Questions tagged [asset-pricing]

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40 views

Double sort portfolios

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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15 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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43 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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77 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 ...
2
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1answer
78 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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0answers
39 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 ...
3
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0answers
53 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
110 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). \...
5
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1answer
194 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
212 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 ...
2
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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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43 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
106 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
292 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
40 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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0answers
30 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 ...
2
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1answer
63 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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0answers
158 views

Determining decomposition long bond yields via Fisher equation and the Expectations Hypothesis 2.0

I've started to get into the weed of UST pricing and was hoping to get some feedback on a "model" I thought about. It is presented in this blog post. https://nonlinearexpectations.blogspot....
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1answer
84 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 ...
2
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1answer
78 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 ...
3
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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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0answers
31 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
102 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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0answers
86 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: $$c_{t+1} = (1+m_t)c_t + s_t c_t e_{t+1} $$ ...
2
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2answers
95 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
190 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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0answers
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
109 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
85 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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0answers
50 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 ...
3
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1answer
136 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
40 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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0answers
82 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
144 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
396 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 ...
2
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0answers
65 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 ...
3
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1answer
514 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 ...
1
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1answer
392 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 ...
3
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1answer
117 views

SML Interpretation

I follow this paper and estimated two different asset pricing models via systems of deep neural networks. Both models have the exact same input: firm-specific features for 10'000 (unique) US stocks ...
3
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1answer
193 views

Why are some metals in contango (inverted) forward curve and some in backwardation (normal) forward curve?

I am scrolling through the various metals on lme.com and some are in contango and some in backwardation. For example: Copper: backwardation Aluminium: contango Further examination of other metals ...
3
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1answer
207 views

ETF pricing papers

May I request for research paper recommendations, if any, on existing models that study how the presence of ETFs affect equilibrium prices of the underlying assets? I am exploring a project on a ...
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0answers
30 views

No Arbitrage condition for assets with different time frame

In the classic literature, one always assumes that the assets in the market are all available from the very beginning ($t=0$). And under such condition the market is arbitrage free iff there exists an ...
2
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0answers
73 views

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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1answer
535 views

What are industry fixed effects?

I have come across the term "industry fixed effects" in some papers in relation to cross sectional regressions in asset pricing. I know what "fixed" regression models are, but not ...
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1answer
95 views

How is CAPM used to price an asset once it has been used to derive the assets expected return?

As I understand it (correct me if I'm wrong) the theoretical price of an asset should be the present value of all future cash-flows that it is expected to yield, discounted at the risk-free rate. I am ...
2
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0answers
47 views

Question on the details of certain parameters in Sharpe Ratio [closed]

I'm puzzled about certain parameters in calculating the annualized Sharpe Ratio using monthly return data. Average excess return: Does this mean the arithmetic average of all the monthly excess ...
2
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2answers
334 views

Cashflow Risk vs Discount Risk

Studying asset pricing, I often hear the terms cashflow risk and discount risk but I'm not sure what they mean? The Campbell/Shiller (1988) decomposition includes cashflows (future dividends) and ...
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1answer
115 views

Vasicek model - Bond price and volatility

Why does the bond price under the Vasicek model increase as the rate volatility increases? What is the intuition behind this?
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2answers
420 views

Clean vs dirty price for bonds

Why the clean price is mostly quoted in the US bond markets and the dirty price is mostly quoted in the European bond markets?

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