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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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 about 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 ...
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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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65 views

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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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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55 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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51 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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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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275 views

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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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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Expected return [closed]

I apologize if similar question has already been asked. I have to calculate expected return on the stocks A & B via CAPM. I know $w_A = 0.2$ & $w_B = 0.8$ (weights computed from given ...
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1answer
59 views

Optimal asset allocation in three-asset portfolio [closed]

I apologize if similar question has been already asked. I have to find optimal weights $w_F,_I,_M$ for the assets $F, I, M$ in the portfolio. $E(r_F) = 0.03$ $σ_F = 0$ $E(r_I) = 0.2325$ $σ_I = 0....
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Optimal asset allocation

I apologize if similar question has been already asked. I have to compute optimal allocation of investment I between market asset and risk free asset. The investor's utility function is $U(w)=E(r_P)-...
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Beta: Cumulative vs. Simple Returns

How would calculating Beta using cumulative returns differ from Beta calculated with monthly returns? Is one more appropriate to use than another? https://en.wikipedia.org/wiki/Beta_(finance)
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CAPM - Expected vs. actual returns

I'm trying to calculate alpha in excess of CAPM and have seen a few slightly different calculations for CAPM. The primary difference I am seeing is that some equations use expected market returns (e....
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1answer
47 views

Gibbons, Ross, Shanken Test derivation by MLE

I Am trying to derive the expression for the GRS test of the CAPM. I am following the book: The Econometrics Of Financial Markets by Campbell, Lo, McKinley (1997). Define $Z_t$ as an $N×1$ vector of ...
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Why is the CAPM Beta defined this way - Beta hedging

Let's say I have two equity indices X and Y. Assume they are negatively correlated with some leverage. I want to hedge X with Y. I have seen many ways of computing a beta to describes the ...
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Investors degree of risk aversion in capm model

I am a bit confused about one assumption of the CAPM. My professor said that in the CAPM model all investors share the same utility function and the same degrees of risk aversion. Then as a final ...
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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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Estimated betas and optimal portfolio

I ran a regression on 20 assets to estimate their beta with different methods. I would like to see the differences of these estimation differences in terms of mean-variance optimal portfolio. How can ...
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Deriving Single Index Model (Market Model)

is the return of the stock of observation is the return of the reference market is the regression coefficient between the observed stock and the reference market is the regression intercept between ...
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Best practice approach for computing beta

I was wondering how one should choose parameters such as "frequency" of returns (daily, monthly etc.), "time frame" (1 or 3 or 5 years of historical data etc), benchmark (same of the portfolio or the ...
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1answer
125 views

Reducing pricing errors (Alpha) in the CAPM with Bitcoin

I have been trying to examine, using the CAPM, if Bitcoin belongs in the market portfolio or not. With 10 industry portfolios from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library....
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How/Why Markowitz model is normatitive while CAPM positive?

I've tried economic books but they only give this "should/is" explanations and I still cannot see how it applies to MPT. On the other hand, almost every paper and book gives these adjectives before ...
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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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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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Convert Geometric Direct Alpha PME to Arithmetic Excess IRR (PME Alpha / Implied Private Premium)

As a followup to this old question, Private Equity: Direct Alpha vs Excess IRR, I have a new one. In automating PME calculations, the Direct Alpha (DA) approach is computationally simpler and ...
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estimate cost of equity (Re) / required rate of return using DCF [closed]

I'd like to estimate Amazon's after-tax cost of equity (Re) using both the DCF and CAPM approaches. Tons of info and resources on how to estimate Re using CAPM, but DCF, I see no relevant resources. ...
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Relationship between CML and SML

I am referring to the book Sharpe et al. (1998), Investments, 6th Edition. I am trying to wrap my head around some lines from the book, pertaining to Security Market Line. It reads: Earlier it was ...
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Is there a robust way to calculate stock beta or factor exposure that's specific to crashes?

Commonly known factors like market, value, momentum etc. have positive expected returns because they draw-down unexpectedly and investors require a risk premium for holding them. This idea is extended ...
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Why is there inconsistency in WACC vs unlevered return?

To evaluate an enterprise we can discount free cash flow by either the unlevered required rate of return or the WACC. With Tax we have: $WACC=R_e \frac{E}{E+D}+R_f\frac{D}{E+D}(1-t)$ where $R_e$ is ...
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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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636 views

Calculating the pricing error in Fama-Macbeth Regression for Fama/French 5 Factor model

I'm very much new to this area and I need to know on how to calculate the pricing error in Fama/French 5-Factor model. The evaluation was done using the Fama-Macbeth approach. I did everything as ...
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Does the CAPM use the single index model?

When we derive the CAPM (i.e. find equations for the capital market line and the security market line), we nowhere assume that the individual security return is linearly dependent on the marker return ...
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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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Calculating beta when holding market portfolio

Suppose that CAPM holds and that you hold a portfolio of the market portfolio and the risk-free asset with weights equal to 0.74 and 0.26 respectively. What is the beta of your portfolio? My ...
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How modern portfolio theory(MPT) and CAPM are related?

1. Question In what sense Capital Asset Pricing Model(CAPM) is related with Modern Portfolio Theory(MPT)? Why do we need to check whether the current price of assets is overvalued or undervalued ...
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Implied Equilibrium Returns Example

I've been trying to work through a simple example using A Step-by-Step Guide to the Black Litterman Model, but I'm having trouble understanding implied risk aversion. Say I have two uncorrelated ...
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Market Portfolio Optimization

Consider the minimization problem $$\min\left\{\frac{1}{2}x^T\Sigma x - \lambda(\mu-r_f)^Tx\right\}$$ and assume the CAPM model, i.e. $$r_i-r_f = \beta_i(r_m-r_f) + \varepsilon_i$$ Assuming $\...
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Can the historical probability be the same as the risk neutral probability measure?

In particular lets consider a zero-beta asset $i$ (in the CAPM sense). Let $R_f$ be the risk free rate $R_i$ the return on the asset $i$ $R_m$ the return on the market portfolio $\beta=\frac{Cov(R_i,...
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CAPM - market portfolio vs real portfolio

I'm trying to understand the relation (if there is any) between the market portfolio, as described by the CAPM theory, and a real portfolio (just like the one I plotted in the image below). More ...
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How to determine the optimal start capital for a strategy?

Suppose my strategy generates a stream of daily profits distributed like 𝒩[μ=1€, σ=10€]. Intuitively, if I trade with 10€ start capital: I could very well be ruined on the first day, if the first ...