Relationship between Alpha and Beta

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17. 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 must come from the market.
c. if the fund has net positive beta, part of the alpha must come from the market. *
d. if the fund has net negative beta, all of the alpha must come from the market.
p. 392 handbook, s 3

In the simplest terms, can you please explain the relationship between alpha and beta? Is alpha essentially a measure of your return/ profit, and beta a measure of risk? In other words, is this way -- for the Garch model, alpha + beta < 1 because it is mean reverting, and for EWMA -- alpha + beta = 1 because it is NOT mean reverting? I know that we use beta throughout the reading for various purposes, namely for calculating hedges, capm models, expected returns, etc. But alpha is not a variable we've dealt with frequently -- so I'd like to understand the direct relationship.

Thank you.

 

[David Harper CFA FRM]

Hi Eva,

Please ignore the sample question; I submitted this question two years ago (2008) to GARP as evidence of a bad use case for "alpha."

Alpha and beta in GARCH(1,1) are completely different; in GARCH, there are merely weights (alpha + beta + gamma = 1.0)

"alpha" (aka, residual risk) in the hedge fund or Grinold context is a regression intercept (just like in CAPM):
Return = alpha + beta(1)*factor + beta(2)*factor + ….

It is what's left over ("residual") to explain the part of the return that is not explained by exposure (beta) to common factors.

David