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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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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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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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165 views

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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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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164 views

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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50 views

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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126 views

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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132 views

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 ...
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Calculating idiosyncratic risk of stock without beta or risk free rate

I have been given the expected returns and standard deviations of 2 stocks A and B, as well as the standard deviation of the market portfolio and correlation between security A and the market ...
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What if CAPM cost of equity is negative?

Dear Community members, I calculate 5 years trailing beta using capm. After that I calculate estimated cost of equity. However, what I have is that most of the observations have negative cost of ...
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Daily idiosyncratic volatility?

I have a long daily times series of individual stocks and would like to obtain daily idiosyncratic volatility (keeping the same frequency). Apparently, the widely used methodology of Ang 2006 would ...
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CAPM: Bond index as proxy for Rf

Is it possible to use a bond index as a proxy for Rf in CAPM? Please let me know what is the issue here.
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107 views

Cost of equity proper way of calculation

Dear Community members, I need to calculate cost of equity following the following description: (Please, correct me if I misinterpret the meaning) "The annualized cost of equity, re(t), is ...
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99 views

Examination of Betting Against Beta

http://pages.stern.nyu.edu/~lpederse/papers/BettingAgainstBeta.pdf In this article the authors explain a theory/strategy called Betting Against Beta. My background is more in Math rather than finance ...
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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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593 views

Testing the statistical significance of alphas in the CAPM

I am trying to test the statistical significance of the alphas in my trading strategy. However, I do not understand the difference between the alphas generated in R. To test the statistical ...
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Measuring size risk in CAPM. How one could go about?

I am using valuation methods (e.g. CAPM) in order to measure some projects "baseline" return. I'm not using these measures for stocks returns, but to evaluate specific projects (e.g. dam constructions)...
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What exactly makes CAPM an equilibrium model?

CAPM comes from Markowitz' portfolio theory. We study agents utility maximization behavior, and get results like two-fund separation. Every agent holds the tangency portfolio, combined with the risk-...
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385 views

Calculating beta to market

Let's say we want to compute beta to S&P500 of a portfolio, using 3 years of weekly returns, as of today. We would take each stock in the portfolio and regress the weekly returns of that stock ...
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In the “betting against beta” paper, what exactly is the “BAB factor”?

I refer here to the paper "Betting against beta" by Pedersen and Frazini. In the model, they construct the following factor, on page 5. I don't quite understand how this portfolio is being ...
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79 views

Markowitz w/ riskless asset & CAPM

If risk free rate ($R_0$) is bigger than expected return on minimum variance portfolio ($\bar{\mu}$), so $R_0>\bar{\mu}$. I.e. the tanget portfolio is on the risky inefficient portfolio frontier ...
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649 views

Proxy for daily risk-free return in CAPM

Say I am estimating the following Capital Asset Pricing Model: $$R_t = R^f_t - \beta(R^m_t - R^f_t)$$ where $R^f_t$ is the risk-free return, and $R^m_t$ is the return for some market index, say the ...
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How to test the CAPM empirically and how do I use this Kenneth French dataset?

I'd like to test whether CAPM holds. My guess is that I first need to find a market portfolio. Then, over some period, I calculate its excess return $R_M - r_f$. Then I calculate the return of some ...
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What Process Does the Market Follow in the CAPM?

Consider a multiperiod version of the CAPM $$E_t[r_{i,t+1}-r_{f,t+1}]=\beta_{i,t}E_t[r_{m,t+1}-r_{f,t+1}]$$ where $E_t[r_{i,t+1}-r_{f,t+1}]$ is the time $t$ expectation of the time $t+1$ excess ...
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141 views

Period length and maximum data points on estimating the 5-year Beta-factor

I currently read chapter 8 Beta from Bali, Engle and Murray's book Empirical Asset Pricing: The Cross Section of Stock Returns and do not understand their estimation on the five-year Beta-factor (...
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CAPM model as a regression

The CAPM model states that the returns of a stock are- $r_s=r_f+\beta (r_m-r_f)+\varepsilon_s$ The $\beta$ defined above is then calculated as $\frac{cov(r_s,r_m)}{var(r_m)}$. My question is ...
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What is the CAPM implication for Sharpe Ratios?

Suppose a world where the CAPM holds, i.e. stocks with higher beta have higher expected returns. What would be in this world the implication for Sharpe Ratios? Would stocks with higher beta also have ...
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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 CAPM a cross sectional or time series model?

Given that CAPM is an equilibrium model, it prices the assets in absolute terms. Asset pricing studies use CAPM/ICAPM/CCAPM in a cross-sectional framework i.e. stocks with higher betas will have ...
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125 views

Finding a minimum variance portfolio when using a regulariser?

I am aware that the minimum variance portfolio of a market with $n$ securities can be shown to be: \begin{equation} w^* = (1^T_n\Sigma^{-1}1_n)^{-1}\Sigma^{-1}1_n, \\ s.t. \ \ 1^T_nw = 1 \end{...
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110 views

Can Black-Litterman-type expected return estimation be used for regional ETFs?

The Black-Litterman approach to return estimation overcomes the problems associated with estimating expected returns via historical averages by determining the equilibrium returns implied by the ...
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138 views

Risk Compensation

I try to understand the different ways to compensate for risk. In the CAPM, when we plot the excess return against the risk, we find that portfolios of interest lie on the efficient frontier (i.e. ...
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144 views

How do you interpret a positive portfolio weight (when using CAPM and CML to calculate efficient portfolios)

I am asked to solve the following homework question: Risk free rate: 2% Expected excess return on market portfolio: 8% Standard deviation of market portfolio: 20% The efficient portfolio has the ...
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121 views

Understanding Fama/Frenchs' Five Factors - Returns or Excess Returns?

two short questions: If I download the five factor data from Kenneth French's website (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html) and for example calculate the average ...
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40 views

Should the valuation decision of the following question be undervalued or overvalued?

The official solution to this question is B, but I don't understand that if the recommendation is given by the CAPM model, then the CAPM estimated return should be regarded as "fair" and benchmark for ...
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433 views

Beta in foreign exchange market

Would it make sense to use a regression to calculate beta for returns on a foreign exchange currency (regressed on a market average of all currencies)? Would the beta make sense? (why/why not) ...
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269 views

How high can Beta be in CAPM?

I recently got an interview question for a junior analyst role asking if risk could be infinite in CAPM, and I wasn't sure how to answer it. I don't see how an asset could be infinitely more volatile ...