Questions tagged [asset-pricing]
The asset-pricing tag has no usage guidance.
157
questions
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27 views
is it possible to make changes to use the affine property of Normal random variables, rather than the Central Limit Theorem?
I have proven the distribution of a discrete time model, evolving over a uniform mesh with $\delta t = T/L$ is given by
$$S(t_{i+1}) = S(t_i) + \mu \delta t S(t_i) + \sigma\sqrt{\delta t}S(t_i)Y_i,$$
...
1
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1answer
37 views
Moments of discrete Asset Price Model
Say if B is standard Brownian motion then:
$S(t) = S0e^{((𝜇- σ^2)/2)t+σB(t)}$
The mean of this SDE would be
$𝐄[𝑆(𝑡)]=𝑆_0𝑒^{𝜇𝑡}$
I know to do this you use the density function and ...
2
votes
0answers
31 views
To price Municipal Bonds and risks I want to know the percent of unfunded pension liabilities ($3.8T) to total state and local gov liabilities
Unfunded pension liabilities keep growing and this seems alarming to both pension holders but also Municipal Bond holders.
I would like to know how large this problem is to better price Munis and ...
1
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0answers
36 views
How do flat demand curves for stocks allow for price changes?
Many models in asset pricing base their assumptions on a flat demand curve for stocks, as they are viewed as goods with perfect substitutes. With this, I understand that any sort of stock sale or ...
2
votes
1answer
47 views
Using the Fama-Macbeth Process to Test CAPM
Here is my understanding of the Fama-Macbeth process:
Assuming a group of $n$ stocks, we first collect risk profiles $\beta_{i, agg} = [\beta_{i, MKT}, \beta_{i, SMB}, \beta_{i, HML}]$ through ...
0
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0answers
33 views
Eliminating factor risk?
Suppose there are two risky assets, related to the same risk factor $f$.
$r_1 = μ_1 + β_1f$
$r_2 = μ_2 + β_2f$
There is also a risk free asset available at $r_f$
How do you eliminate factor risk ...
1
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0answers
34 views
How should I interpret the (insignificant) coefficients of Fama-French 3-factor model?
I am writing a mid-term thesis on the Fama-French factor model.
I have built 5 portfolios sorted by the Book-to-Market ratio. The first portfolio is the lowest-BM group and the last portfolio is the ...
1
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0answers
36 views
Calculating the fundamental value of house price to separate bubble component from the price
The bubble in asset price is defined as the deviation of the asset value from its fundamentals, empirically Mendoza and Terrones (2008) measure the bubble as the deviation of an asset price from the ...
2
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0answers
34 views
Cointegration between prices and dividends. How do I get the following expression?
Actually, I have two questions:
1.
Let us assume that expected returns are constant. Then, we have the following expression for how the prices should be determined, provided that the operators are ...
2
votes
1answer
67 views
How to price a phoenix and snowball type autocallable options?
I'm currently studying the pricing of autocallable options, especially snowball (accumalated coupon) and phoenix (accumlated coupon, but the coupon may also be autocalled if the underlying price ...
2
votes
1answer
40 views
Gibbons, Ross, Shanken Test derivation by MLE
I Am trying to derive the expression for the GRS test of the CAPM. I am following the book: The Econometrics Of Financial Markets by Campbell, Lo, McKinley (1997).
Define $Z_t$ as an $N×1$ vector of ...
3
votes
1answer
41 views
How to model the maturity term of non maturing deposit accounts
My client (bank) currently follows a naive method to model the maturity term of chequing accounts. We need to model the maturity to correctly calculate the FTP pricing of these chequing accounts.
The ...
1
vote
1answer
72 views
Example of complex structured products on FX market?
Lately I have been working a lot with the vol smile and different stochastic volatility models with FX forwards data. Now I want to work with pricing examples through simulations. Can you suggest some ...
1
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2answers
131 views
Risk-neutral pricing and statistical arbitrages
I'm studying the martingale approach to asset pricing. Dealing with the concept of risk-neutral probability, I came up with a question about the possibility of "arbitrages in expectation". I'll be ...
0
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0answers
37 views
What is the effect of covariance on the dynamics of a price
I want to know how can I see covariance affecting the dynamics of the price of an asset. I understand what the value for covariance and it's sign, but I do not get how it plays in the bigger picture. ...
1
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0answers
21 views
Continuous formula for the price of an asset paying one terminal dividend?
I have been trying to come up with ways to come up with an answer for a question we got in my class of "Asset Pricing Theory". The question is as follows:
"Write the price of the asset at time t in ...
0
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0answers
43 views
What is the earliest mention of ROE as an asset pricing factor?
Can anyone tell me, what is the first application of ROE in an (empirical) asset pricing model? I am aware of the 2011 paper by Chen, Novy-Marx and Zhang. Are there any earlier papers on the matter?
2
votes
1answer
180 views
Forward Start Spread Options
Question:
We have a spread option with payoff: $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant.
At time zero only contract $G$ is available for ...
1
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0answers
63 views
Fama-French 3, Carhart 4, Fama-French 5 Factor models return borderline 0% R2 (max. 6.6%). Time series regression
I am currently working on an industry specific time series analysis of European Equities between 201001 and 201812. I use the European Fama French factor returns (plus the momentum factor return) that ...
0
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1answer
42 views
Infinite Binomial Pricing no arbitrage
How to price a contract that pays only 1 at the first stock price drop? The stock follows an infinite binomial with no arbitrage $d<R<u$ condition.
So the probability of the price going down is ...
1
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0answers
30 views
Using CFNAI index for identifying sample periods
I'm doing my Thesis on Asset pricing models and I would like to find out the effects of business cycles on the performance of asset pricing models for industry portfolios.
My initial idea was to ...
1
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0answers
63 views
Brownian motion for modelling future asset values
Assume that an asset price $S$ is given by a Brownian motion. Argue from the definition why it is not possible to predict future values of the asset based on the past values of $S$.
I am not sure ...
3
votes
1answer
94 views
What happens in the binomial model if the real-world probability is $0$
Consider a binomial model.
Suppose we know that the price of a stock will become a certain value at the next timestep. That is, one of the two outcomes has $0$ real-world probability.
Then it should ...
3
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0answers
143 views
How to perform Shanken (1992) correction for errors-in-variables issue?
I have two questions pertaining to the Shanken correction:
The formula of Shanken correction shown in the Cochrane (2001) Asset Pricing book is as follow:
$$\sigma^2(\hat{\lambda}_{OLS})=1/T[(\beta^{...
1
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0answers
30 views
Statistical procedures on comparing the four Asset pricing models [closed]
I'm a business student and currently writing my thesis on comparing asset pricing models on industry portfolio returns. Being a business student, I lack the knowledge for statistical analysis ; so I ...
1
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1answer
155 views
Bond discounting conventions
during the preparation for my thesis, I've come across some strange discrepancies between literature and the information I've been taught.
It comes down to the proper way of discounting cash-flows of ...
6
votes
3answers
440 views
Most significant research articles for practical investors with research perspectives
I am an applied mathematician and recently I have decided to study the portfolio management theory. As a final objective, I want to manage my own portfolio and to try make some money on it using my ...
2
votes
0answers
71 views
Asset pricing and dividend discount model
I want to derive the dividend discount model from the asset pricing formula described in "Efficient Capital Markets: A Review of Theory and Empirical Work" by Eugene Fama 1970. The formula that I am ...
0
votes
1answer
41 views
Is there a robust way to calculate stock beta or factor exposure that's specific to crashes?
Commonly known factors like market, value, momentum etc. have positive expected returns because they draw-down unexpectedly and investors require a risk premium for holding them. This idea is extended ...
6
votes
1answer
142 views
How to perform cross-sectional asset pricing regression?
I'm wondering is that possible to get insignificant beta estimates in the time-series context, but highly significant risk premium associated with that beta in the cross-sectional regression?
Any ...
1
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0answers
59 views
Creating a hedge portfolio out of 10 assets
Suppose I have historical return data on 10 assets. How can I create a hedge portfolio that prices all these assets in a factor model?
I have chosen 3 factors: excess market return, SMB and HML from ...
1
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1answer
62 views
How to modify binomial tree to incorporate one more asset?
I wonder, what would happen if we use the binomial tree to price exchange option, an option to exchange one asset for another at the expiry date. Payoff is $\max(S_1-S_2,0)$
For instance, I have two ...
2
votes
1answer
358 views
Which proxy is the best to calculate daily risk free rate for a capital asset pricing model?
I need to get daily risk free rate to measure my capital asset pricing model. However, I am still confused on which proxy to use for that (my sample comprises German stocks). Some empirical studies ...
2
votes
1answer
68 views
Continuous Time Asset Model in Higham
I read Higham's derivation of the Black-Scholes equation in "An Introduction to Financial Option Valuation". The issue I am having is that it relies on some assumptions related to a continuous time ...
2
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0answers
71 views
Prove unique arbitrage-free price implies attainable
I just read a Corollary in a finance course note:
Suppose the market is arbitrage free and $C$ is a contingent claim. Then $C$ is attainable if and only if it admits a unique arbitrage-free price.
...
3
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1answer
117 views
Asset pricing model factor need to be excess return?
In John Cochrane's Asset Pricing book and his video lecture, he states that asset pricing factors need to be excess returns, a traded portfolio. Is there a reason for that? I can't find explanation ...
1
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1answer
71 views
Unit exposures to Country,Industry and World factors in Fundamental Factor Risk Models
I may have what can be called a rudimentary question about Fundamental Factor models for Risk (ala Barra).
Why is the exposure to World,Countries,Industries set to 1 instead of a real number. The ...
0
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1answer
78 views
How to apply derived beta to daily change?
I've taken three months of price return data for two instruments and calculated a $\beta$ between the two using the formula $\beta = \frac{Cov(x,y}{Var(y)}$ with the goal of estimating what the ...
1
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0answers
74 views
Cointegration between daily time series and intraday time series
I am working with time series data of daily prices, and intraday prices. For simplicity sake I will refer to the daily time series as 'A' and 'B', and the intraday time series of the same instruments ...
1
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0answers
21 views
From one period to multi period risk neutral pricing
For a one period economy, we have the price of an asset as:
$ p_0 = E^Q [p_1 * \frac {B0}{B1}] $
where $B0 = e^{-r_0}$ = time 0 price of risk free bond maturing at time =1 and $r_0$ is known at t0. ...
1
vote
1answer
232 views
Daily idiosyncratic volatility?
I have a long daily times series of individual stocks and would like to obtain daily idiosyncratic volatility (keeping the same frequency). Apparently, the widely used methodology of Ang 2006 would ...
1
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1answer
65 views
Estimating French and Fama 3 - factors for global markets
I am working on this project where I am estimating FF three factors for some European countries. So I collected daily prices in US dollars for these countries since I will be using FF three factors ...
4
votes
2answers
400 views
Why is Fama French model a risk model
I get this question from interviewer about what is alpha model, what is risk model and why is Fama-French a risk model.
As my understanding, alpha model forecast expected return, so the factor could ...
1
vote
2answers
107 views
What is the impact of inflationary expectation on stock price?
It is well known that, at least theoretically, stock prices are expected to rise in an inflationary environment. Now, my question is that does the same go for inflationary expectations; for example if ...
1
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1answer
117 views
Fama French paper regression questions
I am reading the paper and get the following question. I think here is how the regression is constructed:
First step:
$R_t^i = \alpha^i + \beta^i \cdot MarketBeta_t + \gamma_i\cdot Size_t + \nu \cdot ...
8
votes
1answer
203 views
Are returns predictable, Campbell and Shiller (1988)
Following from the thread,
Drivers of equity returns: dividend yield, change in P/E and dividend (or earnings) growth
1) Why are returns predictable from this, is there a reason?
2) Can we expect ...
-1
votes
1answer
205 views
FF 5 factor model Intercept equal 0
In the paper A five-factor asset pricing model from Fama and French (JFE 2015) they say at page 3:
"Treating the parameters in (4) as true values rather than
estimates, if the factor exposures $...
1
vote
1answer
34 views
Where does this proof use the fact that the consumption level is positive?
Consider the following problem.
Now consider the following theorem and proof. My question is, where is it used in the theorem that $c^\star + \alpha D^T \theta \ge 0$? That is, why is that important? ...
6
votes
3answers
151 views
Measuring alpha (Academia vs the Industry)
During academia, I learned to evaluate the performance of a portfolio by calculating alpha as the following:
$\alpha_{i} = (R_{it}-R_{ft})-[\beta_i(R_{BMK_t}-R_{ft})]$
where $\alpha_i$ and $\beta_i$ ...
5
votes
1answer
246 views
Behavioral SDF: modelling sentiment risk premium
With reference to Behavioral Asset Pricing models, I know that the discount factor (or required rate of return) is equal to:
Discount rate = Risk-free rate + Fundamental risk premium + Sentiment ...
