Questions tagged [asset-pricing]
The asset-pricing tag has no usage guidance.
358
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How did the author work this out for CAPM and Utility?
Edit:The book is "Foreign Exchange: Practical Asset Pricing and Macroeconomic Theory" by Adam S Iqbal.
I asked a question relating to these equations a month ago at CAPM and Marginal Utility:...
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Complete market price and incomplete market price specification
We know that if a liquid market of an asset exists, then the standard derivative pricing theorem implies an equivalent martingale measure exists, not necessarily unique, under which the discounted ...
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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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2
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108
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Different risk neutral measure
I don't understand in the following example how there can be a single risk neutral measure.
The risk free asset price $B$ at time $t = 1$ is $1+R$.
An other asset $S$ at time $t=1$ can take two values:...
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2
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Geometric Brownian Motion as the limit of a Binomial Tree?
Consider the price of a stock whose drift and volatility parameters are $\mu, \sigma$ respectively, over the time interval $[0, t]$. Suppose we use an $n$-stage binomial tree to model the price ...
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How to mathematically model Bid and Ask as two separate processes, and combine into a Price process?
Let's say you were modeling bid and ask as two separate processes.
With their own mean and variance. And with the constraint that ask must be greater than or equal to bid.
How would you then ...
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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 ...
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How to price a buffet or, how to price a subscription? [closed]
I've been thinking about a problem that may not be so specific lately. How do we price a buffet, or how do we price a subscription service?
In more detail, let's assume that we are a cosmetics ...
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The economic interpretation of stochastic discount factor (SDF) loadings
I'm trying to use the methodology proposed in the article "Taming the Factor Zoo: A Test of New Factors" to evaluate whether some new factors can have significant explanatory power on asset ...
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Range Accrual pricing calculation
There is a discussion in https://www.investopedia.com/terms/r/rangeaccrual.asp which basically states how the CF from a Range Accrual would be determined.
I wonder if there is any standard pricing ...
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Interpreting Factor Coefficients for an Emerging Markets Fund against the Market and its Benchmark
I ran CAPM, FF3, FF5 and Carhart models for an emerging markets fund against the FF data for emerging markets and against its own benchmark. I am constantly getting negative SMB's which shows relevant ...
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Asset pricing based on stochastic inflation discounting (inflation controlled by stochastic state variable)
Suppose there is an asset that pays fixed nominal payout $\delta_t = \delta$, with a constant real discount rate $\bar{r}$ and stochastic inflation $\pi_t$. Suppose the price follows a controlled ...
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103
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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:
$$
...
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Construct DeFi yield curve
I was wondering if anyone knows how to construct a yield curve for cryptocurrencies (for yTokens like yDAI and yETH for example). It'd be best if yield curves could be dynamic (though I think it could ...
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Measurement of asset quality
In the context of liquidity risk management in a commercial bank, what are the industry best practices to measure the quality of assets? Is it a percentage between 0 and 100, where the higher the ...
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What exactly is the 'continuous asset price model'?
I am reading An Introduction to Financial Option Valuation by Higham. In Chapter 6, the book covers two asset price models, a discrete one and a continuous one. In Section 6.3 (Continuous asset model) ...
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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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IDE to use for Python for Quant Trading [closed]
Dear Quantitative Finance Stack Community,
Since many Quantitative propietary trading firms seem to be using Python over alternatives such as STATA. I have now decided to get myself familiar with ...
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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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Stochastic representation of a zero-coupon bond
In Chapter 9 of Shreve's book Stochastic Calculus for Finance II, the main theorem is the 9.2.1.
Defining the discounting process $D(t)=\mathrm{e}^{-\int_0^t du r(u)}$ and $r(u)$ the, possibly ...
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Alphas vs. portfolio rank w.r.t. factors in Fama-French 3-factor model
In the Fama-French 3-factor model, is there a point in looking at the relationship between the estimated alphas for the 25 test portfolios and the size-rank or value-rank of these portfolios?
Also, ...
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Error (singularity) in the GRS test applied on portfolios that were used for constructing the Fama-French factors
In the context of the Fama-French 3-factor model, we have six portfolios used for creating the SMB and HML factors: SL, SM, SH, BL, BM, BH. (The notation is: S~small, B~big, L~low, M~medium, H~high). ...
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Why should investors be compensated for accepting systematic risk? [closed]
Investors should be compensated for accepting systematic risk, as it cannot be diversified.
Why do the investors need to be compensated for accepting systematic risk? Because no one can avoid it and ...
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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 ...
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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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Understanding completeness in this simple one-period exercise
Let's consider a one period model (t=0, 1) with one risk-free asset that yields r, and one risky asset. $S_t^j$ will be the value of the asset j=0,1 at time t=0,1, where j=0 is the risk-free asset and ...
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Fama-MacBeth regressions to predict stock returns; confusion on which steps to use
When following Lewellen (2015) (open access here), I am confused as to whether I need to estimate any lambdas. As I already have values for lagged firm characteristics such as ROA and accruals etc. ...
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FM regressions for size groups when examining a cross section of expected stock returns
When doing FM regressions for size groups similar to Lewellen (2015) (open access here), should I obtain the cross sectional rolling return window betas using only the size group? (E.g only use large ...
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Testing one asset pricing model against another a la Cochrane via change in $\hat\alpha' \text{cov}(\hat\alpha,\hat\alpha')^{-1}\hat\alpha$
I am reading section section 14.6 of John Cochrane's lectures notes for the course Business 35150 Advanced Investments. On p. 239-240, he discusses testing one asset pricing model against another. ...
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Scaling variables (Fraction vs % vs log) when regressing twelve month returns
Dear Stack community,
My question is the following;
If my dependent variable is twelve month returns.
And as independent variables I have fiscal year variables like ROA and log variables like the log ...
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Testing one asset pricing model against another a la Cochrane: why this works
I am reading section section 14.6 of John Cochrane's lectures notes for the course Business 35150 Advanced Investments. On p. 239-240, he discusses testing one asset pricing model against another. I ...
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1
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Does including an additional pricing factor necessarily reduce the pricing errors?
I am reading section section 14.6 of John Cochrane's lectures notes for the course Business 35150 Advanced Investments. On p. 239-240, he discusses testing one asset pricing model against another.
...
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1
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Testing one asset pricing model against another a la Cochrane: a counterexample
I am reading section section 14.6 of John Cochrane's lectures notes for the course Business 35150 Advanced Investments. On p. 239-240, he discusses testing one asset pricing model against another. I ...
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Power-utility function for calculating Certainty equivalent
I have a question regarding how i should calculate 3.2-3.4, currently studying for an exam. What i don't get is how to acctually derive the certainty equivalent from the expected utility of gross ...
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2
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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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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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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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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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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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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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How to get a Certain Consumption Equivalent using Epstein-Zin preferences?
In many asset pricing models we use CRRA preferences and Epstein-Zin preferences.
Let's say I have an agent that lives $T$ periods with CRRA preferences:
$$ V_0 = \sum_{t=0}^{T} \beta^t \frac{C_t^{1-\...
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Complete market without risk-neutral measure
Let $\mathcal{M}$ be a one-period model with
$\Omega=\{\omega_1,\omega_2\}$ and $S_t^0=1$ for $t=0,1$.
Find a $D$ such that $S^d$, $d=1,...,D$ yields a complete market
without a risk-neutral measure. ...
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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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How to calculate the discount rate from yield when adequate price data does not exist [closed]
I'm creating a pricing model for an asset that is similar to a bond, for which I need a discount rate. Using yield to calculate this discount rate was my first thought, but this seems impossible for ...
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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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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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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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Why not use a time series regression when the factor is not a return?
I am trying to wrap my head around the statement that time series regression should not be used for testing a factor model when the factor is not a return. This has been mentioned in multiple posts, ...
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