Questions tagged [capm]

The capital asset pricing model is a model that allows to determine the theoretical rate of asset returns required by an investor, given the asset systematic risk or market risk.

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92 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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44 views

Event study using sector indices

Analyzing Covid-19's impact on different sectors I would like to use sector indices. Can you use CAPM or similar to calculate abnormal returns of indices or does it only work with stock prices?
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Inverse Covariance Matrix Transformation from CAPM

Beginning with the CAPM model we have (with a risk free rate of 0%): $r_i=\beta_i (r_m)+\varepsilon_i$ with $\varepsilon_i$ the diversifiable risks per assets The variance matrix: $\Omega = \beta'\...
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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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Assumptions of the CAPM

As to my understanding, the CAPM assumes that all investors behave as described in the portfolio theory. Consequently, all investors hold a combination of the risk-free investment and the efficient ...
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Relation between CAPM and Portfolio Theory

can any of you explain to me in simple terms how CAPM and portfolio theory are related to each other? To my understanding: Portfolio theory helps to select the "right" stocks under risk/...
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141 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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69 views

Risk free rate's role in CAPM

I don't understand what is the mathematical and financial role of risk free rate in the CAPM formula . Why do we need to add 10 years treasury yield to the formula then substract it again from the ...
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How is CAPM used to price an asset once it has been used to derive the assets expected return?

As I understand it (correct me if I'm wrong) the theoretical price of an asset should be the present value of all future cash-flows that it is expected to yield, discounted at the risk-free rate. I am ...
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54 views

Asset's Beta and CAPM

The CAPM model calculates the expected return of an asset i, given its beta (i.e., beta of that asset i). Mathematically, CAPM states that: $$ E(R_i) = R_f + \beta_i [E(R_m) - R_f]$$ Meaning that the ...
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1answer
64 views

Low volatility in factor regression

Let's say we are working with the standard Fama-French 3 factor model and we want to add a low volatility factor. Is it alright to add a low volatility risk premium in a model such as the CAPM or FF3. ...
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245 views

Cashflow Risk vs Discount Risk

Studying asset pricing, I often hear the terms cashflow risk and discount risk but I'm not sure what they mean? The Campbell/Shiller (1988) decomposition includes cashflows (future dividends) and ...
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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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Adding more factors to Fama French Carhart 4 factor model

Does it make sense to add more factors such as Quality Minus Junk (QMJ) and Betting Against Beta (BAB) in the Fama-French-Carhart model? Also, if anyone can point me to an article it would be ...
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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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Global portfolio alpha

How does one compute the alpha of a global portfolio. Let's say we are using the Fama French 3 factor model and we have a portfolio of 50% US stocks and 50% German stocks. Should the regression be ...
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Constructing a replicating portfolio of a long-only strategy using long-short factors

Lets say I want to estimate a replicating portfolio by doing a linear regression between the returns of a long-only portfolio and several long-short factors like Fama-French 5-factor or Betting ...
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1answer
124 views

Market Capitalisation Weights for Black-Litterman portfolio

I am implementing the Black Litterman model for a few assets, in particular I am using five ETF: EFA (EAFE stock index: developed markets outside US and Canada) EEM (stocks from Emerging Markets) ...
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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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35 views

Variance of the risk systematic component in Fama and French Three Factor Model

in my assignment i have to compute the variance of the risk systematic component in the Fama and French Three Factor Model. Does anyone know the formula or how to compute it? Thank you
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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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34 views

Interpretation of SML (Security Market Line) parameters

I estimated a SML in terms of excess returns and I get the following parameters: $\gamma_0=0.0286$ $\gamma_1=0.0263$ How can i give an economic interpretation of these two values? How they shape ...
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53 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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CAPM and the Fama-MacBeth (1973)

I need to conduct the Fama-MacBeth (FM) procedure for my thesis to test the ability of the six-factor model to predict future expected returns. In univariate regressions of expected excess returns on ...
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1answer
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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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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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1answer
124 views

Returns on the Fama-French size sorted portfolios

For my thesis, I need to replicate a specific research paper in the field of empirical asset pricing, mentioning the CAPM in particular. The data mainly consists of monthly returns on portfolios ...
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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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Understanding what is 'special' about the security market line

I am trying to get my head around the CAPM model and all the intricacies of portfolio management. I have written some code to help me visualise what happens to the risk-return characteristics of my ...
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1answer
58 views

Measuring Hedge Effectiveness

So I was trying to estimate the performance of a static hedge vs dynamic hedge in the electricity market and I came up with some weird findings. When I used the minimum variance hedge approach using ...
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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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What is risk premium of a portfolio?

I am not an expert in the field. So bear with me if my terminology is bad. I want to understand what risk premium of a portfolio is. I understand that there are different forms of risk. The basic ...
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Central Pricing Relation CCAPM

I need to understand what to do, when i take the covariance of an expression that looks like this: $\operatorname{cov}_{t}\left(\frac{U_{1}\left(\tilde{c}_{t+1}\right)}{U_{1}\left(c_{t}\right)}, \...
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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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Deriving CAPM from APT framework

I was wondering if it is possible to derive the CAPM from the APT? My argument is that CAPM basically just is a 1 factor model, where the APT has multiple factors. Can any of you guys help me?
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Variation in portfolio vs systematic risk

I am currently studying the CAPM, and I stumbled upon something that I can see is different, but I can't make the distinction. This isn't some mathematical question per se, but I hope that you maybe ...
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Asset risk relative to market portfolio risk - derivation problem

I am currently studying the CAPM, and at the moment I am focusing on beta. I am using the following book: Danthine, J-P and J. B. Donaldson (2014): Intermediate Financial Theory (3rd Edition) http://...
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Question about CAPM Betas - Causes of Beta Movement Query

CAPM betas are measures of systematic risks, which include things like the exchange rate, inflation, interest rates, etc. What I'm confused about is described below: E.g. suppose I'm looking at one ...
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Negative Beta and CAPM

In the case of a stock with negative beta and non-zero volatility, under CAPM the required return is less than the risk-free rate. This seems contradictory under CAPM assumptions that investors are ...
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1answer
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Value premium analysis - Equal or Value-weighted Portfolios?

I got a question regarding the analysis of the value premium in the U.S. stock market. The task is to use the market-to-book-value ratio to split the S&P500 in five portfolios (rank 1-100,101-200,...
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74 views

How do weights of a Mean-Variance optimized portfolio change as the Covariance matrix of the risky assets change?

I am learning a bit more about CAPM, and wanted to know if there was a specific way that weightings of assets in the optimal mean-variance portfolio changed (for constant risk aversion, expected ...
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76 views

0.0006 r-squared after trying to test whether the intercepts differ significantly. Did I do it wrong?

I am trying to test if the intercepts of two linear regression (CAPM) differ significantly or not. I have 2 fund's monthly return in the same period and regress them on the same market variable (MKT = ...
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How to interpret CAPM model?

I want to run CAPM model on two portfolios P1 and P2. Where CAPM is Rt - Rft = λ0 + λ1 (Rmt - Rft) Results which I got: Portfolios Intercept Coefficient of Rm-Rf Adjusted R2 P1 0 i.e not sig. ...
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Definitions of Beta

Definition of Beta It is generally understood that the beta of an asset $i$ is given by coefficient of the linear regression of the asset returns on market ($m$) returns, i.e. $$\beta_i = \frac{\rho\...
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Are BARRA's Multiple-Factor Risk models rational asset pricing models?

Barra's Multiple-Factor Models for risk (e.g. USE3, USE4, CNE5) are much like those models used in empirical asset pricing studies such as CAPM, Fama-French three-factor model and others. I'm not ...
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90 views

Expected Return on Stock

Suppose we have the following information on stocks $X$, $Y$, and $Z$: Expected Returns: $E(R_X)=10\%$, $E(R_Y)=12\%$. Standard Deviations: $\sigma_X=10\%$, $\sigma_Y=15\%$, $\sigma_Z=10\%$ Pairwise ...
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Using the Fama-Macbeth Process to Test CAPM

Here is my understanding of the Fama-Macbeth process: Assuming a group of $n$ stocks, we first collect risk profiles $\beta_{i, agg} = [\beta_{i, MKT}, \beta_{i, SMB}, \beta_{i, HML}]$ through ...
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Risk neutral valuation [closed]

In a world with three possible states (1, 2, 3) and three assets (A, B, C), the payoff matrix looks like this: $r_A;_1,_2,_3 = 110, 110, 110$ $p_A = 100$ $r_B;_1,_2,_3 = 100, 50, 40$ $p_B = 70$ $...
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Non-redundant asset?

I've been solving many exercises with three assets that have two possible payoffs each, one payoff per possible future state. The question is always the same, i.e. is any asset redundant. After ...
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Factor model alternative? [closed]

Suppose there is a Fama-French model estimated for a stock of Shoemaker Ltd.: $α = 0.01$ $β_M = 0.9$ $r_M = 0.12$ $β_S = 0.3$ $S = 0.05$ $β_H = 0.2$ $H = 0.06$ $r_F = 0.03$ How would you ...

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