Questions tagged [asset-pricing]
The asset-pricing tag has no usage guidance.
259
questions
0
votes
0answers
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 ...
2
votes
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 ...
1
vote
0answers
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. ...
4
votes
0answers
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 $S$ ...
4
votes
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 ...
4
votes
0answers
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 ...
0
votes
0answers
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 ...
0
votes
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 ...
1
vote
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-...
0
votes
0answers
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 ...
0
votes
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 ...
1
vote
0answers
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 ...
2
votes
0answers
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. ...
0
votes
0answers
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 ...
0
votes
0answers
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/...
0
votes
0answers
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 ...
2
votes
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 ...
0
votes
0answers
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 ...
3
votes
0answers
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:
...
1
vote
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).
\...
5
votes
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 $...
0
votes
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 ...
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
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 ...
1
vote
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, ...
0
votes
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 ...
3
votes
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 ...
0
votes
0answers
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 ...
2
votes
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.
...
1
vote
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 ...
2
votes
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:
$$dx_t = \mu ...
3
votes
1answer
64 views
Cauchy-Euler ODE with indicator function in coefficient
Consider the following Cauchy-Euler ODE, which is in particular the asset pricing equation for a (perpetual coupon defaultable) bond:
$$\frac12 \sigma^2 V^2 F_{vv}(V,t) + \mu V F_{v}(V,t) - r F(V,t) + ...
1
vote
0answers
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:
$$\frac12 \sigma^2 V^2 F_{vv}(V,t) + \...
2
votes
0answers
106 views
Pricing kernel representation
I am reading this paper https://mpra.ub.uni-muenchen.de/4969/1/MPRA_paper_4969.pdf pp.6-7 on discrete-time bond pricing. The model adopted is a a common affine model,
the short rate follows
\begin{...
4
votes
0answers
89 views
Some basic questions using consumption CAPM
Say we are in a world described by the consumption CAPM. All investors in this world have quadratic utility. Also, assume that consumption is as follows:
$$c_{t+1} = (1+m_t)c_t + s_t c_t e_{t+1} $$
...
2
votes
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 ...
1
vote
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 ...
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
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 ...
0
votes
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 $K=150$)...
1
vote
0answers
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 ...
3
votes
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 ...
0
votes
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 \$...
0
votes
0answers
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 ...
0
votes
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 ...
0
votes
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 ...
2
votes
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 ...
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
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 ...
1
vote
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 ...
