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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13
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1answer
484 views

Is Arithmetic Return Bias Basis of Low Vol Anomaly?

An observation in capital markets is that the connection between return and risk (measured as volatility) is not that straightforward (at least not as modern portfolio theory assumes). One interesting ...
12
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1answer
811 views

Estimate Beta of CAPM from Implied Volatility?

In the CAPM theory Beta of asset $i$ are estimated in this way: $ \beta_i = \frac{\sigma_{im}}{\sigma^2_m} $ where $\sigma_{im} = \rho_{im} \sigma_i \sigma_m$ But all these data are historical data. ...
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3answers
11k views

CAPM - Beta of zero and its implications on diversification

I don't know if this is the right forum in which to ask this question, but here goes. I'm working through Luenberger's Investment Science. The form of CAPM model given in the book is $$\bar{r}_i - ...
9
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1answer
6k views

How to test the 5 Factor CAPM of Fama & French (2014)?

I would like to conduct a study testing the 5 factor CAPM, using UK stocks. Does anyone have any suggestions of how I can do this? Could this task be as simple as regressing average returns for a ...
9
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2answers
477 views

How well does CAPM beta track the risk of a particular market relative to world markets?

Can the CAPM beta of emerging markets be less than the beta of the developed markets? As part of my research, I run regressions using market indices. I estimate the beta using a regression of MSCI ...
8
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2answers
777 views

Philosophical Question about Factor Models

This might be a dumb question, but on a purely understanding level it is hard for me to wrap my head around the basic interpretation of some factor models. With the CAPM the interpretation of the $\...
8
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5answers
4k views

Under the CAPM, how do I deal with market returns being below the risk-free rate?

Let's say I'm using CAPM to estimate the cost of equity, so I need expected market returns for the calculations. The standard approach is simply to compute arithmetic mean of an index (or rather its ...
8
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3answers
435 views

CAPM, DCF, and Jensen's inequality

One way to value a cashflow is to first calculate the expected return from CAPM, and then use the expected return to discount the future cashflows. The problem here is that the expected return from ...
7
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1answer
288 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 ...
7
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3answers
766 views

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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1answer
127 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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2answers
885 views

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 ...
7
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1answer
389 views

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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5answers
1k views

Is CAPM a failure?

CAPM says that in order to generate high returns I need to take more systemic risk. But the ex-post results do not seem to validate this theory. There is a ETF SPHB - PowerShares S&P 500 High ...
6
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5answers
2k views

Intuition behind Fama-French factors

In the Fama-French 3-factor model the portfolio returns are explained by the market the SMB factor (Small [market capitalization] Minus Big) and the HML factor (High [book-to-market ratio] Minus Low)...
6
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1answer
508 views

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 ...
6
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1answer
139 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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1answer
1k views

Calculating alpha and its meaning

According to wikipedia, CAPM model is described by: $E(R_{i})=R_{f}+\beta _{{i}}(E(R_{m})-R_{f})$ And according to website such as http://investexcel.net/jensens-alpha-excel/, $\alpha = E(R_{i}) - ...
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3answers
282 views

How to apply the CAPM to 6 stocks from different markets?

I would like to apply the capital asset pricing model (CAPM) for selecting proportions of 6 different stocks. In introductory books, the CAPM model assumes that there is one market index (e.g. the S&...
5
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1answer
1k views

How to use factor models for prediction?

I was looking at this thread here, reading about how to run regressions and thereby construct factor models. Assuming these factor models are properly specified, I am trying to better understand how ...
5
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1answer
348 views

Average beta of index consitutents w.r.t. the index is 0.60

I have 1 year time series data of 300 constituents of the Australian All Ordinaries index (which is composed of 491 firms). The missing firms are mostly smaller firms. I run the market model $R_{it} =...
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3answers
2k views

Why are investors risk-averse?

In CAPM, we assume people are risk-averse and people get compensated for the systematic risk they suffer. The assumption that most people are risk-averse makes sense, but why are the rational ...
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11k views

What are the implication of a negative risk-free rate on SML?

What happens to the Security market line (within the CAPM model) when the risk-free rate turns negative?
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13k views

Difference between CAPM and single index model

which is the difference betwee a model like CAPM and a single index model? Is the first a special case of the second? Best
4
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1answer
140 views

Correlation -1 and standard deviation [closed]

My book says that for a portfolio of two stocks: $\sigma_p = \sqrt{w_A^2 \sigma_A^2 + (1-w_A)^2 \sigma_B^2 + 2 w_A (1 - w_A) \rho_{AB} \sigma_A \sigma_B}$ Elsewhere it says that if the correlation ...
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2answers
827 views

What are the assumptions in the first-stage of Fama-MacBeth (1973)?

According to the CAPM, the expected return of asset $i$ is: $E(Z_i) = \beta_{im} E(Z_m)$ where $Z_m$ is the excess return on the market portfolio, and $Z_i$ is the excess return of asset $i$ over ...
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1answer
194 views

Fit linear model to higher moments of CAPM

How can one fit a linear model to the higher moments of CAPM in R? Fitting a linear model to the second moment (classical CAPM) would be ...
4
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2answers
1k views

“Risk” Factor vs Double Sorts

With regards to a cross-sectional asset pricing (stocks) study, I am testing if one variable can explain another. One common approach to do this, is to use the double-sorting portfolio technique (sort ...
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597 views

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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2answers
1k views

Does Fama French Three Factor Model Work out of Sample (after 1993)?

Does anyone know if the Fama-French three factor model has been re-examined empirically after 1993, when the original paper was first published? I am asking because there seems to be considerable ...
3
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1answer
357 views

Mathematical Derivation of Residual Risk

I understand the difference between Excess, Residual and Active Returns. I also understand what Active Risk; defined as: $\sigma_{r_P-r_B}$ (i.e. standard deviation of the difference in returns ...
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1answer
146 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. ...
3
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1answer
274 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 ...
3
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1answer
213 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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3answers
218 views

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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3answers
35k views

How to calculate unlevered beta

I have derived a firm's cost of equity using the WACC formula (see here), which means that the cost of equity has factored in the firms' debt (i.e. levered beta) and now I need to calculate the firm's ...
3
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1answer
111 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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1answer
113 views

How consequential are violations of the efficient diversification assumption of asset pricing models?

When using asset pricing models such as the CAPM or the Fama-French four factor model to determine the risk-adjusted return of a portfolio, does this strictly require efficient diversification of the ...
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3answers
456 views

Validity of CAPM

I came across some literature regarding "Framing Theory" or "Prospect Theory", and the validity of CAPM. I was wondering if you could shed some light on a few questions I have in this regard: ...
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2answers
858 views

Beta arbitrage in CAPM

i'm following the "Computational Investing 1" course at Coursera.org, I was affascinated by the Beta arbitrage of CAPM Video: https://class.coursera.org/compinvesting1-002/lecture/view?lecture_id=119 ...
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1answer
2k views

How to estimate market integration parameter in Singer-Terhaar model for E(r)?

Singer-Terhaar is part of CFA II and III curriculum. It estimates risk premium for some asset, traded at some local market, as weighted average of expected premiums for the case of (1) local market, ...
3
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1answer
635 views

Unsystematic and systematic risk of a portfolio

I have 8 country stock indexes and 1 world stock index. I do not actually have time series data but I'm given the following data: $\mu$, the vector of expected future returns for all 8 country ...
3
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1answer
95 views

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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2answers
506 views

Does CAPM hold for markets with two risky assets?

Presentations of the CAPM often include statements similar to this: While idiosyncratic risk can be "diversified away", systematic risk cannot, which is also expressed in the CAPM, which states ...
3
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1answer
649 views

Using cointegration to prove that a long-short strategy is market neutral (in CAPM sense)

I am trying to prove that a long-short strategy invested according to the cointegrated relationship from Engle-Granger's. So essentially I'm trying to show that the return $r_{XY}$ of the portfolio (X ...
3
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3answers
589 views

Why is the CAPM securities market line straight?

Let $\gamma$ be the expected return, in terms of its exponential growth rate, of the market asset. If we set $\gamma=\mu-\sigma^2/2$ as explained by the Doléans-Dade exponential, then the expected ...
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0answers
70 views

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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0answers
40 views

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?
3
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1answer
296 views

Beta and the Assumption of IID Returns

For two stocks that are independent and identically distributed (iid), do they have the same beta? Does the number of data points matter?
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2answers
233 views

How much capital to allocate between two trading strategies given average daily P&L and their Sharpe Ratios?

Let's say you have two trading strategies and all you're given is information about their average daily P&L and the Sharpe ratio of each strategy. Trading strategy A's daily average P&L is 10,...