8. Alpha, Beta, and Hypothesis Testing Flashcards
Practice questions
- Provide two common interpretations of the investment term 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).
• Alpha can also refer to the extent to which the skill, information, and knowledge of an investment manager generates superior risk-adjusted returns (or inferior risk-adjusted return in the case of negative alpha).
➢ Note that the first interpretation can include high returns from luck.
- Provide two common interpretations of the investment term beta.
- 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).
- Beta refers to any of a number of measures of risk or the bearing of risk, wherein the underlying risk is systematic (shared by at least some other investments and usually unable to be diversified or fully hedged without cost) and is potentially rewarded with expected return without necessarily specifying that the systematic risk is the risk of the market portfolio.
- Does ex ante alpha lead to ex post alpha?
• Not necessarily. While ex ante alpha may be viewed as expected idiosyncratic return, ex post alpha is realized idiosyncratic return. Simply put, ex post alpha is the extent to which an asset outperformed or underperformed its benchmark in a specified time period. Ex post alpha can be the result of luck and/or skill. To the extent that an investor suffers bad luck, ex ante will not guarantee ex post alpha.
- What are the two steps to an analysis of ex ante alpha using historical data?
- 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.
- The remaining returns, meaning the idiosyncratic returns (i.e., ex post alpha), should be statistically analyzed to estimate the extent, if any, to which the superior returns may be attributable to skill rather than luck.
- List the three major types of model misspecification in the context of estimating systematic risk.
- Omitted (or misidentified) systematic return factors
- Misestimated betas
- Nonlinear risk-return relationships
- What is the goal of an empirical investigation of abnormal return persistence?
• To identify ex ante alpha
- What is the term for investment managers with products trying to deliver systematic risk exposure with an emphasis on doing so in a highly cost-effective manner?
• Beta drivers (or passive indexers)
- Does an analyst select a p-value or a significance level in preparation for a test?
• The significance level. The p-value is the output of the statistical computations.
- What is the relationship between selection bias and self-selection bias in hedge fund datasets?
• Selection bias is a distortion in relevant sample characteristics from the characteristics of the population, caused by the sampling method of selection or inclusion used by the data manager. 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.
- What are two methods of detecting outliers in a statistical analysis?
- Detection through visual inspection of plots
* Ordered listings of the variables and regression residuals
alpha driver
An investment that seeks high returns independent of the
market is this.
alternative hypothesis
is the behavior that the analyst
assumes would be true if the null hypothesis were rejected.
asset gatherers
are managers striving to deliver beta as
cheaply and efficiently as possible, and include the largescale
index trackers that produce passive products tied to
well-recognized financial market benchmarks.
backfill bias fund
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.
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.
backtesting
is the use of historical data to test a strategy that
was developed subsequent to the observation of the data.
beta creep
is when hedge fund strategies pick up more
systematic market risk over time.
beta driver
An investment that moves in tandem with the overall market or
a particular risk factor is this.
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.
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.
causality
The difference between true correlation and causality is that
causality reflects when one variable’s correlation with another
variable is determined by or due to the value or change in
value of the other variable.
cherry-picking
is the concept of extracting or publicizing
only those results that support a particular viewpoint.
chumming
is a fishing term used to describe scattering pieces
of cheap fish into the water as bait to attract larger fish to catch.
confidence interval
is a range of values within which a
parameter estimate is expected to lie with a given probability.
data dredging
or data snooping, refers to the overuse and
misuse of statistical tests to identify historical patterns.
data mining
typically refers to the vigorous use of
data to uncover valid relationships.
economic significance
describes the extent to which a
variable in an economic model has a meaningful impact on
another variable in a practical sense.
ERP
equity risk premium is the expected return of the
equity market in excess of the risk-free rate.
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.
ex ante 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.
ex post 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).
full market cycle
is a period of time containing a large
representation of market conditions, especially up (bull)
markets and down (bear) markets.
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.
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.
overfitting
is using too many parameters to fit a model very
closely to data over some past time frame.
passive beta driver
strategy generates returns that follow
the up-and-down movement of the market on a one-to-one
basis.
process drivers
are beta drivers that focus on providing beta
that is fine-tuned or differentiated.
product innovators
At one end of the spectrum are these, which are
alpha drivers that seek new investment strategies offering
superior rates of risk-adjusted return.
p-value
is a result generated by the statistical test that
indicates the probability of obtaining a test statistic by chance
that is equal to or more extreme than the one that was
actually observed (under the condition that the null hypothesis
is true).
return driver
represents the investments, the
investment products, the investment strategies, or the
underlying factors that generate the risk and return of a
portfolio.
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.
spurious correlation
The difference between true
correlation and this term is that this idiosyncratic in
nature, coincidental, and limited to a specific set of
observations.
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.
test statistic
is the variable that is analyzed to make an
inference with regard to rejecting or failing to reject a null
hypothesis.
type I error
also known as a false positive, is when an
analyst makes the mistake of falsely rejecting a true null
hypothesis.
type II error
also known as a false negative, is failing to
reject the null hypothesis when it is false.
Consider Sludge Fund, a fictitious fund run by
unskilled managers that generally approximates the S&P 500 Index but does so
with an annual expense ratio of 100 basis points (1%) more than other
investment opportunities that mimic the S&P 500. Using Equation 8.1 and
assuming that the S&P 500 is a proxy for the market portfolio, the ex ante alpha
of Sludge Fund would be approximately –100 basis points per year. This can be
deduced from assuming that βi = 1 and that [E(Ri,t) – E(Rm,t)] = –1% due to the
expense ratio.
E ( R(i,t) − R(f) ) = alpha
i + Beta
i (E (R(m,t) ) − R(f))
manipulate for alpha:
Alpha = Beta (E(R(m,t) - R(f)) - E(R(i,t) - Expense Ratio - R(f))
1 (0.1 - 0) - (0.1 + 0.01 - 0)
= -0.01
Consider Trim Fund, a fund that tries to mimic
the S&P 500 Index and has managers who are unskilled. Unlike Sludge Fund
from the previous section, Trim Fund has virtually no expenses. Although Trim
Fund generally mimics the S&P 500, it does so with substantial error due to the
random incompetence of its managers. However, the fund is able to maintain a
steady systematic risk exposure of βi = 1. Last year, Trim Fund outperformed the
S&P 500 by 125 basis points.
R(it) - R(f) = Beta (R(mt) - R(f) + E(it)
rearrange to = E(it)
Beta = 1 R(it) - R(mt) = 1.25% R(it) = 10% R(mt) = 11.25% R(f) = 0 (no risk)
Step One: Press 0.1125 → - → 0 Step Two: Press ÷ → 1 Step Three: Press - → 0.10 + → 0 Step Four: Press = Answer: 0.0125
