Chapter 8 CAIA Flashcards - Alpha, Beta, and Hypothesis Testing
Alpha, Beta & Hypothesis Testing
Overview of Beta and Alpha
In a nutshell, alpha represents, or measures, superior return performance; and beta represents, or measures, systematic risk.
Beta Defined
Intuitively, beta is the proportion by which an asset’s excess return moves in response to the market portfolio’s excess return (the return of the asset minus the return of the riskless asset). If an asset has a beta of 0.95, its excess return can be expected, on average, to increase and decrease by a factor of 0.95 relative to the excess return of the market portfolio.
Alpha
Alpha refers to any excess or deficient investment return after the return has been adjusted for the time value of money (the risk-free rate) and for the effects of bearing systematic risk (beta). For an investment strategy, alpha refers to the extent to which the skill, information, and knowledge of an investment manager generate superior risk-adjusted returns (or inferior risk-adjusted returns in the case of negative alpha).
Exante alpha
Exante alpha is the expected superior return if positive (or inferior return if negative) offered by an investment on a forward-looking basis after adjusting for the riskless rate and for the effects of systematic risks (beta) on expected returns. Exante alpha is generated by a deliberate over- or underallocation to mispriced assets based on investment management skill. Simply put, exante alpha indicates the extent to which an investment offers a consistent superior risk-adjusted investment return.
CAPM
The CAPM implies that no competitively priced asset would offer a positive or negative exante alpha, since every asset would trade at a price such that its expected return would be commensurate with its risk.
Ex post Alpha
Expost alpha is the return, observed or estimated in retrospect, of an investment above or below the risk-free rate and after adjusting for the effects of beta (systematic risks). Whereas exante alpha may be viewed as expected idiosyncratic return, expost alpha is realized idiosyncratic return.
Two Steps of Alpha Based Analysis
Alpha-based analysis typically involves two steps: (1) ascertaining abnormal return performance (expost alpha) by controlling for systematic risk, and (2) judging the extent to which any superior performance was attributable to skill (i.e., was generated by exante alpha). The more problematic issue can often be in the second step of the analysis, differentiating between the potential sources of the expost alpha: luck or skill.
Difference Between Ex Post Alpha and Ex Ante Alpha
A key difference between exante and expost alpha is that exante alpha reflects skill, whereas expost alpha can be a combination of both luck and skill.
Two Steps to Empirical Analysis of ExAnte Alpha
Chambers, Donald R.; Anson, Mark J. P.; Black, Keith H.; Kazemi, Hossein. Alternative Investments: CAIA Level I (Wiley Finance) (p. 180). Wiley. Edición de Kindle.
Two critical steps are used to identify exante alpha from historical performance. First, an asset pricing model or benchmark must be used to divide the historical returns into the portions attributable to systematic risks (and the risk-free rate) and those attributable to idiosyncratic effects. Second, the remaining returns, meaning the idiosyncratic returns (i.e., expost alpha), should be statistically analyzed to estimate the extent, if any, to which the superior returns may be attributable to skill rather than luck.
Expost alpha estimation
Expost alpha estimation is the process of adjusting realized returns for risk and the time value of money.
Model misspecification
Model misspecification is any error in the identification of the variables in a model or any error in identification of the relationships between the variables. Model misspecification inserts errors in the interpretation and estimation of relationships.
Three Types of Model Misspecification
Three primary types of model misspecification can confound empirical return attribution analyses: Omitted (or misidentified) systematic return factors Misestimated betas Nonlinear risk-return relationship
Omitted Systematic Return
The bias caused by omitted systematic return factors in estimating alpha can be illustrated as follows. Assume that a fund’s return is driven by four betas, or systematic factors. If an analyst ignores two of the factors (e.g., factor 3 and factor 4), then the estimate of the idiosyncratic return will, on average, contain the expectation of the two missing effects, both of which would have positive expected values. The performance attribution example throughout Chapter7 illustrated this problem.
Misestimated Betas
In the second case of model misspecification, misestimated betas, when the systematic risk, or beta, of a return series is over- or underestimated, the return attributable to the factors is also over- or underestimated. Underestimation of a beta is a similar but less extreme case of omitting a beta.
Non Linear Risk Return Relationships
The final major problem with misspecification is when the functional relationship between a systematic risk factor and an asset’s return is misspecified. For example, most asset pricing models assume a linear relationship between risk factors and an asset’s returns. If the true relationship is nonlinear, such as in the case of options, then the linear specification of the relationship generally introduces error into the identification of the systematic risk component of the asset’s return.
Beta Nonstationarity
Beta nonstationarity is a general term that refers to the tendency of the systematic risk of a security, strategy, or fund to shift through time.
Beta Creep
A type of beta nonstationarity that is sometimes observed in hedge funds is beta creep. Beta creep is when hedge fund strategies pick up more systematic market risk over time.
Beta Expansion
In periods of economic stress, the systematic risks of funds have been observed to increase. Beta expansion is the perceived tendency of the systematic risk exposures of a fund or asset to increase due to changes in general economic conditions.
Market Timing (Beta Non Stationarity)
Another example of beta nonstationarity is market timing: intentional shifting of an investment’s systematic risk exposure by its manager.
Steps tp Summarising ex ante alpha through abnormal returns
Attempting to identify exante alpha through an abnormal return persistence procedure can be summarized in the following three steps: Estimate the average idiosyncratic returns (expost alpha) for each asset in time period 1. Estimate the average idiosyncratic returns (expost alpha) for each asset in time period 2. Statistically test whether the expost alphas in time period 2 are correlated with the expost alphas in time period 1.