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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Risk-Neutral CAPM
In the paper Measuring Equity Risk with Option-implied Correlations, Buss and Vilkov replace the standard CAPM beta:
$$
\beta_{iM,t}^P=\frac{\sigma_{i,t}^P\sum_{j=1}^N w_j \sigma_{j,t}^P\rho_{ij,t}^P}...
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Clustered vs. GMM-based standard errors: which ones to use in asset pricing?
Consider estimating an asset pricing model such as the CAPM or a multifactor model using monthly data. Petersen (2009) section "Asset pricing application" suggests use of standard errors ...
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Testing asset pricing models with Roll's critique in mind
Roll's critique (Roll, 1977) can be summarized as follows (quoting Wikipedia):
Mean-variance tautology: Any mean-variance efficient portfolio $R_{p}$ satisfies the CAPM equation exactly:
$$
E(R_{i})-...
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Some basic questions using consumption CAPM
Say we are in a world described by the consumption CAPM. All investors in this world have quadratic utility. Also, assume that consumption is as follows:
$$c_{t+1} = (1+m_t)c_t + s_t c_t e_{t+1} $$
...
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Is Consumption CAPM a special case of Intertemporal CAPM?
Intertemporal CAPM state variables are related to the future investment opportunity set. In Consumption CAPM the state variable is consumption ? Is it the correct way to think about it?
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Is this methodology to calculate Alpha using multi-factor regression model correct?
I am trying to find out Historical Alphas of a bunch of fund returns ${F_i}$ by Using Regression Model$(stepwise)$ with regressors as its underlying exposure-returns(risk-free rate subtracted) i.e.
$$...
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What quantities (means, betas) must be constant over time for the GRS test to be valid?
I am interested in testing the CAPM using the GRS test. Consider $N$ assets observed for $T$ time periods. Using the notation of Cochrane "Asset Pricing" (2005), the GRS test amounts to ...
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Using CAPM to find the price of an option
I was reading a textbook about finding the price of an option on a one-period binomial model.
The textbook way of doing it is to replicate the option with cash and stock for $t=T$, and then calculate ...
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How to reconcile CAPM with Discounted Cash Flows valuation?
According to CAPM (in its most basic form) our asset allocation will only depend on the expected returns and the covariance matrix of returns. If we also consider the risk-free asset and assume that ...
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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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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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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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Stochastic Differential equation: CAPM
Let $R=(R_1, \dots ,R_M)$′ denote a vector of excess returns of M assets observed at $n$ time points, $0<t_1<t_2< \cdots <t_n<T$, within a time span $T>0$.
We wish to explain the ...
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Testing the CAPM a la Fama & MacBeth: specific trade-off between expected return and risk
Fama & MacBeth (1973) test a two-parameter model of market equilibrium by examining whether its implications hold empirically. They work with the following generalization of the model:
$$
\tilde ...
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Does a portfolio on efficient frontier also lie on CML(capital market line)?
I am trying to solve this question:
Assume that CAPM is true. The risk-free rate is 3%, the expected return on the market portfolio is 10% and the standard deviation of the return on the market ...
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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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Alpha - Time Series vs Cross Section Approach
I am currently reading Cochranes book on asset pricing. However, I get confused about one thing. He says that one could test a factor model (I will use the CAPM, just as he does), via a time series ...
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linear stochastic discount factor
I have heard some people say something like the following with regards to APT:
Let returns be given by the factor model
$r_t = B_tf_t + e$
with
$E(f_t) = \lambda_t$
Assume that factors are ...
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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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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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Residual Risk and Variance
I've solved part a, but am struggling with b and c. $x_m$ is the market portfolio vector, and I think $T$ should be a diagonal matrix. Any hints greatly appreciated!
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The utility function in Betting Against Beta
http://pages.stern.nyu.edu/~lpederse/papers/BettingAgainstBeta.pdf
Betting Against Beta strategy is presented in the link above. Most of the theory and derivation is based on a utility function given ...
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Liquidity Adjusted Asset Pricing Model
I have a data set with 4000 companies and I have calculated a liquidity measure of each of the company in the dataset as
Where, Turnover is the monthly average ratio of daily volume to shares ...
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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 ...
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Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions
Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions?
During my engineer student days I saw the Markowitz theory for portfolio selection ...
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Question about pricing kernel definition in "Quality minus junk" paper
I'm reading the paper "Quality minus junk" by Asness et al. published in Review of Accounting Studies (2019). The authors present the following definition of the pricing kernel on page 2:
$$
...
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Discuss how you would allocate your budget between the two assets if their correlation is 1, 0, or -1
An asset A is expected to yield a $2\%$ return with a standard deviation of $1\%$, and another asset B is expected to yield a $1\%$ return with a standard deviation of $1\%$.
Discuss how you would ...
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Risk adjusted returns for a portfolio relative to CAPM
This is very likely a simple question. When following Lewellen (2015) (open access here), how should I compute alphas for portfolio returns relative to the CAPM and FF3? Do we simply subtract the (...
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GRS test does not reject a scalar multiple of the market factor
I have been playing with the GRS test (see my R script below) in relation to Why not use a time series regression when the factor is not a return?. I generated a $10,000\times 26$ matrix of returns on ...
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Understanding mean-variance tautology from Roll's critique
One of the points of Roll's critique (Roll, 1977) can be summarized as follows (quoting Wikipedia):
Mean-variance tautology: Any mean-variance efficient portfolio $R_{p}$ satisfies the CAPM equation ...
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Calculating monthly UST3M returns
I am trying compute a variance/covariance matrix for 5 stocks using monthly returns. I plan to use CAPM (using monthly log returns) as the expected return and the US 3-month Treasury Bill (UST3M) ...
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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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Why is it that returns at the efficient market hypothesis has to be risk-adjusted?
Let us assume the following situation:
Average market return: $R_M = 8\%$
Risk-free rate: $R_F = 2\%$
Actual return of share A after one year: $R_{A} = 15\%$
Actual return of share B after one year: $...
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CAPM: Testing for alphas jointly equal to zero
For my project, I need to assess if a certain factor X leads to a CAPM-Anomaly. First, I sorted the monthly stock return (sample size: 500+ observations) according to the X factor in 10 decile ...
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Deriving the tangency portfolio with a condition in Python
If there are sister-sites better suited for this question please let me know, I thought this to be the most fitting
I have the covariance matrix, the return vector and some scores (ESG scores). The ...
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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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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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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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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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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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No risk free security?
Imagine market without a risk free security. How is security market line constructed? How is it interpreted?
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Testing pricing errors on the SML for significance with R
I have been attempting to do a cross-sectional test of the CAPM.
To do this, i have estimated the betas of 49 industry portfolios with time -series data. And then done a cross sectional regression, ...
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Fama-French 3, Carhart 4, Fama-French 5 Factor models return borderline 0% R2 (max. 6.6%). Time series regression
I am currently working on an industry specific time series analysis of European Equities between 201001 and 201812. I use the European Fama French factor returns (plus the momentum factor return) that ...
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Evaluating Fama French 3 factor model Using Fama Macbeth
Hi Can someone please explain me how the cross sectional calculation can be done.
For an example, I'm having a vector like this.
Vector 1: This is the vector where all the excess returns for n ...
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Zero-beta assets and the Sharpe-Lintner CAPM
I'm reading The Capital Asset Pricing Model: Theory and Evidence (Fama and French, 2004) and came across the following statement:
"A risky asset’s return is uncorrelated with the market
return—its ...
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CAPM and expected future spot price
Let $S_t$ be the current spot price at time $t$ and $S_T$ be the spot price in the future (at time $T$). Assume the stock pays continuous dividends $d$.
How does the CAPM imply that the expected ...
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Levered beta with changing equity/debt ratios
I know how to calculate a bottom up levered beta for a privately held and not publicly traded company with Hamada (Proof of Hamada's Formula (Relationship between levered and unlevered beta)) and ...
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Change in portfolio when IPO announced
I'm wondering whether there would be a change to my answer of the change in portfolio when there is a new stock introduced.
My investment strategy is to maximise expected return such that my standard ...
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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 ...
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Shanken's correction for Fama-MacBeth (1973) generalization of the CAPM
Fama & MacBeth (1973) tested the CAPM against an alternative that the dependence between the expected excess return $E(r_{i,t}^∗)$ and the relative systematic risk $\beta_𝑖$ is nonlinear (namely, ...
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