LO 64.7: Describe issues that arise when measuring alphas for nonlinear strategies.

LO 64.7: Describe issues that arise when measuring alphas for nonlinear strategies.
Alpha is computed using regression, which operates in a linear framework. There are nonlinear strategies, such as uncovered long put options, that can make it appear that alpha exists when it actually does not. An uncovered long put option has a payoff profile that is L-shaped (nonlinear), but applying traditional regression tools will yield a positive alpha, which does not exist in reality. This situation is encountered when payoffs are quadratic terms, like R^ or are option-like terms, such as max(Rt, 0). This can be a significant problem for hedge funds, because merger arbitrage, pairs trading, and convertible bond arbitrage strategies all have nonlinear payoffs.
One reason that nonlinear strategies yield a false positive alpha is because the distribution of returns is not a normal distribution. Certain nonlinear strategies will also exhibit negative skewness in their distribution. This will increase loss potential in the left-hand tail and make the middle of the distribution appear thicker. Skewness is not factored into the calculation of alpha, which is an issue for nonlinear payoff strategies.
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Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
Vo l a t il it y a n d Be t a An o m a l ie s

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