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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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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: $$ ...
Newbie's user avatar
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1 answer
133 views

Question about marginal risk contribution / portfolio volatility decomposition

I am trying to understand the rule where you add a new asset to a portfolio if its Sharpe ratio is greater than the product of the portfolio sharpe ratio and the correlation between the portfolio and ...
Steve R's user avatar
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1 answer
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Should I convert monthly data into yearly for CAPM?

I am trying to use the CAPM. I gathered monthly data on German government bonds and DAX40 (it's an index that contains top 40 German firm). Then based on only one company like Volkswagen monthly stock ...
Mostafa Bouzari's user avatar
1 vote
1 answer
238 views

What is the mathematical difference between Mean-Variance Optimization and CAPM?

I have spent some time going through the maths of both Mean-Variance Optimization and CAPM, and I'm trying to pin down the mathematical differences between them. For both, let $p$ be a portfolio ...
SamTheTomato's user avatar
2 votes
0 answers
31 views

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 ...
Richard Hardy's user avatar
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2 answers
144 views

Simple concepts around return, VaR, etc

In a simple setup, let's say $(w_1,w_2)$ are weights invested in assets $1$ and $2$ with prices $S_1$, $S_2$. I only saw discussions when $w_1 + w_2 = 1$, even if short selling is allowed. Suppose $...
Jo''s user avatar
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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 ...
LeFo's user avatar
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1 vote
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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 (...
Julien Maas's user avatar
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1 answer
86 views

What do the existence and parameters of an efficient investment tell you about the value of a risk-free return?

I'm working on an unassessed course problem, Consider the following risky investments \begin{matrix} \text{name} & \text{expected return} & \text{standard deviation of return} \\ A & 9\% &...
mjc's user avatar
  • 105
2 votes
2 answers
190 views

Testing as in Fama & MacBeth vs. comparing models as in Cochrane's lecture notes

Testing a model against its extension as in Fama & MacBeth (1973) Fama & MacBeth (1973) tested the CAPM against an alternative that the dependence between the expected excess return $E(r_{i,t}^...
Richard Hardy's user avatar
1 vote
1 answer
39 views

CML equation - from where does the square come from?

In his textbook Asset management Andrew Ang uses the following CML formula (chapter 6) E(rm) - rf = y * σ^2 Where y is risk aversion factor What is the source of square? When I look at CML graph there ...
Mig's user avatar
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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, ...
Richard Hardy's user avatar
3 votes
1 answer
47 views

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 ...
Richard Hardy's user avatar
5 votes
2 answers
667 views

Question about adding new investment A to portfolio B

I've found a ton of sources that mention the classic rule of "If the Sharpe ratio of the new asset is greater than the Sharpe ratio of the existing portfolio times the correlation of the existing ...
jauyjad's user avatar
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1 answer
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How does one show that the Sharpe Ratio is closely related to the t-statistic of the mean differential return?

I see it being mentioned in many places, such as here, and even here. How should I interpret it? Suppose I have an array of signals, I, and returns of those signals, R Then my regression is R = a + BI ...
Dumb chimp's user avatar
1 vote
0 answers
46 views

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 ...
Richard Hardy's user avatar
2 votes
1 answer
203 views

GRS test does not reject a nonsense factor in place 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 $630\times 26$ matrix of returns on 25 ...
Richard Hardy's user avatar
2 votes
0 answers
141 views

How to interpret the negative volatility of the single stock, after neutralizing against the index? [closed]

I am trying to find the statistical significance of the certain events on volatility, such as divided/earningsdate/M&A, etc on single stock wise compared to no events. Commonsensewise, these ...
celi's user avatar
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4 votes
1 answer
445 views

Can the PDE of Black and Scholes really be derived from the CAPM?

Black and Scholes (1973) argue that their option pricing formula can directly be derived from the CAPM. Apparently, this was the original approach through which Fischer Black derived the PDE, although ...
MMFdW's user avatar
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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 ...
Richard Hardy's user avatar
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18 views

GMM estimation of the CAPM allowing for time-varying expectation of market's excess return

With time-constant expected value of market's excess return, we can estimate the CAPM using GMM as follows. Equation $(12.23)$ in Cochrane "Asset Pricing" (2005) section 12.2 (p. 241) says ...
Richard Hardy's user avatar
0 votes
0 answers
83 views

How to set up a panel data model for estimating the CAPM?

In this question, I asked whether it is better to use clustered or GMM-based standard errors for estimating and testing asset pricing models such as the CAPM. However, I then realized that I am not ...
Richard Hardy's user avatar
3 votes
1 answer
114 views

Nominal vs. real (inflation-adjusted) prices/returns in cross-sectional asset pricing

I have the impression that asset pricing models such as the CAPM or Fama & French 3 factor model typically concern nominal rather than real (inflation-adjusted) prices/returns. If this is indeed ...
Richard Hardy's user avatar
5 votes
0 answers
267 views

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})-...
Richard Hardy's user avatar
3 votes
0 answers
108 views

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 ...
Mango's user avatar
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1 answer
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Non-stationarity and repricing as a source of idiosyncratic and systematic "risk"?

1.Assuming a one period economy with two assets in which cash flows are assigned certain probabilities, using the CAPM, we can derive the P0 given the E(CF) at t1. Within this distribution, we have ...
Leonid Konoplev's user avatar
1 vote
0 answers
34 views

In traditional asset pricing and valuation, why does the cost of equity increase with the AMOUNT of leverage but not with DEFAULT RISK? [closed]

When a firm's default risk increases, the cost of debt obviously rises, which increases the WACC and decreases firm value. However, what happens to the cost of equity in this case? Has the proportion ...
lkonoplev's user avatar
3 votes
1 answer
194 views

Roll Critique - CAPM and mean variance tautology?

Wikipedia introduces the Roll Critique mean-variance tautology: Any mean-variance efficient portfolio $R_p$ satisfies the CAPM equation exactly: $$ E(R_i) = R_f + \beta_{ip}[E(R_p) - R_f] $$ A ...
nemui's user avatar
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7 votes
2 answers
1k views

Fama-French factor model: why mimicking portfolios?

I am trying to understand the Fama-French factor model, or any kind of CAPM extensions really. What is really puzzling me is the use of mimicking portfolios. Fama and French create mimicking ...
deblue's user avatar
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0 votes
1 answer
220 views

Finding latest market price of market portfolio according to No Arbitrage

In Excel, I have the monthly stock price data for the past few years for Asset A and Asset B. I have calculated the monthly returns, mean returns, variances, and standard deviations for both stocks as ...
Red's user avatar
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1 vote
2 answers
76 views

Is there a difference between heterogeneous expectations and heterogeneous cost of capital? How are assets priced in these situations?

How are asset prices set when investors face heterogeneous expectations? Does some form of "negotiation" take place so that the market price is set? Can investors face heterogeneous costs ...
lkonoplev's user avatar
0 votes
1 answer
158 views

Error term, R-square and perfectly holding CAPM?

It is known that if the CAPM holds then the E(R) = CAPM predicted return and all securities lie on the SML. However, in each period, there is an error term that is non-zero in every single observation ...
lkonoplev's user avatar
1 vote
1 answer
53 views

Incorporating idiosyncratic risk as a pricing factor with GMM

Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing an augmented CAPM or a multifactor model with an additional factor: the ...
Richard Hardy's user avatar
0 votes
0 answers
118 views

CAPM model formula for zero cost portfolio?

Let's say I want to run a series of regressions for zero-cost portfolio Y that goes long on stocks based on high variable x and short stocks with a low variable of x. How do I run the regression, for ...
JH1's user avatar
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1 vote
1 answer
460 views

Definition and estimation of $\beta$: raw or excess returns?

The CAPM is a single-period model that says $$ \mathbb{E}(R^*_i)=\beta\mathbb{E}(R^*_m) $$ where $R^*_i:=R_i-r_f$ is an asset's excess return, $R^*_i:=R_m-r_f$ is the market's excess return and $\beta:...
Richard Hardy's user avatar
1 vote
1 answer
154 views

Is beta stable over time for individual securities?

I'm reflecting on whether historically estimated $\beta$ is a "good" estimator of future $\beta$. Consider the problem as follows: Let $r_1$, $r_2$, ...., $r_{36}$ be the last 36 months of ...
MYK's user avatar
  • 175
2 votes
1 answer
129 views

Testing the CAPM: does GRS account for errors in variables (measurement error)?

Suppose we are 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 ...
Richard Hardy's user avatar
2 votes
2 answers
184 views

GMM estimation of the CAPM: why not include sample mean of the market excess return as a moment?

I am trying to wrap my head around GMM estimation of a single factor model such as the CAPM. I started by asking How come the cross-sectional CAPM equation produces $N$ moment conditions (not $1$)? ...
Richard Hardy's user avatar
2 votes
1 answer
82 views

How come the cross-sectional CAPM equation produces $N$ moment conditions (not $1$)?

Reading Cochrane "Asset Pricing" (2005) section 12.2 (p. 241), I got lost in the derivation of the GMM estimator for the single-factor model. Equation $(12.23)$ says the moments are $$ g_T(b)...
Richard Hardy's user avatar
6 votes
0 answers
155 views

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 ...
Richard Hardy's user avatar
1 vote
2 answers
140 views

Imposing diagonality of error covariance matrix when the CAPM holds

Assuming that the CAPM holds, the total risk of an asset can be partitioned into systematic risk (associated with the market factor) and idiosyncratic risk. Idiosyncratic risk is asset specific. Does ...
Richard Hardy's user avatar
2 votes
1 answer
153 views

Why estimate the (known) market return in the cross-sectional regression of Fama-MacBeth?

Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing the CAPM. Using Fama-MacBeth style analysis, we first estimate $N$ time ...
Richard Hardy's user avatar
4 votes
1 answer
243 views

Incorporating idiosyncratic risk as a pricing factor Fama-MacBeth style

Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing the CAPM or a multifactor model. Take the CAPM: $$ r^*_{i,t}=\alpha_i+\...
Richard Hardy's user avatar
0 votes
1 answer
254 views

Market portfolio and portfolio with three risky assets

I'm trying to solve a problem with portfolios, but I cannot get to the solution. There are three risky assets A, B and C whose betas are respectively 0.6 (A), 1.5 (B) and 1.1 (C). Besides, we know ...
AVR's user avatar
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4 votes
1 answer
707 views

CAPM yields very poor fit (low R-squared). Is that normal?

I am playing around with the CAPM for a small European stock market (about 100 stocks). First, I use five years of monthly data (January 2017 to December 2021) to estimate betas for each firm using ...
Richard Hardy's user avatar
1 vote
1 answer
168 views

How do asset prices behave in a single-period and multi-period model?

When we talk about the single-period CAPM, the return in a particular period t can be defined as $(P_t - P_{t-1})/P_{t-1}$. Investors plan at t-1 and get a payoff at t. After this period, the same ...
lkonoplev's user avatar
1 vote
2 answers
161 views

Can there be different Sharpe Ratios for the same index? [closed]

I am reviewing a fellow students paper, and it is argued in this paper that the Sharpe Ratio can differ based on which model is used to analyze the portfolio returns. Here a model based on the ...
Simon Rydstedt's user avatar
0 votes
1 answer
184 views

The common interpretation that CAPM is about diversifiable and non-diversifiable risk cannot be justified by CAPM alone?

Look in any finance textbook or search about CAPM, it will say that CAPM is a model about how portfolios have systematic risk (risk that can't be diversified away) and idiosyncratic risk (risk that ...
fe2084's user avatar
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0 votes
1 answer
61 views

Two specific questions about CAPM's assumptions and implications

I have two questions about the CAPM model: the first is theoretical while the second is related to observed market data. First question: let's say we have company A and company B and we want to ...
Andrei's user avatar
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1 vote
0 answers
73 views

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) ...
Tony STRATAN's user avatar

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