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14
votes
4answers
790 views

Approximately what proportion of a stock’s volatility is explained by market movement?

Assume we decompose the daily (log) returns of a stock as beta times market movement plus an idiosyncratic part. If this is done ex-ante, what proportion of the variance is explained by the market ...
14
votes
1answer
4k views

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

There are many approaches to estimating fundamental factor equity models. I would like to focus on two traditional methods: The time-series regression approach of Fama and French. Factors are ...
12
votes
5answers
2k views

is beta of a portfolio always meaningful?

Consider the following strategies: a stat arb strategy with no overnight exposure, but significant market exposure intraday. a market timing model which is always long or short the market. etc is ...
10
votes
1answer
2k views

Why is the first principal component a proxy for the market portfolio, and what other proxies exist?

Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you ...
9
votes
1answer
117 views

Estimate Beta of CAPM from Implied Volatility?

In the CAPM theory Beta of asset $i$ are estimated in this way: $ \beta_i = \frac{\sigma_{im}}{\sigma^2_m} $ where $\sigma_{im} = \rho_{im} \sigma_i \sigma_m$ But all these data are historical data. ...
8
votes
2answers
2k views

Beta vs. Implied Volatility statistical arbitrage using options

Let two underlyings, $S_{1}$ and $S_{2}$, are correlated and $\beta$ is the slope of their returns linear regression, that is, it says how much $S_{1}$ co-variates with $S_{2}$ variance. For ...
7
votes
3answers
641 views

How to account for jumps in intraday data when calculating beta?

I am calculating betas on intraday trade data at 15-minute intervals. For simplicity sake, let's assume I am modeling \begin{equation} Y = \beta * X + c \end{equation} where $Y$ is the return of XLF ...
7
votes
4answers
427 views

How google finance calculates beta of a stock

How google finance calculates beta of a stock - What is the proxy for the market? - What is the time period it uses for regression?
6
votes
2answers
315 views

How well does CAPM beta track the risk of a particular market relative to world markets?

Can the CAPM beta of emerging markets be less than the beta of the developed markets? As part of my research, I run regressions using market indices. I estimate the beta using a regression of MSCI ...
6
votes
1answer
2k views

How does Kalman filtering of beta in pairs trading model work in R?

Could anyone show how this could be done in R? The dlm package seems to be a good start, but I can't really find any good examples to learn from. Currently I have ...
6
votes
2answers
417 views

How to interpret beta meaningfully?

Although this is probably a basic question, this is probably also the right forum to post it in :) I thought I understood beta, but know I am really confused... The beta between my portfolio (weekly ...
5
votes
2answers
158 views

Beta Constrained Markowitz Minimum Variance Portfolio - Closed Form Solution

This question is related to recent rule changes in the Quantopian Open. I am trying to figure out a closed form solution to a beta constrained minimum variance portfolio problem but it doesn't seem ...
5
votes
0answers
88 views

Is Least Median Squares (LMS) regression commonly used in Finance?

Least Median Squares is often argued to give more stable results than does OLS. Whereas in OLS one minimises the mean of squared residuals, in LMS, one instead minimises the median of squared ...
4
votes
4answers
505 views

Given two portfolios with identical correlation matrices, which one will have a better risk/reward ratio?

I have one portfolio with high beta stocks, and one with low beta stocks. Is it better to have higher expected return with high volatility, or medium expected return with medium volatility? (All from ...
4
votes
2answers
95 views

Fama French model-small market beta (weird)

I am analyzing if good governance portfolios outperform bad governance portfolios. After dividing firms with good governance into one pf and bad ones into another for European companies I tried to run ...
3
votes
1answer
865 views

Proof of Hamada's Formula (Relationship between levered and unlevered beta)

Hamada's formula is presented as follows: $$\beta_{U}=\left[\frac{1}{1+\frac{D}{E}(1-\tau)}\right]\beta_{L},$$ where $\beta_{U}$ and $\beta_{L}$ are the unlevered and levered beta's of a firm ...
3
votes
1answer
81 views

How to get Correlation using Options data?

I can calculate the "Implied Beta" using implied volatility for the option stock, and implied volatility for the market (VIX). Is there any way to calculate also the correlation without performing a ...
3
votes
2answers
111 views

How to get Multivariate Betas from an Estimated EWMA co variance Matrix?

I have a portfolio of 4 assets. I also have returns for 3 indices. I want to get the multivariate betas for these 4 assets-based on these assets. I only have the 7 x 7 covariance matrix estimated by a ...
3
votes
2answers
348 views

Beta arbitrage in CAPM

i'm following the "Computational Investing 1" course at Coursera.org, I was affascinated by the Beta arbitrage of CAPM Video: https://class.coursera.org/compinvesting1-002/lecture/view?lecture_id=119 ...
3
votes
1answer
178 views

Estimating Beta from unevenly spaced price history

I have a certain non-stock asset that has 1 transaction every 1 to 8 months. I also have a price index of that class of asset compiled by another party on monthly basis. If I regress $price = \alpha' ...
3
votes
1answer
284 views

Beta and Frequency of Data

Why are the betas of individual securities essentially the same whether we use daily or weekly data when calculating?
3
votes
1answer
307 views

Average beta of index consitutents w.r.t. the index is 0.60

I have 1 year time series data of 300 constituents of the Australian All Ordinaries index (which is composed of 491 firms). The missing firms are mostly smaller firms. I run the market model $R_{it} ...
3
votes
1answer
157 views

Beta and the Assumption of IID Returns

For two stocks that are independent and identically distributed (iid), do they have the same beta? Does the number of data points matter?
2
votes
4answers
76 views

How to estimate the beta of corporations?

Are there certain strategies and general rules on how to estimate the beta of certain companies? How do I instantly know that it's a beta < 1 or a beta >> 1 corporation? Any helpful ratios that ...
2
votes
2answers
84 views

What do you do with low r-squared when calculating high-frequency beta

I am calculating a high-frequency beta. For example I have 90 days of data of the S&P and GOOGLE and I have 10-minute percent returns for each instrument. Each day has 34 10-minute percent returns ...
2
votes
2answers
66 views

Is portfolio beta additive under all return distributions?

If beta is additive i.e. ${\beta}_P =\sum w_i \beta_i$, shouldn't the two methods below yield the same number? Method 1: Estimate beta for each asset in the portfolio. Then ${\beta}_P =\sum w_i ...
2
votes
2answers
112 views

How to get twice the expected return of S&P 500

If I create a diversified portfolio of 2*beta stocks, can I expect to get twice the return of S&P 500. Example: Out of the universe of stocks available to me I randomly choose 10 stocks whose ...
2
votes
2answers
3k views

Why do stocks with a negative beta return less than the risk free rate?

Let's say we have two stocks, Stock A and Stock B. Both of them have the same standard deviation $\sigma$, and therefore have the same risk. The only difference is that Stock A has a perfect ...
2
votes
2answers
2k views

Are two stocks with the same beta have a correlation of 1?

If two stocks have the same beta over same time period, does it mean they are 100% correlated over that time period? In a CAPM framework, a stock's beta is defined as $$\beta_1={\rm Cov} (R_1, M) / ...
2
votes
3answers
27k views

How to calculate unlevered beta

I have derived a firm's cost of equity using the WACC formula (see here), which means that the cost of equity has factored in the firms' debt (i.e. levered beta) and now I need to calculate the firm's ...
2
votes
1answer
439 views

annual excess returns from CAPM on monthly total returns

I want to calculate annual excess returns on portfolios using monthly returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on the ...
2
votes
1answer
1k views

Counterintuitive time varying Beta with Kalman filter

If you're used to play with R, you'll enjoy the following reproducible code: ...
2
votes
1answer
470 views

Unsystematic and systematic risk of a portfolio

I have 8 country stock indexes and 1 world stock index. I do not actually have time series data but I'm given the following data: $\mu$, the vector of expected future returns for all 8 country ...
2
votes
3answers
7k views

Relationship between Beta and Standard Deviation

I was doing some financial analysis on two firms in the coffee industry. After calculating Beta and Standard Deviation for both firms, I seem to have stumbled on some weird phenomenon. It appears ...
2
votes
0answers
112 views

Best method for determining the market value of a stock before it is issued

I am attempting to determine the hypothetical market value of a stock for a company emerging from bankruptcy as of a date prior to actual the issuance of the stock. For example, let's say the formerly ...
2
votes
0answers
193 views

Good criteria to sort state-space $\beta_{t}$ according to Kalman filter output

Let the usual state-space linear model (without constant term for the sake of simplicity): $y_{t}=\beta_{t} X_{t}+\epsilon_{t}$ If we use Gaussian Kalman filter to estimate $\beta_{t}$ we get ...
1
vote
3answers
7k views

How does Yahoo finance calculate Beta?

I am trying to replicate the beta value that yahoo calculates but I am getting different results. According to Yahoo, its beta is calculated using 5 year returns against the SP500: yahoo beta I ...
1
vote
1answer
2k views

Calculating portfolio allocation beta with different asset classes?

I'd like to calculate portfolio allocation beta on a portfolio that has different asset classes. The portfolio may be made up of: ...
1
vote
2answers
2k views

How can I calculate Fama-French betas for a particular stock?

For a particular stock, what's the simplest way to calculate betas for the Fama-French factors SMB and HML?
1
vote
1answer
435 views

Why does $\hat{\epsilon}'\hat{\epsilon}$ of a factor model measure risk?

$\hat{\epsilon}'\hat{\epsilon}$ from the market model: $R_{it} - \hat{\alpha} - \hat{\beta}R_{mt} = \hat{\epsilon}$, or from a factor model such as the Fama-French 3 factor model, is often used in the ...
1
vote
1answer
30 views

Adjusting index betas for spread DV01

If you have an index and have measured its beta with respect to the overall market, how would you go about adjusting it against spread dv01 and why would you want this number?
1
vote
3answers
325 views

Portfolio Optimization - Zero beta portfolio

I am trying to solve a optimization portfolio in R in which I do the following constraints: Set weight sum to within a boundary Set return to a certain value Set portfolio beta to 0 The purpose ...
1
vote
2answers
76 views

different amount of information on return correlations from shorter and longer periods?

I want to calculate annual excess returns on portfolios using monthly (total) returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on ...
1
vote
1answer
55 views

Rebucketing Risk using PCA/other methods

was working on a project and could use some help. New to the community and looking fwd to being an active part of it. My question is, let's say we have a vector of securities V, and it trades with ...
1
vote
1answer
153 views

Interpret alpha's on Dual-Beta Model regression Results

I am trying to calculate the Dual-Beta for Apple (AAPL) by running a regression against the Spyder's ETF (SPY) & using the 10-yr Risk Free rate. The formula for the dual beta is: ($r_{AAPL}-r_f) ...
1
vote
1answer
115 views

right benchmark for an incompletely diversified international portfolio (for a CAPM): MSCI World or MSCI ACWI IMI?

I want to calculate annual excess returns on portfolios using monthly returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on the ...
1
vote
1answer
2k views

how to chain monthly excess returns into annual?

I want to calculate annual excess returns on portfolios using monthly returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on the ...
1
vote
3answers
5k views

Annualized Covariance

I have two time series. One with monthly returns on an asset and one with monthly returns on a benchmark index. I have calculated the covariance using the ...
1
vote
0answers
28 views

How to derive what effect funding shocks have on conditional market betas? [closed]

I am unable to derive the correct result eq2 all my answers seem circular, any help would be much appreciated. It should basically end up saying that shocks that affect all securities compress betas ...
1
vote
0answers
30 views

Generalized method of moments concept in CAPM testing

In the course of my master thesis I’ve come across a paper by Carr and Wu (2009) where the authors evaluate whether returns on variance swaps can be explained by the simple CAPM. (really only market ...