Questions tagged [asset-pricing]
The asset-pricing tag has no usage guidance.
126
questions with no upvoted or accepted answers
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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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124
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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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2k
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Newey-West standard errors in Fama-MacBeth regressions
I noticed that during the recent decade most of papers, which use Fama-MacBeth regressions compute Newey-West standard errors. I tried to find detailed description of this procedure in the books on ...
6
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373
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What are the essential characteristics of asset prices?
I think the question has already been asked about stylized facts of asset returns; this question regards the essential characteristics and normative assumptions used to evaluate asset prices. I.e., ...
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487
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GMM time-series regression factor model with factors that are not returns
Factor models with factors that are not returns are usually estimated and tested by cross-sectional regressions. However, there is a way to use time-series regression to estimate and test the model. ...
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282
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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:
$$
E(R_{i})-...
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674
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CRSP: Return including dividends
Using CRSP data, I tried to compute the historical returns (including dividends) of stocks according to
Total Return = (adjprc + (divamt / cumfacpr / facpr)) / prev_adjprc – 1,
where divamt is the ...
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5
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318
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ERP and FF 3-factor model
In a more conservative estimate than a simple historical average, Fama & French estimate (US) equity risk premium at 3-4% (e.g., Equity Risk Premium, JF, 2002).
This suggests that in an APT-like ...
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4
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257
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Principal Portfolios Prediction Matrix estimation (Bryan Kelly)
I have recently discovered Bryan Kelly's paper on Principal Portfolios (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3623983) and had some doubts about the prediction matrix $\Pi$. He defines $\...
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Some basic questions using consumption CAPM
Say we are in a world described by the consumption CAPM. All investors in this world have quadratic utility. Also, assume that consumption is as follows:
$$c_{t+1} = (1+m_t)c_t + s_t c_t e_{t+1} $$
...
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74
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Is Consumption CAPM a special case of Intertemporal CAPM?
Intertemporal CAPM state variables are related to the future investment opportunity set. In Consumption CAPM the state variable is consumption ? Is it the correct way to think about it?
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3k
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Creating Factor mimicking portfolio returns
I have some trouble understanding how to create factor mimicking portfolio returns. As pointed out in this question, Tsay provides a small description, but I am unsure if my procedure is correct. In ...
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333
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Arrow-Debreu Equilibrium Pricing
I have this problem in asset pricing that I don't know how to solve. Here it is:
Consider an economy with a complete set of Securities and $N$ states of the world Tomorrow. Assume that there are two ...
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100
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Budget Constraint in Duffie's book
On Page 5 of Duffie's Dynamic Asset Pricing Theory, the budget-feasible set is defined as:
$$X(q,e) = {e+D^T\theta \in R_+^s:\theta \in R^N, q\theta \leq 0}$$
Compared to Kerry Back's presentation of ...
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3
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193
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Option-like behaviour of momentum strategy
this may come as rather vague question, since I do not have something very exact issue on my mind. Nevertheless, I think this is an interesting question and must have been thought by some other people ...
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Understanding the Intersection of "Advances in Financial Machine Learning" and "Asset Pricing in Stock Market Prediction"
I have been reading "Advances in Financial Machine Learning" by Marcos Lopez de Prado and "Machine Learning in Asset Pricing" by Stefan Nagel, and I noticed that there seems to be ...
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1
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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 ...
- 3,166
3
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Arbitrage Opportunities in a Two-Zero Coupon Bond Market
Question:
Suppose we are in a market where there are only two zero coupon bonds, both with a face value of 100: the first one with a maturity of one year and a price of 90, and the second one with a ...
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3
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1
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Question about the footnote in page 33 of the Asset Pricing and Portfolio Choice Theory by Kerry E. Back
The following question is from Kerry E. Back's textbook, and I struggle with it many days, but I wonder this question could be trivial for expertises. If anyone can help, I will really apreciate it!
...
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530
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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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3
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137
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Manual Computation of Python QuantLib's NPV for Pricing of a Forward Rate Agreement
Following the question that I have asked on this link and response obtained, I have managed to price a 3x6 FRA using QuantLib Python, using the following codes:
...
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3
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75
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Fama and French HML and SMB factors
I am investigating the Fama and French model using a Bayesian selection procedure laid out by Barillas and Shanken (2018). When I plot the cumulative probabilities of each factor, I notice that for ...
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2
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61
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CAPM and Marginal Utility: How does this derivation work?
I came across this obstacle in the book Foreign Exchange: Practical Asset Pricing and Macroeconomic Theory by Adam.S.Iqbal(I have attached screenshots below)
For 1.40 the author claims that we must ...
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89
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Stambaugh inference for Investment Analysis when History Lengths Differ
This pertains to Stambaugh in the JFE (vol. 45, 1997 pp 285-331), and I have a question about Proposition 1 results (page 292). (link)
To set the background, let's take the smallest relevant ...
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35
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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 ...
- 3,166
2
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107
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French and Fama - Alpha vs Residuals (Error)
When running a regression to empirically test models like CAPM or the Fama and French Model, why do we test the statistical significance of the intercept? Do we ignore the residual error?
Why not ...
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362
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Counterexample for the Second fundamental theorem of Asset Pricing
so the The Second Fundamental Theorem of Asset Pricing says:
An arbitrage-free market (S,B) consisting of a collection of stocks S and a risk-free bond B is complete if and only if there exists a ...
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2
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62
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Benchmark Model for Path-Dependant Monte Carlo Simulations?
As part of my research for my masters thesis, I'm testing out the effectiveness of some different models in Monte Carlo simulations for path dependant options.
I will be attempting a model-free ...
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46
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Pricing equation with two correlated states
Consider the following asset pricing setting for a perpetual defaultable coupon bond with price $P(V,c)$, where $V$ is the value of the underlying asset and $c$ is a poisson payment that occurs with ...
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2
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129
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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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2
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507
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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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205
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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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J-stat question on Linear Factor Models + Simulation, Wald test
I am exploring the wonderful library by K. Sheppard et al. on linear models applied to asset pricing. In particular, Fama Macbeth and two-step regression (leaving GMM for later)
My question is ...
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Pricing kernel representation
I am reading this paper https://mpra.ub.uni-muenchen.de/4969/1/MPRA_paper_4969.pdf pp.6-7 on discrete-time bond pricing. The model adopted is a a common affine model,
the short rate follows
\begin{...
- 21
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353
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Alpha - Time Series vs Cross Section Approach
I am currently reading Cochranes book on asset pricing. However, I get confused about one thing. He says that one could test a factor model (I will use the CAPM, just as he does), via a time series ...
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linear stochastic discount factor
I have heard some people say something like the following with regards to APT:
Let returns be given by the factor model
$r_t = B_tf_t + e$
with
$E(f_t) = \lambda_t$
Assume that factors are ...
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290
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Stocks with same volatility but different drifts
In the book Quant Job Interview Questions & Answers, in section 2, question 2.4 says suppose two assets in a Black-Scholes world have the same volatility but different drifts. How will the price ...
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86
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Applying GRS-test on non-normal residuals with autocorrelation
Is it valid to apply GRS-test (Gibbons, Ross and Shanken 1989) on non-normal and autocorrelated residuals?
I got residuals using 10 test-assets regressed on 3-factor and carhart.
If it is valid, how ...
2
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0
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204
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Fama Macbeth and Momentum factor
I am working on a Fama MacBeth regression with excess returns on the LHS and Size, Value an Momentum factors on the RHS. In literature, the Momentum factor is often definded as the cumulative past 6 ...
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735
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Volatility Managed 6 Factor Model (Fama French) - Does it make sense?
after weeks of intense research and in spite of the current situation, I decided to ask the following question to some experts (you):
I would like to develop/investigate a volatility managed six ...
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To price Municipal Bonds and risks I want to know the percent of unfunded pension liabilities ($3.8T) to total state and local gov liabilities
Unfunded pension liabilities keep growing and this seems alarming to both pension holders but also Municipal Bond holders.
I would like to know how large this problem is to better price Munis and ...
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48
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Cointegration between prices and dividends. How do I get the following expression?
Actually, I have two questions:
1.
Let us assume that expected returns are constant. Then, we have the following expression for how the prices should be determined, provided that the operators are ...
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105
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Asset pricing and dividend discount model
I want to derive the dividend discount model from the asset pricing formula described in "Efficient Capital Markets: A Review of Theory and Empirical Work" by Eugene Fama 1970. The formula that I am ...
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Creating a hedge portfolio out of 10 assets
Suppose I have historical return data on 10 assets. How can I create a hedge portfolio that prices all these assets in a factor model?
I have chosen 3 factors: excess market return, SMB and HML from ...
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322
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Prove unique arbitrage-free price implies attainable
I just read a Corollary in a finance course note:
Suppose the market is arbitrage free and $C$ is a contingent claim. Then $C$ is attainable if and only if it admits a unique arbitrage-free price.
...
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J-test and Empirical Model Performance of Conditional and Unconditional Estimations (as for example in Cochrane (1996))
Take for example the Consumption-based model with a power utility function estimated by Cochrane in his paper "A Cross-Sectional Test of an Investment-Based Asset Pricing Model" (1996). The following ...
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why many option contract price less than minimum boundary price?
I downloaded data from NSE(National Stock Exchange) website regarding closing price of European Call Option written on Index.
From standard textbook, I read that option contract must satisfy
$C(t) \...
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2
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278
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Pricing options under a specific framework
I have a specific framework in mind and I would like to value options under this framework. I am not sure whether a closed form solution exists or Monte Carlo methods would work.
The framework I have ...
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Terminal wealth in multiperiod asset pricing?
I am studying an asset pricing problem and I am having a tough time using finite horizon because I cannot properly define the terminal wealth.
I consider agents with exponential utility, who can ...
1
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0
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72
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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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