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Definitions of Beta

I slightly disagree with Alex’s comment. The CAPM does not read as \begin{align*} r_{i,t} = r_{f,t}+ \beta_{i} (r_{m,t}-r_{f,t}) + \varepsilon_{i,t}. \end{align*} There is an important difference ...
Kevin's user avatar
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8 votes

Creating a Beta-Neutral Portfolio

There are more ways to approach this but the method I propose should work reasonably well in practice, especially if you increase the number of assets you hold. Calculate the beta of the stocks you'...
Bob Jansen's user avatar
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8 votes
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How high can Beta be in CAPM?

Infinity is rather non-sensical. A better question perhaps is whether you can put some theoretical bounds on an asset's market beta. An asset's volatility bounds its market beta Let $R_i$ be the ...
Matthew Gunn's user avatar
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Marginal Risk Contribution Formula

concerning your first question: the derivative does not disappear: $\sigma(R_p)$ contains the square root. To be more precise, set $$ \sigma(R_p) = \sqrt{w_1^2\cdot\sigma(R_1)^2 + w_2^2\cdot\sigma(R_2)...
Cettt's user avatar
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6 votes
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Dollar-Neutral in addition to Market-Neutral?

Imagine a scenario where a beta neutral portfolio comprised being long one very high beta stock and short many low beta stocks. Such a portfolio clearly has extreme concentration of risk. ...
Yugmorf's user avatar
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Using cross-sectional factor model (BARRA type) returns in a time series factor model (Fama-French type)?

What you're describing sounds like the reverse of a Fama-Macbeth regression. The original Fama-Macbeth approach estimated rolling time series regressions to get CAPM betas and then doing a cross-...
John's user avatar
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6 votes
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Why stock beta is not equal to its index weight?

It's trivial to calculate the betas given the index weights $w$ and the covariance matrix of all stocks $\Sigma$: The index return is $$ r_{\rm index} = w^T r $$ The beta of stocks to the index is $$ \...
Chris Taylor's user avatar
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5 votes

Are smart beta and risk-parity the same?

This is a very good question. It can be argued that risk parity is one example of a smart beta strategy. Yet it is important to understand that both are coming from two different directions: risk ...
vonjd's user avatar
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5 votes

In the "betting against beta" paper, what exactly is the "BAB factor"?

An excess return is the payoff of a zero cost portfolio. For example: $R_i - R_f$ is an excess return. $c \left( R_i - R_f \right) $ is an excess return for any $c \in \mathbb{R}$,. More generally, $...
Matthew Gunn's user avatar
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Calculating beta to market

In a word, yes. That's a correct and valid view to take but, as you'll always find in finance, it really depends on context and the question that you're trying to answer. This is the case in markets ...
RobAbMo's user avatar
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What is the industry standard way of calculating and annualizing performance metrics?

To give you an idea of industry standards for funds (although not hedge-fund specific), Morningstar and Trustnet both use monthly returns and annualize their data. See, for an example plucked at ...
Tim Wilding's user avatar
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5 votes

CAPM and Beta: problem with regression (Beta is too low yet statistically significant?)

You are right to be sceptical of the beta of an international portfolio when it is calculated using daily returns. Beta estimates are often low for international portfolios because stock market ...
Tim Wilding's user avatar
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5 votes
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Beta anomaly (t statistics)

Yes. That is pretty easy. You have the returns for the high portfolio and for and low portfolio. You subtract one from the other and you have a time-series of returns for the High-Low portfolio. Then ...
phdstudent's user avatar
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Trying to replicate the Beta of Yahoo in R but am getting an answer that is way off

You need returns for 36 months, in particular data from 37 months. Yahoo also uses unadjusted closing prices for the reference index as far as i know. The data from 8/1/2015 got to be an error, I ...
Andrew's user avatar
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3 votes

Two definitions of Beta

As @Rosetta states in the comment above, I think the difference between the two formulas you represent can be explained by either focusing on estimating the coefficient $\beta$ or by taking into ...
Stefan Voigt's user avatar
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Is Least Median Squares (LMS) regression commonly used in Finance?

Interesting idea. I'm guessing this isn't used for two reasons: First, the only algorithm I could find is $O(n^3)$, which is horrible if you're using a moderately-sized high-frequency dataset. ...
Marc Shivers's user avatar
3 votes

Relationship between Beta and Standard Deviation

The standard deviation (and variance) of the returns of an asset has two sources: the market beta times the market's standard deviation, and the asset's own idiosyncratic (market independent) standard ...
Mats Lind's user avatar
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Efficient algorithm for calculating Beta coefficient

I don’t know how naïve your nested loops are, but I assume you are using the OLS calculation $\beta = (X’X)^{-1}X’Y$, where $X$ contains the index returns and $Y$ contains the security returns. If ...
Tim Wilding's user avatar
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3 votes

Efficient algorithm for calculating Beta coefficient

You might find this code snippet helpful. It's the vectorized beta calculation used by Zipline, an open source backtester written in python. It is computed over a lookback window, with data for all ...
ernestoeperez88's user avatar
3 votes

Best practice when computing beta coefficient

A widely accepted method to estimate Beta is the Vasicek (1973) method, which computes a preliminary estimate of Beta by linear regression and then "shrinks it" (adjusts it) towards 1 to compensate ...
nbbo2's user avatar
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3 votes

What is the intuition of CAPM model with Intercept at 0?

Jensens $\alpha$ stays for return or risk premia, which the asset pays when all factor returns are zero. The $\alpha$ hence tells you if you were rewarded accordingly to the risk taken. If $\alpha$ ...
Question Anxiety's user avatar
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Relationship between Beta and implied volatility

Beta is a measure of the historical volatility of a security compared with the volatility of an index which contains many stocks. So its value depends on the historical volatility of both ...
Bob Baerker's user avatar
3 votes

How to get the weights for a beta neutral portfolio?

The author did not define what optimal means, therefore I assume here that we want to find portfolio that has $\beta=0$ and has minimum variance $\sigma^2_{\pi}$ for the expected return $\mu_{\pi}$. ...
emot's user avatar
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What is the meaning of Beta of an individual asset in relation to a portfolio, not the market?

Not directly answering your question, but is this theoretical or did you actually do this? If so, I hope you do know that beta is not stable over time, only measures a linear relationship and that the ...
AKdemy's user avatar
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Relationship between Beta and Standard Deviation

TLDR: Beta = systematic risk Standard deviation = total risk Long Answer: There are two types of risk, systematic and unsystematic risk. Systematic risk affects the entire stock market. The ...
Luke_0's user avatar
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2 votes

Correlation between asset A and Portfolio X (which contains A)

You only need to note the following \begin{align*} corr\left(X_1, \sum_{i=1}^nw_i X_i\right) &= \frac{cov\big(X_1, \, \sum_{i=1}^nw_i X_i \big)}{\sqrt{var(X_1)} \sqrt{var(\sum_{i=1}^n w_i X_i)}}\\ ...
Gordon's user avatar
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2 votes

Beta = 1 and 0. Type of portfolios

Portfolio beta is a linear combination of each asset's beta times the weight of the asset in the portfolio. Thus in general we have $$ \beta = \sum_{i=1}^N w_i \beta_i $$ where $w_i$ is the weight of ...
Richi Wa's user avatar
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2 votes

Interpretation of Excess Return

They are both excess returns even though the standard convention is to talk about risk premium for $R_{t+1}-R^f$ and excess return on the market for $R_{t+1}-R_M$. If you believe in CAPM, then you ...
fni's user avatar
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2 votes

Which approach to estimating fundamental factor models is better, cross-sectional (unobservable) factors or time-series (observable) factors?

A simple addendum, that doesn't seek to supplant either the learned question and answer above. The short answer is the initial distinction drawn between ex-ante and ex-post is critical. What do you ...
demully's user avatar
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2 votes
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What is the best benchmark index for computing the beta of a multinational company?

Matthias, I would create a bespoke index weighted on the percentages you mentioned above. In that way you can be sure of capturing risk at the appropriate levels without overexposing your valuation ...
SolitonK's user avatar
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