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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 ...
Bumblebee's user avatar
0 votes
0 answers
57 views

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 ...
Tristan's user avatar
  • 113
1 vote
0 answers
24 views

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 ...
Ignacio Canabal's user avatar
-1 votes
1 answer
73 views

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 ...
Allonsy Jia's user avatar
3 votes
1 answer
77 views

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 ...
Pima's user avatar
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0 votes
0 answers
36 views

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 ...
Bogaso's user avatar
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0 answers
28 views

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 ...
Gugu's user avatar
  • 1
0 votes
0 answers
51 views

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 ...
my name's user avatar
1 vote
1 answer
99 views

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
  • 13
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0 answers
20 views

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 ...
Jenn Gunawan's user avatar
0 votes
0 answers
32 views

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 ...
ps0604's user avatar
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0 answers
42 views

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) ...
herbhofsterd's user avatar
2 votes
0 answers
88 views

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 ...
Woodpecker's user avatar
2 votes
0 answers
333 views

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 ...
Julien Maas's user avatar
3 votes
0 answers
176 views

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 ...
blizzard16's user avatar
0 votes
1 answer
141 views

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 ...
apelle's user avatar
  • 3
0 votes
0 answers
34 views

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, ...
Richard Hardy's user avatar
0 votes
0 answers
13 views

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). ...
Richard Hardy's user avatar
0 votes
1 answer
95 views

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 ...
Boodombie's user avatar
2 votes
0 answers
34 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
1 vote
0 answers
70 views

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
0 votes
1 answer
216 views

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 ...
Confused Quant's user avatar
1 vote
1 answer
113 views

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. ...
Julien Maas's user avatar
1 vote
1 answer
48 views

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 ...
Julien Maas's user avatar
1 vote
0 answers
61 views

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. ...
Richard Hardy's user avatar
1 vote
1 answer
52 views

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 ...
Julien Maas's user avatar
1 vote
0 answers
50 views

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 ...
Richard Hardy's user avatar
1 vote
1 answer
54 views

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. ...
Richard Hardy's user avatar
1 vote
1 answer
101 views

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 ...
Richard Hardy's user avatar
0 votes
0 answers
63 views

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 ...
Jens's user avatar
  • 1
2 votes
2 answers
202 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
3 votes
0 answers
135 views

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 ...
RRR's user avatar
  • 31
2 votes
0 answers
100 views

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 ...
Lusitano's user avatar
0 votes
0 answers
60 views

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
53 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
3 votes
0 answers
155 views

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 ...
Roberto Palermo's user avatar
3 votes
1 answer
130 views

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! ...
Maynard's user avatar
  • 31
1 vote
0 answers
61 views

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-\...
phdstudent's user avatar
  • 8,441
0 votes
0 answers
36 views

Complete two-period model with specific replication strategy

Find a complete two-period model in which the unique replication strategy of a call (with a suitably chosen strike) shorts the stock in the first period (i.e. the call price falls if the stock rises ...
Analysis's user avatar
  • 133
0 votes
1 answer
148 views

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. ...
Analysis's user avatar
  • 133
2 votes
0 answers
332 views

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 ...
Analysis's user avatar
  • 133
4 votes
0 answers
92 views

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 ...
user68199's user avatar
4 votes
0 answers
246 views

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 $\...
SL133's user avatar
  • 41
1 vote
0 answers
52 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
220 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
1 vote
0 answers
112 views

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
6 votes
2 answers
578 views

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, ...
Richard Hardy's user avatar
3 votes
1 answer
119 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
276 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
2 votes
0 answers
58 views

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 ...
Rudy S's user avatar
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