Questions tagged [asset-pricing]

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Using monthly CRSP EWRET to build equally weighted portfolios based on market equity and book to value ( SAS)?

I was wondering if it is possible to download the EWRET variable from Wharton in order to construct equally-weighted portfolios and rebalance every June? I have seen a few fancy codes for this ...
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2answers
46 views

Asset pricing: Is Beta priced or not?

What does it mean in asset-pricing if something is priced or not?
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14 views

Fama-MacBeth - Why are factor loadings estimated?

I would like to know why factor loadings in the first step of the Fama-MacBeth procedure are estimated and used as input in the second part. Thanks!
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34 views

SMB risk premium positive in Fama-French three factor model

I performed a Fama-MacBeth procedure on the Three-Factor model. I used 25 portfolios sorted to size and B/M and the longest possible time-line. When analyzing the coefficients (factor loadings) of ...
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1answer
28 views

What is the consumption constraint in writing the continuous version of Asset Pricing Model?

In the first chapter of John Cochrane's Asset Pricing textbook, in order to calculate the price in discrete time, we solve the maximization problem of $Max\space E(\Sigma\beta^j U(c_{t+j}))$ when our $...
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67 views

Volatility Managed 6 Factor Model (Fama French) - Does it make sense?

after weeks of intense research and in spite of the current situation, I decided to ask the following question to some experts (you): I would like to develop/investigate a volatility managed six ...
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17 views

How to build a Fama & French model based on the international data provided by French?

I am trying to obtain a 3 factor Fama French model based on the "International Research Returns Data" provided on French home page https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library....
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11 views

Central Pricing Relation CCAPM

I need to understand what to do, when i take the covariance of an expression that looks like this: $\operatorname{cov}_{t}\left(\frac{U_{1}\left(\tilde{c}_{t+1}\right)}{U_{1}\left(c_{t}\right)}, \...
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57 views

Derive Q-dynamics of $\ln S_t$ having multiplicative error structure

From Kwon, T. Y. (2012). Three essays on credit risk models and their bayesian estimation (Doctoral dissertation): Assume the following log equity price model: $$\ln S_t = g_S(V_t,t,\Theta_V) + Z_T$$...
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1answer
112 views

Some aspects of the market price of risk

I am a little confused about the market price of risk. Take the following geometric Brownian motion: $$dS_t = \mu S_t dt+\sigma S_t dW_t$$ The market price of risk is defined as: $$\frac{\mu-r}{\...
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41 views

Why price with lower volatility yield higher expectation under risk neutral measure

Suppose $S_1$ and $S_2$ are two asset prices, such that, E[$S_1$] = E[$S_2$] under physical measure and $\sigma(S_1)$ > $\sigma(S_2)$. Then why E[$S_1$] < E[$S_2$] under the risk neutral ...
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87 views

Risk-neutral price of $H=e^{X_T^1+X_T^3}$

Let $B=(B_t^1,B_t^2,B_t^3)$ a $\mathbb R^3$-valued Brownian motion. Let $r_t$ (risk free rate) be bounded and deterministic. Let consider the DISCOUNTED market $$d\overline X_t^1=\frac52dt+2dB_t^1-...
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1answer
58 views

Understanding Fama Macbeth Regressions of Returns

I'm trying to understand what the Fama-Macbeth regressions of returns actually mean. The source of confusion is a 2013 Novy-Marx paper, in which he states the following: "The first specification of ...
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33 views

Deriving CAPM from APT framework

I was wondering if it is possible to derive the CAPM from the APT? My argument is that CAPM basically just is a 1 factor model, where the APT has multiple factors. Can any of you guys help me?
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37 views

Replication of the paper: “A Comprehensive Look at the Empirical Performance of Equity Premium Prediction”

I recently replicated the paper "A Comprehensive Look at the Empirical Performance of Equity Premium Prediction" and found out that my estimation of the equity premium differs from the data provided ...
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1answer
51 views

Question is about the data in the paper: “A Comprehensive Look at The Empirical Performance of Equity Premium Prediction”

I would like to ask a question if you download the data from the Amit Goyal website: http://www.hec.unil.ch/agoyal/ You will see that there are two columns "CRSP_SPvw" "CRSP_SPvwx", they are ...
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57 views

Pricing of the compound coupon bond with PDE

I am now studying finance math using Steven E.Shereve's book. Using Interest Rate models, We can the price for zero-coupon with maturity price $1$ under Hull-White interest rate model[page 274] and ...
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1answer
57 views

Time of Nasdaq daily close price

On the Nasdaq website It Is stated that the market closes at 4:00pm. However I have historic intraday minute prices and I can see that that are minutes with prices after 4:00 PM (I am assuming its ...
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1answer
263 views

Libor to SOFR transition Yield Curve Construction

With the imminent transition from LIBOR to SOFR next year, what are the data points practitioners are using to the yield curve? Also, since LIBOR implicitly took into account credit risk of the ...
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2answers
80 views

Question regarding No Arbitrage price of a call option

I have a question regarding how to solve the NA price for a slightly modified call option. Say that I have a money account $B(T)=e^{r(T-t)}$ and a stock dynamic $\frac{dS(t)}{S(t)}=(r-\delta)dt+\...
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1answer
48 views

How to determine the no arbitrage price of following claim? (change of numeraire)

How do I determine the no arbitrage price for claims such as $min(S_1(T),S_2(T))$ or $max(S_1(T),S_2(T))$? We can consider a standard Black Scholes model. Hence $S_i(T)=S_i(t)e^{(r-\sigma_i^2/2)(T-t)+\...
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1answer
72 views

What should happen to the equity risk premium as rates change?

Suppose I set forward-looking expected returns for capital markets using a dividend discount model framework, under which expected return for equities is the sum of dividend yield, expected trend ...
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1answer
67 views

What is market sensitivity and momentum sensitivity?

I have daily data of about 29 stock prices and 1 index prices of past 7 years I calculated beta as the ratio of covariance(Rm,Ri) / variance(Rm) I also calculated 200 days rolling momentum score as ...
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1answer
74 views

A financial market is complete if and only iff there exists a unique equivalent martingale measure

Do you have any intuition behind the following theorem : A financial market is complete if and only iff there exists a unique equivalent martingale measure. I understand the easier version of ...
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1answer
57 views

How do weights of a Mean-Variance optimized portfolio change as the Covariance matrix of the risky assets change?

I am learning a bit more about CAPM, and wanted to know if there was a specific way that weightings of assets in the optimal mean-variance portfolio changed (for constant risk aversion, expected ...
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1answer
119 views

What does “first-order effect” mean?

In the textbook Asset Pricing by John Cochrane, on p. 25, it says: "This prediction holds even if the payoff $x$ is highly volatile and investors are highly risk averse. The reason is simple: if you ...
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29 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 $$S(t_{i+1}) = S(t_i) + \mu \delta t S(t_i) + \sigma\sqrt{\delta t}S(t_i)Y_i,$$ ...
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1answer
39 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 ...
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33 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 ...
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37 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 ...
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1answer
433 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 ...
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34 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 ...
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89 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 ...
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0answers
37 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 ...
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0answers
38 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 ...
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1answer
336 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
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1answer
60 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 ...
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1answer
75 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 ...
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1answer
163 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 ...
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2answers
155 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 ...
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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. ...
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0answers
22 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 ...
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44 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?
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1answer
191 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 ...
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0answers
106 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 ...
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1answer
43 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 ...
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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 ...
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0answers
67 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 ...
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1answer
120 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 ...
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252 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^{...