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[MUSIC]

Â Welcome to this lecture on portfolio performance estimation using asset pricing

Â models.

Â Let me walk you through the main learning objectives of this session.

Â So first of all, we're going to define what is alpha,

Â what is risk-adjusted performance.

Â Then we're going to talk about how we estimate the alpha, or the selectivity,

Â of the manager using the capital asset pricing model.

Â Next, we're going to turn to a more complicated model,

Â the Fama-French 3-factor model, and ask the same question.

Â Namely, how do you measure the alpha, or the selectivity, of the manager?

Â And finally, we're going to ask,

Â is estimated alpha really capturing the true managerial skills?

Â So what is alpha in theory?

Â In theory, alpha is simply the expected return

Â generated by the hedge fund manager or the mutual fund manager.

Â E[Rp] above E[Rb].

Â And what is E[Rb]?

Â E[Rb] is the benchmark return in expectation, and

Â typically the one would be provided by the capital asset pricing model.

Â So that's the normal return,

Â given a level of risk that the portfolio manager should on average outperform.

Â And if he outperforms the alpha will then be positive.

Â So when we measure alpha, we have to keep two things in mind.

Â What does alpha represent?

Â Alpha represents the selectivity skill of the manager.

Â And the selectivity skill asks the following question,

Â does the manager on average, generate a better,

Â a higher return than the benchmark capital asset pricing model?

Â And how would he do that?

Â Well, he would do that by buying stocks that will outperform, and

Â selling short the stocks that underperform.

Â In order to estimate this alpha, we need to abstract from the timing ability.

Â What is timing?

Â Timing is the ability of a given manager to time the portfolio risk factor.

Â Namely, entering into the S&P 500,

Â if he thinks the market in the US will overperform.

Â And to measure the selectivity, we assume no timing ability for this manager.

Â And imperial studies have shown that indeed,

Â most managers do not have any timing ability.

Â So that's a pretty realistic assumption.

Â So how do we do that empirically?

Â Well empirically, on the x-axis of this graph,

Â you have the return on the market portfolio in excess

Â of the risk-free rate of return, that's RM-f,t.

Â And on the y-axis you have Rp-f,t, which would be the returns

Â in excess of the risk-free rate generated by managers.

Â Each dot corresponds to one realization.

Â We've run ordinary least squares regression, the beta of that

Â regression is the slope, the systematic risk, followed by the manager.

Â And the alpha, the intercept,

Â would be precisely the selectivity that you are trying to capture.

Â So in this case, we have a good manager who generated a positive,

Â abnormal performance.

Â 3:40

So typically, we have many asset pricing models.

Â And the problem is, which one would we choose?

Â So we could choose the CAPM, as we did until now.

Â Or we can choose a more sophisticated model,

Â like the Fama-French 3-factor model and its extensions.

Â For instance, some people would use a CAPM and add a liquidity

Â risk factor, because liquidity risk is also important in the financial markets.

Â Now, let me give you just a little bit of a theoretical background.

Â Anytime you chose an asset pricing model, there's three facts that have to be noted.

Â First of all, all the factors need to be systematic.

Â What does it mean that they are systematic?

Â It means that the impact of these factors cannot be

Â diversified away,it's a shock to the return of the securities.

Â All securities, for instance, in a given asset class.

Â Secondly, the factor generates unexpected changes.

Â What does that mean?

Â It means, these are surprises that hit the returns.

Â And finally, the factory is priced.

Â It means, its risk premium.

Â Namely, the difference between the expected return on the benchmark factor,

Â and the the risk-free rate,

Â has to be priced strictly positive in absolute terms.

Â 5:03

Now let's turn to the Fama-French 3-factor model.

Â This equation looks maybe a little bit difficult, but in fact, it's not.

Â The Fama-French 3-factor model is basically an extension of the capital

Â asset pricing model, which rests on the market factor as the first factor.

Â And here, we add two additional factors.

Â First, the SMB factor, which is a factor where you

Â go long the stocks that are of small market capitalization, and

Â we show those stocks that have large capitalization.

Â And then, an HML factor, which is the third factor, which is constructed

Â by going long, high book-to-market stocks, and shorting low book-to-market stocks.

Â So what does this equation tell us?

Â It tells us that the expected return on the portfolio,

Â in excess of the risk-free rate, is equal to its beta with respect to the market

Â portfolio beta iM, multiplied by the risk premium for

Â stock market risk, plus the beta of the security or

Â the portfolio with respect to the SMB factor multiplied by the risk premium for

Â the SMB factor, and finally the beta of the security with respect

Â to the HML factor multiplied by the premium for

Â how much HML risk the security, or the portfolio, is generating.

Â So, many empirical tests have been conducted, and

Â the question is, what is the right model?

Â So typically,

Â one thing that we know is that all these tests have rejected the CAPM and

Â other theoretical model in the family of the capital asset pricing model.

Â Typically nowadays, practitioners, and also academics,

Â would use the Fama-French 3-factor model.

Â And the reason why they would use it is surprising.

Â Why is it surprising?

Â Well, because the factors, per se,

Â that means the book-to-market factor that has been added, and the Small Minus Big

Â factors that had been added to the market factor, are totally add talk.

Â But it turns out, that this model fits the data pretty well.

Â 7:24

So let me remind you of a crucial slide and a crucial point.

Â The choice of the asset pricing model, the proper model,

Â the accurate model, is very important.

Â If the model is wrong, the selectivity alpha that you estimate is also wrong.

Â And typically, what happens is that if you omit a risk factor,

Â let's say that in fact there are three factors,

Â the market, the Small Minus Big, and the HML factor.

Â If you forget the HML factor,

Â what's going to happen is you're going to artificially increase the alpha,

Â and you're going to increase it by the premium for the HML factor.

Â So basically, if you omit risk factors,

Â you generate alpha which is not representing managerial skills.

Â Now another point is important, you need to have enough data.

Â Enough data means enough days, weeks, or

Â months over which you estimate the performance.

Â Because if the sample is too small, the confidence interval is too large,

Â and the alpha is less precise.

Â