The evolution of CAPM and the valuation of portfolios

In this Blog post, I am going to explain the:

  • CAPM
  • Farma French Model
  • 4 Factor Model
  • Momentum Strategy
  • How to evaluate portfolios
  • Why passive investment is more successful?

Financial models are only theoretical and give us estimations. They  are developed to calculate estimations. These models assume that we are living in a perfect world, where investors are rational, the market portfolio is the most efficient portfolio, we do not have transaction costs or taxes and the same information are available to everybody. This is only an introduction to portfolio valuation methods, there are a lot more details to it (I mean people won Nobel prices with CAPM and Farma French).

CAPM = Capital Pricing Model

The CAPM argues that the market is the most efficient portfolio, with the highest Sharpe ratio, so every investor wants to hold it. That means the market portfolio is the mean-variance efficient portfolio, which means it has the best ratio of return and risk. You can not get a higher return with this volatility (risk). Hence it gives you the best portfolio choice.


The MVE (mean variance efficient portfolio) is located on the Capital Allocation Line. This line gives you the best and most efficient options to allocate your money. The more risk averse you are the more you would be on the left (less risk = less return). So the place to be is one the MVE instead of holding single stocks or taking no risk. If the CAPM would hold, every investor would invest into the market portfolio, because it has the highest Sharpe ratio (SR = (Return - risk-free rate) / volatility) and mixes it with a risk-free asset.

That is the formula to calculate the return of your asset if CAPM holds. The ß comes from a regression (Covariance of asset and the market / standard deviation of the market; a regression shows you how two assets interact or don't interact with each other).

Let's see what happens if we have an alpha?

The alpha shows idiosyncratic risk (firm-specific/individual) risk. In the CAPM model the investor holds the market portfolio, so a diversified portfolio. Therefore the idiosyncratic risk is diversified away and should be 0. In the CAPM there is a return for every asset and all these returns are on the Security Market Line if Alpha = 0, but if CAPM doesn't hold, they are above or below the line.

This can have two reasons:

Mispricing: which could be an investment opportunity, if the price is too low, you would buy the asset, because the price is expected to go up . 

Model misspecification: some risks or circumstances are not captured in the model

How can we evaluate a portfolio or one asset let's say Apple with the CAPM?

We know that return and risk are correlated. We can divide the risk of one asset in two parts: The systematic risk (if the market goes down people stop buying iPhones) and the idiosyncratic risk (Steve Jobs died and the stock went down).

We would run a regression with Apple and the market to get the beta or look it up on the Bloomberg tower. (We don't pay attention to the unexpected return), with the beta and the historic returns of the market and the stock, we calculate the alpha. As we saw in the second diagram with the security market line: Alpha is the difference between the prediction of CAPM and the actual return.

Here you see the HEINZ Stock and the beta and alpha, because the stock is obviously not on the SML on conclusion alpha is greater than 0, and CAPM doesn't hold.


So maybe it is time for a more sophisticated model!


Farma French showed that the SML does not always hold, so maybe it is time to put more factors into the equation to make a more precise calculation. They found out, that value stocks did better than growth stocks and that small companies did better than big companies. Value stocks are stocks from companies with a low book to market ratio, which means there are fair priced as well as stable companies, which are paying good dividends (ask Waren Buffet he knows a lot about them ;)) and growth companies are shiny companies like Tesla or Amazon ,where everybody invests because they think they will grow, even though most of them do not even pay dividends and are overpriced (so are Michael Kors handbags and I buy them, because they look good ;)). Small companies are performing better than big companies, probably because fewer people know about them and invest in them.

In conclusion we can build a better portfolio than the one from the CAPM, if we use the Farma French Model. The turquoise line is the Farma French portfolio. (SMB = Small minus big, HML= High book to market ratio minus low book to market ratio).

How to calculate the return on the portfolio: (w are the weights and r(f) is the risk free rate


Now we have a more sophisticated model with three factors instead of one but we can do better let's add one more factor.

Momentum Strategy

Momentum strategy calculates the return of a stock during the last year and only invest into the ones that went up. This would be our fourth and last factor even though there are a lot out there by now. You can see that the momentum effect is quite significant (UMD Up minus down).

Why do we need this model?

  1. To build efficient portfolios => Farma and French are pretty well off
  2. To measure the performance of assets or portfolios

How to calculate the return of one asset or portfolio:

We can use this formula to see if the portfolio did better than an investment in an index funds or ETF. A portfolio with a positive or high alpha would do better than the index portfolio. 

For example, Waren Buffet has a high alpha, he is one of the few investors that can beat the passive funds. Farma and French used in 2010 the CAPM, F3, and F4 Model to compare active funds with passive funds. The result was that active funds underperform the market by 0.18% before fees and by 1.13% after fees.


The FT got the same results in 2016.

So most alphas for active managed funds are actually negative that is the reason why it is better to invest into the market because active funds underperform especially after costs. Of course, there are good investment managers, who beat the market. T



If you see an advertisement like this you should bevery careful.


  1. That always shows past returns and can not make predictions about the future
  2. Active Funds can close funds that didn't run well so they only keep the good ones active, which is good for the statistic!

The models are helpful to give us estimates about expected returns. Especially the F4 Model is quite sophisticated and accurate, but we have to consider that we can always be certain about the past, never the future.

Written by: Philine Paschen

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