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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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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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\% &...
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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}^...
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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 ...
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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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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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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 ...
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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
...
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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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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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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:
$$
E(R_{i})-...
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Using CAPM to find the price of an option
I was reading a textbook about finding the price of an option on a one-period binomial model.
The textbook way of doing it is to replicate the option with cash and stock for $t=T$, and then calculate ...
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Non-stationarity and repricing as a source of idiosyncratic and systematic "risk"?
1.Assuming a one period economy with two assets in which cash flows are assigned certain probabilities, using the CAPM, we can derive the P0 given the E(CF) at t1. Within this distribution, we have ...
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In traditional asset pricing and valuation, why does the cost of equity increase with the AMOUNT of leverage but not with DEFAULT RISK? [closed]
When a firm's default risk increases, the cost of debt obviously rises, which increases the WACC and decreases firm value. However, what happens to the cost of equity in this case? Has the proportion ...
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Roll Critique - CAPM and mean variance tautology?
Wikipedia introduces the Roll Critique mean-variance tautology:
Any mean-variance efficient portfolio $R_p$ satisfies the CAPM equation exactly:
$$
E(R_i) = R_f + \beta_{ip}[E(R_p) - R_f]
$$
A ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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)
$$
where $R^*_i:=R_i-r_f$ is an asset's excess return, $R^*_i:=R_m-r_f$ is the market's excess return and $\beta:...
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Is beta stable over time for individual securities?
I'm reflecting on whether historically estimated $\beta$ is a "good" estimator of future $\beta$.
Consider the problem as follows:
Let $r_1$, $r_2$, ...., $r_{36}$ be the last 36 months of ...
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Testing the CAPM: does GRS account for errors in variables (measurement error)?
Suppose we are interested in testing the CAPM using the GRS test. Consider $N$ assets observed for $T$ time periods. Using the notation of Cochrane "Asset Pricing" (2005), the GRS test ...
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GMM estimation of the CAPM: why not include sample mean of the market excess return as a moment?
I am trying to wrap my head around GMM estimation of a single factor model such as the CAPM. I started by asking How come the cross-sectional CAPM equation produces $N$ moment conditions (not $1$)? ...
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How come the cross-sectional CAPM equation produces $N$ moment conditions (not $1$)?
Reading Cochrane "Asset Pricing" (2005) section 12.2 (p. 241), I got lost in the derivation of the GMM estimator for the single-factor model. Equation $(12.23)$ says the moments are
$$
g_T(b)...
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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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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 ...
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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 ...
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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+\...
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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 ...
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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 ...
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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 ...
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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 ...
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How does a mispricing affect CAPM/MPT statistical parameters?
In the CAPM/MPT context, would a mispricing affect the various statistical parameters? For instance, if Alpha is 2% and the CAPM E(R) is 10% (in equilibrium) and the E(Ra) = 12%, when calculating all ...
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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 ...
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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 ...
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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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Derive the Probability of Default (PD) of private companies with Merton Model
Do you know a well used method how to calculate the PD of private companies using the Merton Model.
The main challenges I am facing is to get the appropriate volatility of the assets and the drift.
...
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Relation between CAPM and efficient market hypothesis [closed]
I am coming from a machine learning/time series forecasting background and are currently studying Asset Pricing.
I have a good understanding of what Markowitz Mean-Variance Optimization (MVO) does, ...
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Is CAPM + additions actually used in industry-level portfolio optimization? [closed]
I've been wondering how do institutional investors actually perform portfolio optimization, i.e., do the traditional methods work when combined together with superior data collections and quality, and ...
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Cross section of expected returns vs cross section of returns [closed]
Typically, one estimates the CAPM beta of stock $i$ of a time series regression of stock excess returns $R_t$ on the market excess return $MRP$:
$R_{t} = \alpha + \beta MRP_t + \epsilon_t$,
where $t$ ...
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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 ...
