14
votes
Accepted
Estimate Beta of CAPM from Implied Volatility?
Yes it is a better way.
Just take a look to figure 3, from Buss and Vilkov (2012, RFS):
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9
votes
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 ...
- 15.3k
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'...
- 8,438
8
votes
Accepted
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 ...
- 6,924
7
votes
Accepted
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
$$
\sigma(R_p) = \sqrt{w_1^2\cdot\sigma(R_1)^2 + w_2^2\cdot\sigma(R_2)...
- 1,446
6
votes
Accepted
Dollar-Neutral in addition to Market-Neutral?
Imagine a scenario where a beta neutral portfolio comprised being long one very high beta stock and short many low beta stocks. Such a portfolio clearly has extreme concentration of risk. ...
- 791
6
votes
Accepted
Using cross-sectional factor model (BARRA type) returns in a time series factor model (Fama-French type)?
What you're describing sounds like the reverse of a Fama-Macbeth regression. The original Fama-Macbeth approach estimated rolling time series regressions to get CAPM betas and then doing a cross-...
- 5,391
6
votes
Accepted
Why stock beta is not equal to its index weight?
It's trivial to calculate the betas given the index weights $w$ and the covariance matrix of all stocks $\Sigma$:
The index return is
$$
r_{\rm index} = w^T r
$$
The beta of stocks to the index is
$$
\...
- 5,891
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 ...
- 27.3k
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, $...
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5
votes
Accepted
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 ...
- 131
5
votes
Accepted
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 ...
- 1,396
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 ...
- 1,396
5
votes
Accepted
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 ...
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4
votes
Accepted
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 ...
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3
votes
Accepted
Is portfolio beta additive under all return distributions?
Mathematically they must be the same:
$\frac{Cov(Portfolio_{returns},r^m)}{Var(r^m)} = \frac{Cov(\sum w_i r_i,r^m)}{{Var(r^m)}} = \frac{\sum w_i Cov(r_i,r_m)}{Var(r^m)} = \sum w_i \beta_i = ...
- 8,062
3
votes
What do you do with low r-squared when calculating high-frequency beta
This simply suggests the linear model is a poor fit in high frequency. But is this that surprising, even before you crunch the numbers? I argue not, for the following reasons:
Even at low ...
- 515
3
votes
Accepted
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. ...
- 811
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 ...
- 1,352
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 ...
- 1,456
3
votes
Accepted
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 ...
- 1,396
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 ...
- 126
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 ...
- 10.9k
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 $\alpha$ ...
- 342
3
votes
Accepted
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 ...
- 610
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 $\mu_{\pi}$. ...
- 866
2
votes
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 ...
- 121
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 ...
- 5,041
2
votes
What do you do with low r-squared when calculating high-frequency beta
A high R-squared (1.0) means that you can explain the movements of one time series using the other. The lower your R-squared is, the worse your explanation is -- that includes the 'quality' of your ...
- 788
2
votes
How to estimate the beta of corporations?
There are many approaches to calculate however mostly people prefer to calculate industry beta and then apply financial leverage on that to get company beta.
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