Questions tagged [asset-pricing]

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27 views

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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2answers
134 views

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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22 views

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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79 views

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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1answer
222 views

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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55 views

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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36 views

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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1answer
70 views

What are the most common methods to model fat tails in the changes of asset prices?

I was wondering what the most common, or most popular, ways - in both academia, and industry - there were to model the fat tails of volatility in asset prices changes. I am presuming a basic Brownian ...
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1answer
73 views

Using the risk neutral version of the First Fundamental Theorem of Asset Pricing to derive a partial differential equation

I have to use the risk neutral version of the First Fundamental Theorem of Asset Pricing to derive a partial differential equation (PDE) that the price/value process, $V_t = F(t,S_t)$, of a self-...
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26 views

The minimal entropy martingale measure for insurance-linked securities pricing

Suppose that we have a CAT bond contract that pays coupons at discrete points in time as well as a principal at maturity time $T$ if no triggering event happens during the term of the contract. More ...
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1answer
102 views

Why individual investors are attracted to lottery stocks is a puzzle?

Han et al. 2021 mention one puzzle in investment is individual investors are attracted to stocks with high skewness, so-called lottery stocks(...). This behavior is not consistent with standard ...
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77 views

Closed form expression for $\Bbb E(\mathbb{I}_{\{S_{1,T}>S_{2,T}>K \}})$

Is it possible to calculate analytically $\Bbb E(\mathbb{I}_{\{S_{1,T}>S_{2,T}>K \}})$, using the 2-dimensional normal probability function $\Phi_2$, where $S_{1,T}$ and $S_{2,T}$ follow ...
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62 views

Double sort portfolios [closed]

I am studiying the impact of two variables A and B on stocks returns. When I sort the stocks individually, I find that the long-short portfolios returns obtained for A and B exhibit high correlation. ...
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17 views

Factor Loading Precision/Details in Fama-French 3 Factors Model

I have a few questions regarding details about FF3F model. In the equation like following, $$ E(R_P)-r_f = \alpha +\beta_M[E(R_M)-r_f] + \beta_SSMB + \beta_V HML $$ Are SMB and HML factors are ...
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46 views

How the spread portfolio t-test is calculated?

within my master thesis I am calculating the Pastor and Stambaugh (2003) liquidity factor (https://static1.squarespace.com/static/5e6033a4ea02d801f37e15bb/t/5f629437c9d51c5d00ad3ff3/1600295992687/...
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83 views

Matrix with two columns - ESG Momentum Strategy

Background: I am conducting some research on equity returns on portfolios sorted on ESG Scores from Asset4. Specifically, I am trying to test if trading on long-short ESG momentum portfolios yields ...
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1answer
88 views

Breaking points of Fama French portfolios

My question is about the size breakpoint of Fama French portfolios. Anyone knows why in US market data they used the median as a size breakpoint to construct the six portfolios, but when they used the ...
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41 views

Local Evaluation Date in QuantLib

I am trying to construct a price history for swaps in QuantLib, i.e. to have a timeseries of daily prices for a given swap. I have my rates data on each day, but what I'm struggling with is the ...
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59 views

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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1answer
125 views

Variance of Random Walk with Drift

For Gaussian random variables $\xi_t$ with mean $\mu_t$ and standard deviation $\sigma$, consider the random walk with initial condition $P_0=100$, such that \begin{equation} P_t=P_{t-1}(1+\xi_t). \...
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1answer
213 views

Show a model is complete but not free of arbitrage

Let $\mathcal{F}=\{\Omega, \emptyset\}$ be the trivial $\sigma$ -algebra, and consider the deterministic financial market model with zero interest rates, $S_{0} \equiv 1$, and $n=1$ additional asset $...
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1answer
238 views

Trade anything?

I have a question after reading the post below. https://www.onlinebetting.org.uk/betting-guides/can-you-bet-on-anything-you-want.html Question: I want to bet on a niche topic or asset or anything that ...
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0answers
50 views

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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49 views

Is the initial value of the portfolio replicating a forward zero?

This is from the book Financial Calculus: An Introduction to Derivative Pricing by Martin Baxter. By choosing appropriate weights in a portfolio of a stock and cash bond you can replicate the payoff ...
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1answer
122 views

Carhart 4 factor model and six factor model

The value of SMB of Fama French 3 factor model is calculated as follows: $$ \frac{1}{3} (Small Value + Small Neutral + Small Growth) - \frac{1}{3} (Big Value + Big Neutral + Big Growth). $$ However, ...
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3answers
295 views

Asset Pricing and Negative Prices

I am running an asset pricing study. The data is from 1990 to 2020. When the data is adjusted for dividends and splits, stock prices of several firms become negative. How does one handle negative ...
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0answers
44 views

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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40 views

Fama French: daily or weekly returns?

I am conducting a performance comparison analysis among sustainable and conventional mutual funds. I want to analyse the last 6 years and focus also on the subperiod of the COVID-19 crisis. I have ...
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1answer
76 views

Fama French regression with dummy variable

I am looking to run Fama-French regression on a portfolio of stocks. I am looking to specify a regime using a dummy variable. This dummy variable could be a low volatility/ high volatility marker. ...
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1answer
98 views

Replicating Portfolio / Complete Market / Attainable Claim

Attempt So Far: 1) First Part: I have shown that the market is arbitrage-free since the only possible portfolio for which $V_1^h\geq0 \ $ given that $V_0^h=0 \ $ is $h=(0,0,0)$ and this clearly ...
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1answer
84 views

Feynman-Kac representation of Black-Cox model

Consider the standard setup from Black and Cox (1976, Journal of Finance). A firm issues a defaultable coupon bond to finance a productive asset that follows a geometric brownian motion: $$dx_t = \mu ...
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1answer
64 views

Cauchy-Euler ODE with indicator function in coefficient

Consider the following Cauchy-Euler ODE, which is in particular the asset pricing equation for a (perpetual coupon defaultable) bond: $$\frac12 \sigma^2 V^2 F_{vv}(V,t) + \mu V F_{v}(V,t) - r F(V,t) + ...
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36 views

Derivation defaultable bond price in Leland 1994 (Merton)

Consider the model in Leland (Journal of Finance, 1994). The partial differential equation that describes the price of the (perpetual coupon defaultable) bond is: $$\frac12 \sigma^2 V^2 F_{vv}(V,t) + \...
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0answers
106 views

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{...
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89 views

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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2answers
118 views

Why in Fama-French factor model relative market capitalization and book-to-market aren't used directly for predicting return rate?

Fama and French use the following formula for predicting stock returns \begin{align*} r=r_{riskfree} + \beta_1(r_{market}-r_{riskfree})+\beta_2(SMB)+\beta_3(HML) \end{align*} which basically means ...
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2answers
234 views

Pricing binary options

A binary option pays an amount of money if an event takes place and zero otherwise. Binary options are usually used to insure portfolios against large drops in the stock market. On March 25, 2021 the ...
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16 views

Inflation and growth due to inflation canceling out in cap rate formula?

A cap rate can be described as: K = RFRr + i + RPi + RPp – Gr – Gi + D Where K = cap rate RFRr is the real risk free rate, or index-linked bond i = average expected inflation RPi = the inflation risk ...
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2answers
110 views

How does one actually create a derivative of a given underlying security? [closed]

Let's say I'm an investment bank and I want to create a derivative whose value tracks that of gold. I don't want this derivative to in any way trade in the underlying security, so no futures or ...
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1answer
87 views

Misconception about replicating portfolio [closed]

I am solving a problem in which following payoff is provided: With $S_0=100$ and $T=8$. Looking at the payoff it seems obvious that it is replicated with two european put options ($K=100$ and $K=150$)...
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58 views

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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1answer
145 views

Does CRR Model lose completeness if we add another instrument?

Consider the multiperiod binomial/CRR model with one risky asset $S^{1}$ and a numeraire $S^{0}$. By seeing that the equivalent martingale measure is uniquely determined, we obtain that the market is ...
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0answers
41 views

Hypothetic derivative that absorbs underlying volatility

Market participants are usually assumed to be risk-averse and striving to improve the Sharpe ratios of their portfolios. Thus, if we have an asset A, which is expected to return between \$900 and \$...
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88 views

SDF derivation by a stochastic process

I have a stochastic process to model the stochastic discount factor (SDF) with M: \begin{equation} dM_t = aM_tdt + bM_t d Z_t \end{equation} where, $Z_t$ is a standard brownian motion. How do I show ...
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3answers
163 views

How to calculate a Corporate Bond Transaction Price (Bond returns?)?

I am struggling with the concepts and variables of corporate bonds returns. Bai, Bali and Wen (2019) define monthly corporate bond returns as: Where where is transaction price, , is accrued ...
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5answers
403 views

What mechanisms does the market use to brining an asset back to the market line, as defined by CAPM?

The Capital Asset Pricing Model (CAPM) model states that, on efficient market, expected return of an asset should be given by a linear function of its volatility (as measure by standard deviation of ...
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0answers
68 views

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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1answer
1k views

Is market price of risk always negative?

I might have a gap in understanding, so clarifying: Basic pricing equation $E(R) = - cov(m, R)$ where $R$ = excess return and $m$ = stochastic discount factor (I think this is continuous case, in ...
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1answer
657 views

Anyone has detailed explanation on how to use epstein-zin preferences in asset pricing models

I'd be interested to know how Epstein-Zin preferences are used in, say, consumption-based asset pricing models. I'm looking for specific derivations (how you get the SDF) and possible numerical ...
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1answer
450 views

Covariance, stochastic discount factor (SDF) and risk aversion

John Cochrane states, that if the covariance between the stochastic discount factor and the payoff is zero - then risk aversion should have no impact on the pricing. I do not fully understand why this ...

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