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.
Return Driver
The term return driver represents the investments, the investment products, the investment strategies, or the underlying factors that generate the risk and return of a portfolio. A conceptually simplified way to manage a total portfolio is to divide its assets into two groups: beta drivers and alpha drivers.
Beta Drivers
Briefly, in the context of a portfolio, an investment that moves in tandem with the overall market or a particular risk factor is a beta driver.
Alpha Driver
An investment that seeks high returns independent of the market is an alpha driver.
Alternative Investments
Alternative investing tends to focus more on alpha drivers, whereas traditional investing tends to focus more on beta drivers.
Equity Risk Premium
The equity risk premium (ERP) is the expected return of the equity market in excess of the risk-free rate. This risk premium may be estimated from historical returns or implied by stock valuation models, such as through the relationship between stock prices and forecasts of earnings.
Equity Risk Premium
The equity risk premium puzzle is the enigma that equities have historically performed much better than can be explained purely by risk aversion, yet many investors continue to invest heavily in low-risk assets.
Equity Risk Premium Puzzle
The equity risk premium puzzle is the enigma that equities have historically performed much better than can be explained purely by risk aversion, yet many investors continue to invest heavily in low-risk assets.
Linear Risk Exposure
Passive investing, such as employing a buy-and-hold strategy to match a benchmark index, is a pure play on beta: simple, low cost, and with a linear risk exposure. A linear risk exposure means that when the returns to such a strategy are graphed against the returns of the market index or another appropriate standard, the result tends to be a straight line. Options and investment strategies with shifting betas have nonlinear risk exposures.
Passive Beta Driver
A passive beta driver strategy generates returns that follow the up-and-down movement of the market on a one-to-one basis. In this sense, pure beta drivers are linear in their performance compared to a financial index.
Asset gatherers
Asset gatherers are managers striving to deliver beta as cheaply and efficiently as possible, and include the large-scale index trackers that produce passive products tied to well-recognized financial market benchmarks. These managers build value through scale and processing efficiency.
Product Innovators
Product Innovators, which are alpha drivers that seek new investment strategies offering superior rates of risk-adjusted return. At the other end are passive indexation strategies, previously described as asset gatherers, which offer beta exposure as efficiently as possible without any pretense of alpha seeking.
Process Drivers
Process drivers are beta drivers that focus on providing beta that is fine-tuned or differentiated.
Hypotheses
Hypotheses are propositions that underlie the analysis of an issue.
Hypothesis Tests
Hypothesis tests typically follow the same four steps, in which the analyst does the following:
States a null hypothesis and an alternative hypothesis to be tested
Designs a statistical test
Uses sample data to perform the statistical test
Rejects or fails to reject the null hypothesis based on results of the analysis
Null Hypothesis
The null hypothesis is usually a statement that the analyst is attempting to reject, typically that a particular variable has no effect or that a parameter’s true value is equal to zero. For example, common null hypotheses are that a fund’s alpha is zero or that a fund’s exposure to a particular risk factor, or beta, is zero.
The alternative hypothesis is the behavior that the analyst assumes would be true if the null hypothesis were rejected.
Chambers, Donald R.; Anson, Mark J. P.; Black, Keith H.; Kazemi, Hossein. Alternative Investments: CAIA Level I (Wiley Finance) (p. 189). Wiley. Edición de Kindle.
The alternative hypothesis is the behavior that the analyst assumes would be true if the null hypothesis were rejected.
Test Statistic
The test statistic is the variable that is analyzed to make an inference with regard to rejecting or failing to reject a null hypothesis.
Significance Level
Generally, the term significance level is used in hypothesis testing to denote a small number, such as 1%, 5%, or 10%, that reflects the probability that a researcher will tolerate of the null hypothesis being rejected when in fact it is true.
Confidence Interval
A confidence interval is a range of values within which a parameter estimate is expected to lie with a given probability. The confidence interval is typically based on a large probability such as 90%, 95%, or 99%. A 90% confidence interval defines the range within which a parameter estimate is anticipated to lie in 90% of the tests given that the null hypothesis is true.
Economic Significance
Economic significance describes the extent to which a variable in an economic model has a meaningful impact on another variable in a practical sense.
Type I Error
A type I error, also known as a false positive, is when an analyst makes the mistake of falsely rejecting a true null hypothesis. The term α is usually used to denote the probability of a type I error and should not be confused with investment alpha. The symbol α is the level of statistical significance of the test, and 1 − α is defined as the specificity of the test.
Type II Error
A type II error, also known as a false negative, is failing to reject the null hypothesis when it is false. The symbol β is usually used to denote the probability of a type II error and should not be confused with the use of that symbol to denote systematic risk. The statistical power of a test is equal to 1 − β. An analyst may lower the chances of both types of errors by increasing the sample size.
Selection Bias
Selection bias is a distortion in relevant sample characteristics from the characteristics of the population, caused by the sampling method of selection or inclusion. If the selection bias originates from the decision of fund managers to report or not to report their returns, then the bias is referred to as a self-selection bias.
Survivorship Bias
survivorship bias is a common problem in investment databases in which the sample is limited to those observations that continue to exist through the end of the period of study. Funds that liquidated, failed, or closed, perhaps due to poor returns, would be omitted.
Data Mining
Data mining typically refers to the vigorous use of data to uncover valid relationships.
Data Dredging
Data dredging, or data snooping, refers to the overuse and misuse of statistical tests to identify historical patterns.
Backtesting
Backtesting is the use of historical data to test a strategy that was developed subsequent to the observation of the data. Backtesting can be a valid method of obtaining information on the historical risk and return of a strategy, which can be used as an indication of the strategy’s potential going forward.
Overfitting
Overfitting is using too many parameters to fit a model very closely to data over some past time frame. Models that have been overfit tend to have a smaller chance of fitting future data than a model using fewer and more generalized parameters.
Backfilling
In alternative investments, backfilling typically refers to the insertion of an actual trading record of an investment into a database when that trading record predates the entry of the investment into the database. An example of backfilling would be the inclusion of a hedge fund into a database in 2015, along with the results of the fund since its inception in 2010.
Backfill Bias
Backfill bias, or instant history bias, is when the funds, returns, and strategies being added to a data set are not representative of the universe of fund managers, fund returns, and fund strategies.
Cherry Picking
Cherry-picking is the concept of extracting or publicizing only those results that support a particular viewpoint.
Chumming
Chumming is a fishing term used to describe scattering pieces of cheap fish into the water as bait to attract larger fish to catch. In investments, we apply this term to the practice of unscrupulous investment managers broadcasting a variety of predictions in the hope that some of them will turn out to be correct and thus be viewed as an indication of skill.
