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Questions tagged [beta]

The beta of an investment strategy corresponds to its relation with the systematic moves of the prices, i.e. the one driven by very common factors. Typically market indexes are benchmarks used to measure the beta against.

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Producing hedge ratios via regression via returns and not price

I'm a quant student and I need someone to clearly and plainly explain to me better than my professor did about this topic. Please be patient if my question seems very basic. to find hedge ratios or ...
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Some questions about beta hedging

Sorry if this is obvious to you. I've got my brain spinning for a while and think I should seek some insights. Question 1: What's the definition of $\beta$ between a stock and hedger/market portfolio, ...
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Should I convert monthly data into yearly for CAPM?

I am trying to use the CAPM. I gathered monthly data on German government bonds and DAX40 (it's an index that contains top 40 German firm). Then based on only one company like Volkswagen monthly stock ...
Mostafa Bouzari's user avatar
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Simple Beta Neutral Intuition in Pairs of Two Assets

I'm having trouble understanding the intuition of a simple beta hedge using a linear regression. Assuming an asset has a beta of 0.5 against the market. That implies for a percent move in the market, ...
abstract'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?

Assume I've got a portfolio "A" with an expected return of 14% and a volatility of 20% and my broker suggests to add a new share "H" to my portfolio which has an expected return of ...
j3141592653589793238's user avatar
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1 answer
275 views

Why stock beta is not equal to its index weight?

Index is a linear combination of stock prices with known weights. In case index is equally weighted, the weights are fixed. Beta measures stock sensitivity to index - by how much stock moves when ...
Kreol's user avatar
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Supervised metric including beta?

I am working in a supervised ML framework. I'd like to define one metric to evaluate a strategy. Naturally I was initially enclined towards overall returns or sharpe ratio. I'd like to implement a ...
Lucas Morin's user avatar
2 votes
1 answer
129 views

Definition of Market-Neutral

I'm reading Qian, Hua and Sorensen's Quantitative Equity Portfolio Management and one part in section 2.3.2 (page 44) states that: "For a long-only portfolio managed against a benchmark, the ...
PerplexedPelican's user avatar
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Why reduce number of short contracts to reduce beta, and take long positions to increase it?

My question is about chapter 3 in the ninth edition of "Options, futures and other derivatives" by John C. Hull, subchapter 5 under the heading "Changing the Beta of a Portfolio". ...
Tosca's user avatar
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How to calculate the ex-ante beta of a portfolio between several rebalancing?

I have a portfolio composed of $ N $ assets. I know the one-year beta of these assets, I also know the past (ex-post) beta ($\beta$) of my portfolio. My portfolio changes allocation every month. So I ...
TLS's user avatar
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Definition and estimation of $\beta$: raw or excess returns?

The CAPM is a single-period model that says $$ \mathbb{E}(R^*_i)=\beta\mathbb{E}(R^*_m) $$ where $R^*_i:=R_i-r_f$ is an asset's excess return, $R^*_i:=R_m-r_f$ is the market's excess return and $\beta:...
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Is beta stable over time for individual securities?

I'm reflecting on whether historically estimated $\beta$ is a "good" estimator of future $\beta$. Consider the problem as follows: Let $r_1$, $r_2$, ...., $r_{36}$ be the last 36 months of ...
MYK's user avatar
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Simulate correlated credit spread

I want to simulate a credit spread index which is negatively correlated to a given random walk of a stock index. They should be correlated in such a way that larger than average stock growth tend to ...
thijs818's user avatar
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132 views

Adjusted beta for short positions, should we re-adjust the formula?

I see in BBG that the beta of XSPS (an inverse SP500 ETF) to SPX Index is -1.05 and the adjusted beta is -0.37. I get that -1.05 * 2/3 + 0.33 matches the adjusted beta. However, does this adjusted ...
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Beta anomaly (t statistics)

I would like to analyze the beta anomaly following the method used in the following paper "The low-risk anomaly: A decomposition into micro and macro effects" by (Baker et al, 2018). (the ...
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Difference between Treynor ratio and market premium

The definition of Treynor ratio is given by $$ T = \frac{r_i-r_f}{\beta_i}, $$ where $r_i$ is the portfolio $i$'s return, $r_f$ is the risk-free rate and $\beta_i$ is the portfolio $i$'s beta. I am ...
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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 ...
DLW's user avatar
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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 ...
Harsh Sharma's user avatar
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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 ...
Seh-kai 's user avatar
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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 ...
T123's user avatar
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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 ...
user3138766's user avatar
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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 ...
cephalopod's user avatar
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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 ...
user3138766's user avatar
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1k views

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?
jeheran sankti's user avatar
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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 ...
Macro RV's user avatar
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2k 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 ...
loco.loop's user avatar
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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 ...
user3138766's user avatar
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326 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 ...
Deepankar Joshi's user avatar
2 votes
0 answers
74 views

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 ...
jeetkamal's user avatar
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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 ...
IIJHFII's user avatar
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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 ...
theone's user avatar
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1 vote
1 answer
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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 ...
tweedi's user avatar
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1 vote
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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 ...
theone's user avatar
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2 votes
1 answer
209 views

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 ...
Grumpy Civet's user avatar
2 votes
0 answers
56 views

% 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. ...
Taopayoh's user avatar
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2 answers
115 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 ...
Bernheart's user avatar
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-1 votes
1 answer
241 views

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?
Ernani Mercadante's user avatar
1 vote
1 answer
833 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 ...
Oscar's user avatar
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2 answers
66 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 ...
beeba's user avatar
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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: ...
LossModels's user avatar
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2 answers
2k 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 ...
asfjbkjabf's user avatar
2 votes
2 answers
264 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
mbz0's user avatar
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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 $$ ...
mbz0's user avatar
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2 votes
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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? ...
Urja's user avatar
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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 ...
Ernest's user avatar
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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 ...
Kadiri's user avatar
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1 answer
567 views

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 ...
Renee Fong's user avatar