Questions tagged [asset-pricing]
The asset-pricing tag has no usage guidance.
299
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Profitability and Investment factors of Fama French [closed]
I have empirically tested CAPM, three factor model of Fama French (1993), four factor model of Carhart (1997) and five factor model of Fama French (2015) in India. I found that three factor model ...
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Difference between Trader Behavior and Analysis/Inference
In the academic literature - often "momentum" and "positive feedback" traders are used interchangeably. Like "Most researchers have found that institutional investors are ...
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Testing predictability of a proposed predictor in case of multiple returns
Say I have a T daily observations for the last ten years on a new predictor $x_t$ which I think is a predictor of the expected weekly return on the stock market, $r_{t,t+5} = r_{t+1}+...+r_{t+5}$, ...
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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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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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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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Does Black-Scholes imply that the expected return for an asset is fixed as the volatility increases? [closed]
I'm new to this, and just trying to understand what options prices imply about asset growth. I'm looking at the following expression for the underlying asset price in the Black-Scholes model, in ...
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Forward pricing of cashflows with QuantLib - Python
I am building a tool with Quantlib (Python) to work on the forward pricing of different types of assets (inflation linked, amortizing, vanilla, zero coupon bonds).
For a number of reasons I am 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 (Pt - Pt-1)/Pt-1. Investors plan at t-1 and get a payoff at t.
After this period, the same mechanics ...
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Methods for Constructing Mimicking Portfolios for Observable Factors
I've created some macroeconomic factors (e.g. analogs of real GDP growth) that I believe have explanatory power for asset returns. By a factor here, I mean a stationary time-series of real numbers.
I'...
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How do I interpret my Fama-French and Carhart factor coefficients?
I am required to prepare a portfolio containing 10 companies and analyse their returns over 10 years utilising the Fama-French 3 factor and Carhart 4 factor models. I chose the largest market cap ...
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intercepts in spanning regression
what does a negative and a positive intercept imply in spanning regression or factor redundancy test? For example, value factor is regressed on the mkt, smb, rmw, and cma and the intercept is negative ...
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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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Existence of an upper bound for risk-factor betas/coefficients
Theory:
Based on Hansen/Jagannathan, the set of means and variances of returns is limited. With $R^f$ as the risk-free rate, $R_i^e$ as the return of stock $i$ in excess of $R^f$ and a stochastic ...
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Expected vs required return in valuation
This is a rather simple question, so this is maybe not the right place, but...
I have done quite a bit of reading on predicting asset returns, i.e. determining return expectations. I have now started ...
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Understanding the asset pricing theory and numeraire
While reading about asset pricing theory and numeraire, I had faced some confusion.
Short summary of asset pricing theory from my book
We start our journey with a risky asset $S_t=\mu S_tdt+\sigma ...
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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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Existence of limit of expected discounted stochastic function
Consider a smooth function that satisfies the following ODE:
$$R P(V) = c + V \mu P'(V) + V^2 P''(V)$$
where $V$ is a GBM with drift $\mu$ and s.d. 1.
Does the following limit exists for $r<R$?
$$\...
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Discounted expectation of generic $\mathbb{C}^2$ function
Consider a standard geometric Brownian motion $V_t$ with drift $\mu<r$ and standard deviation $1$.
It holds that the discounted expectation is
$$E\left[\int_t^\infty e^{-r(s-t)} V_s ds | V_t \right]...
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Comparative statics on $c/r$ using fundamental asset pricing equation
Consider the fundamental asset pricing equation for a perpetual coupon bond:
$$rP = c + \mu P' + \sigma^2/2 P''$$
with standard boundary conditions $P(\bar x) = \bar x$ and $\underset{x\rightarrow \...
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Definition of continuously compounded yield for perpetual defaultable coupon bond
In continuous-time asset pricing, the price of a defaultable perpetual coupon bond is given by
$$P(V) = \frac{c}{r}\left[ 1- \left(\frac{V}{V_b}\right)^{-\gamma}\right] + (1-\alpha)V_b \left(\frac{V}{...
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Fama Macbeth regression results [closed]
I am doing the Fama Macbeth regression analysis for finding the relation between Idiosyncratic volatility and Expected stock return. Stock return is dependent variable and independent variables are: ...
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How to interpret the results of Fama-MacBeth regressions? [closed]
I recently conducted a project for university, where I calculated the risk factors of the Fama-French 3Factor Model. For "SMB", the "size-premium", I get a negative result. What ...
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Beta anomaly (t statistics)
I would like to analyze the beta anomaly following the method used in the following paper "The low-risk anomaly: A decomposition into micro and macro effects" by (Baker et al, 2018). (the ...
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Liquidity Rebate
I have one question regarding the liquidity rebate that liquidity providers receive. I've read on investopedia that it refers to the traders/investors who place limit orders since they then "...
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Cross Sectional vs. Time-Series Risk Premia Estimate
Consider the single factor model in time series form, e.g:
$$
r_t^i = \alpha_i + \beta^i f_t +\epsilon^i_t \quad (1)
$$
Here $i$ is not an exponent but a superscript, e.g. it represents the return ...
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Optimal consumption process [Munk (2011)]
I'm trying to solve problem 4.4 in Munk (2011). The problem is as follows:
Assume the market is complete and $\xi = (\xi_{t})$ is the unique state-price deflator.
Present value of any consumption ...
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Dynamics of discounted prices (multi-dimensional)
My objective is to find the dynamics of the discounted prices, given by $\mathbf{y}_{t} = \mathbf{P}_{t}\mathrm{e}^{-\int^{t}_{0} r_{s} ds}$. I know the dynamics should be $d\mathbf{y}_{t} = \mathrm{...
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Special Exotic Option Pricing Approach [closed]
I am currently stuck with the following problem:
You need to price the following exotic option, where the share price of Stock ABC is the underlying:
• Time to maturity: 2 years
• Right to exercise: ...
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Why is there a lot of focus on derivatives pricing and much less on stock pricing?
I am a quantitative finance student, and during the first year of this Master’s Degree I couldn’t help but notice that there’s a lot of focus on derivatives pricing and little or none on stock pricing....
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Most complete list of investment mistakes in stock markets
I'm looking for a (hopefully exhaustive or at least extensive) list of behavioral biases that are currently observable in the stock market. I'm well aware and replicated some of the evergreens such as ...
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how to merge these two crsp data sets
I'm not totally confident on how to merge these two monthly CRSP data sets. As I write this, it comes from two databases: crsp.mse and ...
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Is the market price of an asset always lower than the expected discounted value under the REAL WORLD measure?
The risk neutral measure is often said to reflect the risk aversion of investors. So intuitively, I would think that an asset's expected discounted value should be lower under the risk neutral measure ...
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Value of trading strategy
A trading strategy is defined as follows: starting capital $v_0 = 5$ and 1 risky asset holdings $\varphi_t = 3W_t^2-3t$ where $W$ is a Wiener process.
The problem is to find the probability of the ...
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Epstein-Zin utility intuition
I working a lot with Epstein-Zin utility (standard in asset pricing models). But I am having some issues wrapping my head around some intuition for how this utility function works.
Let's think about a ...
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Fama MacBeth regression standard errors: sampling variations in the first stage
Following the notation of this post, the standard errors of the second stage coefficients is computed as $$\sigma^{2}(\hat{\lambda})=\frac{1}{T^{2}} \sum_{t=1}^{T}\left(\hat{\lambda}_{t}-\hat{\lambda}\...
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Hybrid Derivatives Modelling
Could you please recommend any good books and papers that thoroughly describe the pricing and modelling of Hybrid derivatives? I.e. this question is a "big list" question, the more the ...
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Pricing of factors - portfolio sorts
if I read that someone is using portfolio sorts to determine whether a factor is priced in the cross section ( risk premium ) is it the two-pass Fama-MacBeth regression?
Is there a material that would ...
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How to determine the fair value of "off-the-run" U.S. Treasury securities
In the U.S. Treasury securities market, there are seven (7) "on-the-run" coupon-bearing issues:
2 year
3 year
5 year
7 year
10 year
20 year
30 year
I believe the Fed uses a monotone convex ...
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Replication of results shown in 'Empirical Asset Pricing: The Cross Section of Returns' by Bali, Engle, and Murray
I'm currently trying to reproduce some results shown in the book 'Empirical Asset Pricing: The Cross Section of Returns' by Bali, Engle, and Murray. More precisely, I try to compute Table 7.3 and 9.1. ...
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What are the requirements for no arbitrage to exist in a chaotic/dynamical system?
Consider the continuous dynamical system
$$\alpha\ddot{S}+\dot{S}=\mathcal{F}(S,t),$$
such that $\alpha\in\mathbb{R}$ and $\mathcal{F}$ is real and analytic. We assume that if a solution for $S$ ...
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Pricing a contract
I'm currently trying to price some different kinds of contracts. I'm stuck on this following exercise, which I can't seems to find a good solution for. The following is assumed:
We are in a standard ...
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CRSP: Return including dividends
Using CRSP data, I tried to compute the historical returns (including dividends) of stocks according to
Total Return = (adjprc + (divamt / cumfacpr / facpr)) / prev_adjprc – 1,
where divamt is the ...
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Why the Esscher transform is the right transform for pricing formula?
A Wiener process has infinitely many states of the world at any time step. Does that not mean that there are infinitely many EMM's for any model that uses the Wiener process?
But then if there is only ...
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