Questions tagged [asset-pricing]
The asset-pricing tag has no usage guidance.
248
questions
2
votes
0answers
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. ...
0
votes
0answers
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 ...
0
votes
0answers
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/...
0
votes
0answers
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
votes
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 ...
0
votes
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
votes
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:
...
1
vote
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
votes
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 $...
0
votes
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
votes
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 ...
0
votes
0answers
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 ...
1
vote
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, ...
0
votes
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 ...
3
votes
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 ...
0
votes
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
votes
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.
...
1
vote
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....
1
vote
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
votes
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:
$$dx_t = \mu ...
3
votes
1answer
64 views
Cauchy-Euler ODE with indicator function in coefficient
Consider the following Cauchy-Euler ODE, which is in particular the asset pricing equation for a (perpetual coupon defaultable) bond:
$$\frac12 \sigma^2 V^2 F_{vv}(V,t) + \mu V F_{v}(V,t) - r F(V,t) + ...
1
vote
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:
$$\frac12 \sigma^2 V^2 F_{vv}(V,t) + \...
2
votes
0answers
102 views
Pricing kernel representation
I am reading this paper https://mpra.ub.uni-muenchen.de/4969/1/MPRA_paper_4969.pdf pp.6-7 on discrete-time bond pricing. The model adopted is a a common affine model,
the short rate follows
\begin{...
4
votes
0answers
86 views
Some basic questions using consumption CAPM
Say we are in a world described by the consumption CAPM. All investors in this world have quadratic utility. Also, assume that consumption is as follows:
$$c_{t+1} = (1+m_t)c_t + s_t c_t e_{t+1} $$
...
2
votes
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 $K=150$)...
1
vote
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
votes
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 ...
0
votes
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 \$...
0
votes
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 ...
0
votes
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 ...
0
votes
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
votes
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 ...
1
vote
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
votes
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
vote
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
votes
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
votes
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
votes
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 ...
1
vote
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
votes
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 ...
1
vote
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 ...
0
votes
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
votes
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
votes
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 ...
0
votes
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?
1
vote
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?
