Questions tagged [beta]

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CAPM estimation model alternatives [closed]

Let's take a look at the standard CAPM: $$ r_{i} -r_F = \alpha+\beta(r_{MKT}-r_F) + \varepsilon $$ I would like to consider the alternative formulation: $$ r_{i} = \alpha+\beta(r_{MKT}-r_F) + \...
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Simple beta hedging questions

This might sound really naive but I am really confused by this beta hedging idea. So it seems the standard way to do it is to run a simple OLS on returns (say asset A and B only 2 assets in the ...
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Should I annualise returns for beta calculation?

I am working on a Python library for financial calculations based on Time series data. One of the functions I'm implementing is beta. This will allow the user to pass two sets of time-series data, one ...
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Betas and weighted average ERP

Whenever analyzing a particular company through CAPM, I used to take the Equity Risk Premium (ERP) of the country where the company was listed/headquartered. However, recently I came to know that some ...
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Part of return on asset uncorrelated with market

I've been told (and have done problems) involving the part of the return of an asset $X$ that is uncorrelated with returns on the market $M$, which can be written as $X - \beta X$. This sort of makes ...
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CAPM and Beta under Prospect Theory

I'm thinking about some sort of behavioral risk factors such as whether different utility functions, such as Prospect Theory according to Kahneman and Tversky, might change the way betas are derived ...
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How do you hedge a portfolio against a factor using index Futures?

How do you hedge a portfolio against a factor using index Futures? I constructed a long/short portfolio and dynamically hedge against an index, beta hedge. I realized that my portfolio is highly ...
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Does it make sense to only interpret one side of dual beta?

Assume we separate return pairs in this way (one bucket for return pairs where excess benchmark return > average benchmark excess return, and another bucket for returns pairs where excess benchmark ...
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What details must be considered when assessing an asset’s inflation beta?

The inflation beta of an asset is described as: $$ r_{i,t}-r_f = \alpha_i + \beta_\pi^i \epsilon_{\pi, t} + u_{i,t} $$ For shorthand, I will use “return” to mean excess return. In academic literature ...
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65 views

Upside and downside beta?

Assuming we are talking about the dual-beta idea where we restrict benchmark returns to negative (downside beta) and positive (upside beta), then I have the following confusions. Do we only interpret ...
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Interpret interaction term between dummy and continues variable /bank risk (Beta and stock return)

I am using OLS regression to answer my research question.Well, I have two types of banks( Commercial banks and bank holding company's).My dependent variable is banks stock return in the first quarter ...
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Why does Beta of a stock not correlate well with market sell off

I posted a question a few days back: (Quantatively identifying stocks to short when overall market starts to roll-over) @rubikscube09 suggested that stock beta ...
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2 answers
154 views

Beta using only price returns?

It is my understanding that one can use both excess returns and price returns to compute a beta coefficient. In the former way, beta would be interpreted in the standard way (a 1 unit change in market ...
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In-sample forecast accuracy of Beta (Kalman filter) CAPM

One can calculate time-varying betas (known from the CAPM) using the Kalman filter. For example, one can calculate the in-sample forecast accuracy using the MAE. $MAE = \frac{1}{T}\sum_{t=1}^T|\hat{R}...
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How to get the weights for a beta neutral portfolio?

Given a ranking of 100 long stocks and 100 short stocks. Looking at these 200 betas: How can I find the optimal weights to get a beta = 0 long/short portfolio?
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Compare rich / cheap options on 2 underlyings

this question can turn out to be very basic but its something that has been bugging me. Say I want to buy/sell an option on A vs sell/buy an option on B. Facts I know A and B are different ...
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2 answers
302 views

What is the relation between "Capital Market Line" and "Capital Asset Pricing Model (CAPM)"?

I asked this question on Personal Finance and Money but since I don't know where to place it I placed it here also. On the Coursera course Portfolio and Risk Management, on Week 2, I am having trouble ...
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Hedge 3 securities against 3 other securities

I have a portfolio of 6 securities, 3 long 3 short. I need to hedge them against each other so directional exposure = 0. How would I decide how to weight each security? Is there a model to do this?
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Real estate returns with incomplete dataset?

I have a dataset of real estate returns in markets A, B, and C. I also have national returns, denoted market N. I have 10 columns representing the time period for each data point. Market A only has ...
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1 answer
135 views

Understanding Look Back Period

When people say look back period of 6 months, how does that data look like? Are that 6 months of raw data or a weighted average of that data? I am a little confused on how you come up with beta values ...
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2 votes
0 answers
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Portfolios sorted by TED volatility

I was reading a paper titled "Betting against Beta" (link). The paper has five major propositions. The fourth proposition is that betas are compressed towards one when funding liquidity risk ...
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Checking Regression Inputs & Outputs (Factor Regression)

I am looking to check the assumptions and interpretation of the output of a regression that I have run for factor exposures in a long/short equity portfolio: Portfolio is long/short equity with a net ...
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Time horizon of estimation period CAPM beta

When calculating CAPM beta, it is done by rolling regressions. If it is only the beta we want to obtain, am I correct to assume that we can estimate rolling correlations and stds, and use this to ...
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High Beta, low specific risk, and no leverage?

My risk model shows a Beta of 2 for the stock APTIV (maker of car components). The model looks at the past 3 years with no decay. Total vol is high but specific vol is very low. Typically when this ...
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Daily weights and returns of portfolio that rebalances monthly

I am to replicate the Betting against beta strategy by Pedersen and Frazzini. We use daily returns of the stocks and construct two portfolios based on their ranked betas. Weights is also based on the ...
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2 votes
1 answer
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Build a portfolio with $\beta=1$ and minimize $\sigma^2$ using CAPM

Suppose there are two stocks A and B: expected returns are $E[R_A]=0.1$, $E[R_B]=0.15$; standard deviations are $\sigma_A=0.1$, $\sigma_A=0.2$; correlation is $corr(A,B)=0.6$; their betas to some ...
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2 votes
0 answers
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% of allocation in a portfolio based on beta

Just an amateur investor hoping to minimise loss by using beta for portfolio allocation. Tried using individual beta/summed beta but that would result in a higher allocation for the highest beta. ...
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2 answers
108 views

Nonsystematic risk in a random rate of return [closed]

Good evening, I am studying the CAPM and I have a doubt regarding the variance $σ_i^2$ of the expected return of an asset $i$. In particular, how can I derive the following formula? $$σ_i^2 = β_i^2 ...
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-1 votes
1 answer
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Yahoo Finance Beta Calculation - foreign stock [closed]

How does Yahoo Finance calculate Beta for stocks quotes in foreign markets? Does it consider the volatility against local markets indexes or US S&P 500?
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1 vote
1 answer
357 views

Relationship between Beta and implied volatility

Is there any way to make use of the Beta of an underlying and index, and the implied volatility of options on that underlying and the index? To specify, if we have available the implied volatility of ...
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60 views

Should diverging valuation multiples affect beta estimate?

Suppose we experience a significant equity market crash. All equities are affected, but the drawdown disproportionately affects equities in a specific sector - for example, say the broad equity market ...
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Arbitrage in a Single Index Model

Simple question really, but I'm very confused by the starting point. Let's assume that we have a portfolio whose excess returns can be described by the following equation from the single index model: ...
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2 answers
818 views

How can beta be negative? [closed]

I've been reading about the security market line and the definition of beta as $$\beta_i = \frac{Cov(R_i, R_m)}{Var(R_m)} $$ for any asset (doesn't have to be an efficient portfolio), and have read ...
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3 votes
2 answers
252 views

Why Index Futures can be used as a Market benchmark?

I heard that we can use, say, Eurostoxx Futures as a benchmark to compute the beta of the index's components. Is this relevant? If so, how do we deal with the futures' expiry? Thanks
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Beta Adjusted Return

I'm a bit confused about the definition of the 'Beta Adjusted Return', say I have benchmark whose return is $r$ and a stock whose return is $R$, the beta adjusted return is defined as $$ ...
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2 votes
0 answers
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Why is the efficient portfolio assumption necessary for the CAPM model?

One of the main assumption in the CAPM model is that all the investors are rational and they hold the most efficient portfolio for a given level of risk. What difference does this assumption make? ...
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1 answer
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What is the intuition of CAPM model with Intercept at 0?

I only have a very general theory-based knowledge on Jensen's Alpha. I'm very curious about Capital Asset Pricing Model with intercept at 0. May I know what is the intuition behind this? What does it ...
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-1 votes
1 answer
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How to build a portfolio following the Smart beta process by dividend? [closed]

I'm having trouble finding the method to track smart beta dividend management. I have an Excel file which contains the prices and the dividends of certain companies, and I want to build a portfolio ...
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1 answer
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Beta and standard deviation

IS beta of a stock formula equals to correlation coefficient multiply with annualized standard deviation of stock A divide annualized standard deviation of market . i am not sure whether to use ...
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1 vote
3 answers
584 views

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

I have two time series of daily return calculated as $\frac{Price_{t}}{Price_{t-1}} -1$. One is the daily returns of a portfolio, the other the daily returns of the index (MSCI World). Period is 2020 ...
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1 vote
0 answers
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covariance matrix in the CAPM model

I'm running a simulation for a 5 asset portfolio, calculating the optimal weights of each asset both with the statistical model (i.e. single index) and with the CAPM. my question is: how do you ...
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0 votes
1 answer
150 views

relationship between the expected rate of return and the value measured by the beta factor

Assume that only two companies are listed on an effective capital market: companies A and company B. Capitalization (market value of all shares) of both companies is the same. Expected rate of return ...
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1 answer
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Beta of sum or sum of betas

When interested in the beta of a portfolio, I see people make a weighted sum of the portfolio components' betas. Intuitively, I would have calculated the beta of the portfolio based on its aggregate ...
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1 answer
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CAPM Model, is this exercise done correctly?

Hey i need to know if the task is done correctly, please help :) Standard deviation of the rate of return on the market portfolio is equal to $\sigma_{MP}=1,5\%=\frac{15}{1000}$. I have portoflio ...
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1 vote
2 answers
1k views

Hedge backtesting: ex-ante Beta vs observed Beta (is this even possible?)

A global equity portfolio has for objective to outperform a benchmark (MSCI World). I hedge the sensitivity of the portfolio to MSCI World (the beta) so that only the alpha remains unhedged. The ex-...
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0 answers
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Performance attribution and monthly rebalance: Is a month enough data to calculate Beta and Alpha?

A portfolio is built systematically by calculating scores and rebalanced each month to invest only in the 80 best scores. Scores change frequently and therefore the portfolio changes each month, ...
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3 answers
141 views

Hedge performance in times of volatility: Beta changes impacting PnL during market rebound

I hedge a portfolio of Global Equities (200 stocks within MSCI World universe) by shorting futures on MSCI World Net Total Return. The hedge is calculated using Beta. Beta is calculated using a risk ...
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0 answers
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Calculation of portfolio beta (CAPM)

Let the market risk be $\sigma_m=28\%$. A portfolio consists of four stocks, all with the same weight ($w_i=0.25$ for all $i$). We also know that $\sigma_a=18\%,\sigma_b=36\%,\sigma_c=22\%,\sigma_d=17\...
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1 vote
2 answers
133 views

Outperform the market with a Beta lower than 1, is it possible? [closed]

I have a portfolio which seems to have outperformed the benchmark for the past 2 years however the risk system I use advises that using recent past data (lookback period of 2 years) the Beta to this ...
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3 votes
0 answers
460 views

How to derive the CAPM from maximizing the Sharpe ratio?

I know how to derive at the CAPM from a microeconomic foundation. In a recent University course I stumbled over a slide that derived the CAPM solely from the Sharpe ratio: I cant come up with that ...
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