world.
The following is a fictional, illustrative case. Cedar Ridge Endowment, an invented university fund, held an active equity manager who had beaten the broad market index by an average of 2.4 percentage points a year over eight years and charged fees to match.
The investment committee ran the manager's monthly returns through the three factor model. The regression produced a market beta of 1.05, a size sensitivity of 0.62 and a value sensitivity of 0.51, which together explained 2.1 percentage points of the 2.4 point excess. Only 0.3 percentage points remained as genuine stock selection skill, against an active fee of 0.85% of assets.
Cedar Ridge kept a reduced allocation with the manager but moved the majority of the money into a low-cost fund that targeted the same size and value tilts for 0.15%. The illustrative point is not that the manager was doing nothing useful, but that the committee could only price the skill once it separated factor exposure from selection.
Watch out
Common mistakes.
- Treating the three factor model as a prediction of what a share will do next year. It estimates a long-run required return, and actual returns in any single year can be far away from it.
- Applying published factor sensitivities from one market to a company in another. The factor premiums differ by region and period, so the inputs must match the market being modelled.
- Assuming a higher expected return under this model means a better investment. A higher number reflects higher risk, and it raises the hurdle a project must clear rather than lowering it.
Questions
People also ask.
What is the difference between this and the capital asset pricing model?
The capital asset pricing model uses market risk alone, while this model adds size and value factors, which usually explains historical returns more completely.
Does a bigger value sensitivity always increase the expected return?
Only when the value premium is assumed to be positive; if the HML premium used is negative, a positive sensitivity reduces the expected return.
Is the three factor model still current?
It is still widely taught and used, though many practitioners now prefer the five factor extension that adds profitability and investment.
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