[MUSIC]

Welcome to this lecture on portfolio performance estimation using asset pricing

models.

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

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

what is risk-adjusted performance.

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

of the manager using the capital asset pricing model.

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

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

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

And finally, we're going to ask,

is estimated alpha really capturing the true managerial skills?

So what is alpha in theory?

In theory, alpha is simply the expected return

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

E[Rp] above E[Rb].

And what is E[Rb]?

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

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

So that's the normal return,

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

And if he outperforms the alpha will then be positive.

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

What does alpha represent?

Alpha represents the selectivity skill of the manager.

And the selectivity skill asks the following question,

does the manager on average, generate a better,

a higher return than the benchmark capital asset pricing model?

And how would he do that?

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

selling short the stocks that underperform.

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

What is timing?

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

Namely, entering into the S&P 500,

if he thinks the market in the US will overperform.

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

And imperial studies have shown that indeed,

most managers do not have any timing ability.

So that's a pretty realistic assumption.

So how do we do that empirically?

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

you have the return on the market portfolio in excess

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

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

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

Each dot corresponds to one realization.

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

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

And the alpha, the intercept,

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

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

abnormal performance.