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1answer
52 views

Mathematically: How does increasing the number of assets reduce idiosyncratic risk?

As part of an Asset Pricing Module I'm currently taking, whilst looking at APT Ross (1974), we looked at how according to this model, risk originates from both systematic and idiosyncratic asset ...
1
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1answer
48 views

When are factors returns in asset pricing and how do we construct them?

I am very certain that the temperature in New York's Central Park plays a super-significant role in stock returns, so I take its daily averages and I want to test it in factor model. Cochrane ...
1
vote
1answer
21 views

What is the intuition of a spread portfolio and how exactly is it constructed?

In a lot of papers spread portfolios are constructed, like in Harvey and Siddique (1999), Table IV, or in Fama and French (2005 from SSRN), page 15. First, why is it important to construct such ...
2
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2answers
101 views

The portfolio whose return is the stochastic discount factor

I am trying to construct a portfolio whose return is $a + bm_{t+1}$ where $a$ and $b$ are some constants for a certain investor. $m_{t+1}$ is the stochastic discount factor at time $t+1$. I am ...
0
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1answer
54 views

State Variables in a Bellman Equation

Can anyone explain to me exactly what a state variable is in a Bellman equation?? $$ V(x,y)=max\space u(c)+\beta V(x',y')$$ In some models with capital savings it's the capital $k_t$ you walk into ...
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0answers
40 views

Calculating expected annual returns [closed]

An economy contains these three assets: Asset A has standard deviation of returns (per annum) of 25% and market capitalisation $600m Asset B has standard deviation of 20%, market capitalisation ...
3
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2answers
99 views

Derive an expression for the value of the asset as a function of time, V(t), t>=0

An investor deposits USD 300 in a bank account at time 0, reinvests all interest payments and continuously invests USD 300 per annum, until the total value of the deposits reaches USD 3312. At that ...
4
votes
2answers
124 views

Fama-Macbeth second step confusion

I am confused on how to run the second step of the Fama Macbeth (1973) two step procedure. I have monthly stock returns and monthly Fama-French factors, for around 10,000 stocks. This creates an ...
0
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0answers
12 views

Transaction costs estimate for investment strategy

I'm examining a strategy based on profitability. I sort UK stock into 10 portfolios based on their gross profits-to-total assets ratio. Then, I create long-short portfolios by subtracting the high ...
0
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0answers
27 views

commodity asset pricing

This is not a quant question but more a fundamental question. At the moment, WTI next month’s contract is trading at $29/B. My question are: Is it safe to assume delivery cost at Cushing is priced ...
8
votes
2answers
187 views

Why aren't the Fama-French 3 factors orthogonal to each other?

I am confused whether the factors in a multi-factor model should be orthogonal or not. Google searches do not give a well documented answer and I couldn't find one in our library's limited catalog ...
0
votes
1answer
86 views

Price of a Stock: What is it?

My limited understanding of stock prices is that according to theoretical arguments, the price of an asset is generally given as:$$P_{A}=E_{0}\,\sum_{t=0}^{\infty}\frac{C_{t}}{(1+r)^{t}}$$ whereby ...
2
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2answers
225 views

Pricing options under a specific framework

I have a specific framework in mind and I would like to value options under this framework. I am not sure whether a closed form solution exists or Monte Carlo methods would work. The framework I have ...
1
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0answers
31 views

How to derive what effect funding shocks have on conditional market betas? [closed]

I am unable to derive the correct result eq2 all my answers seem circular, any help would be much appreciated. It should basically end up saying that shocks that affect all securities compress betas ...
3
votes
1answer
138 views

Asset pricing - Technology

I am working a bit on this paper, which is about Long-run risk through Consumption Smoothing. In equation (8) and (9) the authors define the stochastic process for the technology as: $$Z_t = ...
7
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2answers
5k views

What are the main differences between discrete and continuous time models when modeling asset price dynamics?

My intuition says that both approaches, discrete time models and continuous time models will be models (i.e. approximations) of reality. Therefore it should be possible to develop useful models in ...
3
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0answers
19 views

Why should a factor not priced and yet is relevant to the return generating process

I am reading Elton's AFA presidential adress article here. http://people.stern.nyu.edu/eelton/working_papers/Expected_Return_Realized_Return.pdf In the paper, he is warning against using the average ...
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0answers
25 views

How to understand stock return comovement

In his book "Asset Pricing" chapter 20, Cochrane said For example, suppose that average returns were higher for stocks whose ticker symbols start later in the alphabet. (Maybe investors search ...
1
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1answer
30 views

Consumption Based Asset Pricing

I am working on some consumption based asset pricing models. I am modelling consumption growth in several different ways. An obvious one is to model consumption growth as an AR(1) process: $g_{t+1} = ...
5
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3answers
79 views

Jegadeesh and Titman 1993 Power of their test

I am reading this classic paper(http://www.business.unr.edu/faculty/liuc/files/BADM742/Jegadeesh_Titman_1993.pdf) and got confused by one of their arguments on their overlapping portfolio strategy to ...
2
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1answer
15 views

Distress firms and cross section returns

In George and Hwang's 2010 JFE paper, they are trying to resolve the so called distress risk and leverage puzzles. This is their explanation: This is a puzzle because high distress intensity or ...
0
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1answer
76 views

What is some book that is complete and easy but hard enough to serve as prerequisite for asset pricing and portfolio choice theory?

What is some book that is complete and easy but hard enough to serve as prerequisite for asset pricing and portfolio choice theory by kerry back? I wonder how come a beginning graduate textbook is so ...
3
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0answers
71 views

why many option contract price less than minimum boundary price?

I downloaded data from NSE(National Stock Exchange) website regarding closing price of European Call Option written on Index. From standard textbook, I read that option contract must satisfy $C(t) ...
4
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1answer
106 views

Fit linear model to higher moments of CAPM

How can one fit a linear model to the higher moments of CAPM in R? Fitting a linear model to the second moment (classical CAPM) would be ...
5
votes
1answer
146 views

Simulate (imaginary) asset prices using random numbers that follow a Frank Copula

I didn't understand how to simulate asset prices by using non normal random numbers. I am assuming that it would be incorrect to use the standard Geometric Brownian Motion, since it is based solely ...
5
votes
3answers
208 views

Bayesian estimation of asset pricing models

I am interested in Bayesian methods in the context of financial economics and quantitative finance and have been looking for research which uses Bayesian parameter estimation on asset pricing models, ...
1
vote
1answer
29 views

Intrepreting the Capital Market Line plot

I am looking at plots of the Security Market (SML) line and Capital market line (CML). The X axis is the beta for the SML and Standard deviation for CML; the y axis is labeled with excess return. ...
3
votes
1answer
62 views

According to Lo and MacKinlay (1990), momentum profits can be divided in 3 parts. What do they represent exactly?

At first, Lo and MacKinlay (When are Contrarian Profits Due to Stock Market Overreaction?, 1990) didn't do it for momentum precisely. However,Kyung-In Park and Dongcheol Kim (Sources of Momentum ...
2
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0answers
33 views

Budget Constraint in Duffie's book

On Page 5 of Duffie's Dynamic Asset Pricing Theory, the budget-feasible set is defined as: $$X(q,e) = {e+D^T\theta \in R_+^s:\theta \in R^N, q\theta \leq 0}$$ Compared to Kerry Back's presentation of ...
3
votes
2answers
629 views

What's the meaning of the intercept in asset pricing model?

I would like to understand the role of alpha (intercept) in the regression-based asset pricing model or $n$-factor models; one of the most famous of those one is the Fama-French 3-factor model. ...
1
vote
3answers
657 views

Is the CAPM beta equivalent to the coefficient estimate of an OLS regression?

The $\beta_i$ of an asset or portfolio is defined as its covariance with the market (which itself therefore has a beta of $\beta_m = 1$). The CAPM looks a lot like a simple linear regression model. Is ...
2
votes
1answer
1k views

How to estimate market integration parameter in Singer-Terhaar model for E(r)?

Singer-Terhaar is part of CFA II and III curriculum. It estimates risk premium for some asset, traded at some local market, as weighted average of expected premiums for the case of (1) local market, ...
1
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3answers
131 views

The Law of One Price in a discrete model

The following question assumes familiarity with the discrete model described in chapter 5 of Steven Roman's "Introduction to the Mathematics of Finance", 2nd edition, Springer 2012. I will not ...
1
vote
1answer
152 views

Proving there exists no arbitrage opportunities given 3 states and 2 assets

Assume there are 3 states of the world: w1, w2, and w3. Assume there are two assets: a risk-free asset returning Rf in each state, and a risky asset with Return R1 in state w1, R2 in state w2, and R3 ...
3
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2answers
3k views

What is the price pressure?

What is the definition of price pressure and what does it imply? In a number of paper I read that the price pressure can influence the portfolio returns; can you explain why and in which way it can ...
4
votes
1answer
312 views

How to prove the “Law of one price” theorem?

There are two subparts to Fundamental Asset Pricing theorem. The Law Of One Price (LOOP thereafter) holds if and only if there exists a state price vector. In a market in which the LOOP holds, the ...
1
vote
1answer
432 views

What is the proper discounting of PIK and non-compounding bullet loans?

This question pertains to two types of loans. Pay-in-kind (PIK) and bullet loans with quarterly payments. 1. PIK Loans A PIK loan is a loan where periodic interest is NOT paid, but added to the ...
5
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6answers
604 views

Semi-strong efficiency and HFT

The semi-strong efficient market hypothesis states that In semi-strong-form efficiency, it is implied that share prices adjust to publicly available new information very rapidly and in an ...
3
votes
1answer
235 views

Constant Relative Risk Aversion

The question: Consider a person with constant relative risk aversion p. (a) Suppose the person has wealth of 100,000 and faces a gamble in which he wins or loses x with equal probabilities. ...
0
votes
1answer
442 views

What constitutes an “odd lot” in corporate bonds trades?

This is important in price discovery and pricing of bonds based on trades. "Odd" lots are traded at lower prices than "round" lots. However I wasn't able to find a definition of "odd" lot anywhere. ...
2
votes
1answer
103 views

Law of large numbers necessary for APT derivation?

The question refers to the well-known Ross (1976) paper with the derivation of the Asset Pricing Theory. In the APT, the return of asset $i$ is driven by a linear factor model: $$ R_i = \alpha_i + ...
2
votes
1answer
94 views

Price an option whose strike price is always lower than the future price of the security

Suppose it is known that the price of a certain security after one period will be one of the $m$ values $s_1,\ldots,s_m$. What should be the cost of an option to purchase the security at time $1$ for ...
4
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0answers
168 views

ERP and FF 3-factor model

In a more conservative estimate than a simple historical average, Fama & French estimate (US) equity risk premium at 3-4% (e.g., Equity Risk Premium, JF, 2002). This suggests that in an APT-like ...
4
votes
1answer
126 views

What are the empirical limitations to testing market efficiency?

I have encountered a rather elegant argument about the limitations of empirically testing for market efficiency, involving the central point that we do not know whether a result is due to the "true ...
3
votes
1answer
65 views

How consequential are violations of the efficient diversification assumption of asset pricing models?

When using asset pricing models such as the CAPM or the Fama-French four factor model to determine the risk-adjusted return of a portfolio, does this strictly require efficient diversification of the ...
0
votes
1answer
47 views

What are the technical events that fluctuate quoted asset (e.g. forex) prices? How does it relate to the purchase of currency contracts?

This is a generic question about the quotations of assets but for the sake of reducing ambiguity, let's consider the EUR/USD exchange rate. If the answer varies for other asset classes, please note ...
5
votes
1answer
293 views

Proving that Absence of Arbitrage does not imply law of one price

I am trying to prove that the Absence of arbitrage statement (AOA) does not necessarily imply the law of one price (LOP). For the definitions of these concepts I am using Cochrane's book "Asset ...
3
votes
2answers
346 views

Validity of CAPM

I came across some literature regarding "Framing Theory" or "Prospect Theory", and the validity of CAPM. I was wondering if you could shed some light on a few questions I have in this regard: ...
3
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0answers
186 views

GMM time-series regression factor model with factors that are not returns

Factor models with factors that are not returns are usually estimated and tested by cross-sectional regressions. However, there is a way to use time-series regression to estimate and test the model. ...
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0answers
52 views

How to map shocks from VAR to news? (Academics)

I am trying to map shocks from VAR to discount-rate and cash-flows news following the paper of Campbell and Vuolteenaho (2004). It is said that news are a linear combination of shocks from VAR at ...