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# Portfolio Alpha

#### itsyourz

##### New Member
Hi,

thanks for quick response! really!

following is a question from FRM HandBook

EXAMPLE16.5ERFORMANCEEVALUATION

Assume that a hedge fund provides a large positive alpha.The fund can take
leveraged long and short positions in stocks.The market went up over the
period.Based on this information,
a. If the fund has net positive beta,all of the alpha must come from the
market.
b. If the fund has net negative beta,part of the alpha comes from the market.
c. If the fund has net positive beta,part of the alpha comes from themarket.
d. If the fund has net negative beta,all of the alpha must come from the
market.

Rp - Rf = a + B(Rm-Rf) -> a is alpha right?

-> explanation : Because the market went up,a portfolio with positive beta will have part of
its positive performance due to the market effect

i understand it but we should think about alpha
having a look at that equation, alpha and beta term are separated
how can i decide?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi suk,

I too am confused by the questions, perhaps somebody else can shed light on why it appears to be so flawed?

Here is my opinion:

* I am unclear what is meant here by NET beta (implies something is netted out), I don't know exactly what that means
* The answer (c) does not make sense to me: I believe it contradicts to say "part of the alpha" comes from the market

Regarding CAPM:

Rp - Rf = a + B(Rm-Rf)
"a is alpha right?" Yes, you are correct - alpha is the intercept

But please note, from Grinold, we consider this a special case of:
excess return (i.e., Rp - Rf) = a + Beta*(BENCHMARK-Rf)

where, in CAPM, the market is the benchmark. So, a better encompassing definition is Grinold's

ALPHA = intercept = RESIDUAL RETURN above the benchmark portfolio
(which a special case of this is benchmark portfolio = market portfolio)

David

#### skcd

##### New Member
I concur! with Suk n David.
It surely has to do something with the word "Net Positive or Net Negative" Beta.
Because it is widely known factor among funds n fofs that beta eats into alpha.
Mathematically also, if beta is negative (market is negatively correlated to portfolio) then alpha will improve to keep the return (Rp) constant if thats what the question means. So answer will be b)
If beta were positive, for the same Rp alpha or residual return will have to go down.

ON THE OTHER HAND, IF WE TAKE Rm TO BE A BENCHMARK RETURN (AS PER GRINOLD'S DEFN AND AS PER DAVID'S SUGGESTION), THEN Rm IS CONSTANT APRIORI SO THE EXTRA RETURN BY THE MARKET WILL FEED TO ALPHA AND HENCE WE WILL HAVE HIGHER Rp AND THE EXTRA PART WILL BE DUE TO MARKET RETURNS (BECAUSE NOTE THAT NOW WE HAVE BOTH BETA AND RM CONSTANT AS WE SET BENCHMARKS AT THE START). ONLY THAT CAN MAKE SENSE TO ME FOR C) TO BE CORRECT AND I GUESS THATS WHAT THEY MEAN BY NET BETA.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi skcd,

That is an admirable try! I can not do a better job myself to make sense of it. But, for the sake of the upcoming exam (given I think this question is incorrect and may add confusion), I'd like to remind what we mean by alpha per the assignments (Grinold and Andrew Lo):

The (realized or ex post) alpha is the intercept in a multivariate regression of returns against common factors;
e.g., in CAPM, it is the intercept (univariate regression)
e.g., in Andrew Lo's hedge fund factor replication, it is the intercept

Because alpha is source of return not correlated--"the uncorrelated residual"--with common factor exposures (e.g., examples of common factors are the equity risk premium in CAPM; US dollar in A. Lo). Given this definition, IMO, the statement 'part of the alpha comes from the market' has no useful meaning.The alpha, by definition, comes from no common factors.

Finally, the alpha (which cannot be explained by common factor exposure), ex post may be luck or skill (Grinold). Ex ante, it is arguably skill; i.e., E[alpha] is the value-added return we expect the manager to contribute that is uncorrelated/unexposed to common factors (note this also excludes so called exotic beta: the manager's decision to over- or under-weight factor exposure). Although, Andrew Lo attributes the ex post alpha to "manager-specific skill" or "security selection" (i.e., skill)

Beta is: sensitivity to a common factor. In CAPM, beta is sensitivity to the common factor that is the equity risk premium. So, this is why it may be helpful to think in terms of multivariate regression terms. We regress the returns against common factors, then:

The partial regression coefficients (the beta) are sensitivities to common factors; the beta(s) reflects (explains) the effect of the common factor on the total return
The intercept is the alpha; it is part of the total return that is not explained by common factors.

David

#### skcd

##### New Member
Yes, i don't know about exam questions but there are tons of articles clarifying what alpha means and most of it is to show "ALPHA IS THE RETURN OVER AND ABOVE THE MARKET" thats how they sell their alpha to clients and get investment. However, again, exam trick could be to assume a benchmark before start of year and end of year see your alpha based on that and if market overperformed the benchmark, take that as alpha (that is incorrect in reality but again why argue the examiner). Andy Lo's Ex post and Ex Ante make proper sense here.