# Questions tagged [asset-pricing]

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121 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 ...
22 views

### GRS TEST decision rule [closed]

I have a question regarding the interpretation of the GRS test. I have already looked into a question previously posed by some other users. One can find it here: how to interpret the GRS F test values?...
32 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 ...
15 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 ...
105 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 ...
195 views

### SDF as an affine transformation of the tangency portfolio

I'm studying this paper. In the formulation of the theoretical setup they state: Our goal is to explain the differences in the cross-section of returns $R$ for individual stocks. Let $R_{t+1, i}$ ...
2k 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 ...
127 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 ...
79 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 $K=150$)...
38 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 ...
611 views

### Asset pricing textbooks

What are some asset pricing textbooks that give a solid introduction into the field? I suggest one textbook per answer with a list of its pros and cons.
77 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 ...
39 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 \$...
68 views

### SDF derivation by a stochastic process

I have a stochastic process to model the stochastic discount factor (SDF) with M: $$dM_t = aM_tdt + bM_t d Z_t$$ where, $Z_t$ is a standard brownian motion. How do I show ...
382 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 ...
59 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 ...
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 ...
504 views

### Numeraire correlated to the traded asset

The Fundamental Theorem of Asset Pricing states that: \begin{align*} \frac{X_0}{N_0} &= \mathbb{E}^N{ \left[ \frac{X(t)}{N(t)}|\mathcal{F}_0 \right] } \end{align*} The usual conditions apply (both ...
356 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 ...
212 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 ...
108 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 ...
1k 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 ...
143 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 ...
6k views

### What is the Most Efficient Way to Calculate the Internal Rate of Return IRR?

I have built a program that prices financial assets and it does this in part by calculating the IRR. The problem is that it does not run as quickly as I would like it to. I currently use the Newton-...
41 views

### By how much do specific asset correlations increase during a market downturn?

It is well-known that asset return correlations of stocks increase during market downturns. But are there any general properties derived from empirical observation or evidence regarding by how much ...
199 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 ...
83 views

### How to simulate asset prices/returns that display market regimes?

Are there any techniques that can make a multivariate random number generating process for stock prices/returns, like geometric Brownian motion via Cholesky, also include the simulation of a finite ...
27 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 ...
62 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 ...
161 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 ...
78 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 ...
46 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 ...
294 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 ...
93 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?
278 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?
37 views

### Some questions to canonical correlations between principle components and asset pricing factors using R

I have done a asympotical principle component analysis (APCA), using eigen() in R, of the covariance matrix of a global dataset of excess returns. I took the ...
85 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 ...
43 views

### Use of Macaulay Duration to calculate the Funds Transfer Pricing Cost of an Amortizing Mortgage

I am asked to comment on the Funds Transfer Pricing methodology used by our Treasury to assign a Cost of Funds to a Loan. This is the current methodology: Let us say there is a 2 year loan with an ...
173 views

### GRS Test in R with robust residuals

I'm testing certain asset pricing factor models (e.g. Fama and French 3 factor model) and want to check if the alphas of my time series regressions are jointly zero. Most papers use the Gibbons, Ross,...
70 views

### Arbitrage strategy from Arrow Securities

I had this exercise and I calculated the prices of the Arrow Securities, π1 = 0.5 and π2 = -0.2. I know that π2 is not arbitrage-free because -0.2 < 0, but I do not understand that how to interpret ...
89 views

### Can we use risk-neutral pricing to price a stock or a bond?

Can you please tell me whether if I can used risk-neutral pricing approach to price a stock or a bond ? (i.e. discount with risk free rate the future cashflows) ? Thank you very much!
78 views

### Stock Price as Numeraire, Two Stocks & One Money Market Account

We have two uncorrelated Stock price processes and the classical Money-Market (MM) account. Under the MM Numeraire, both stocks are Martingales when discounted by the MM, as usual. Question: I would ...
46 views

### Applying GRS-test on non-normal residuals with autocorrelation

Is it valid to apply GRS-test (Gibbons, Ross and Shanken 1989) on non-normal and autocorrelated residuals? I got residuals using 10 test-assets regressed on 3-factor and carhart. If it is valid, how ...
111 views

### Asset Pricing and inferences - Intercept and relationship to returns

Ideally this question is very similar to What's the meaning of the intercept in asset pricing model? I am regressing a "buys minus sells" portfolio returns to the Carhart factors. The intercept ...
94 views

### true or false: the risk-neutral measure is useless in this situation

Example 2 of this Wiki article on the risk-measure describes how a stock price $S_t$ that is modeled with Geometric Brownian motion with drift $\mu$ $$dS_t = \mu S_t dt + \sigma S_t dW_t$$ can be ...
20 views

### Adding an economic policy uncertainty (EPU) variable to Fama French model

I would like to do test the significance of a new variable that I would include in the Fama French 5 factor model. The new variable would be the Economic Policy Uncertainty (EPU) index from Baker et ...
103 views

### Risk Neutral Pricing, a quick question [closed]

I am a newbie. The risk neutral pricing has the following formulation: $$P=\frac{\hat{E(d)}}{R}$$, But the discounted expected value has the formulation of: $$P=\frac{E(d)}{R}$$. The text book ...
84 views

### Fama Macbeth and Momentum factor

I am working on a Fama MacBeth regression with excess returns on the LHS and Size, Value an Momentum factors on the RHS. In literature, the Momentum factor is often definded as the cumulative past 6 ...
54 views

### How to find the derivative for a multi-factor geometric brownian motion model

Does anyone know how to find the derivative for a multi-factor geometric brownian motion model $\frac { dS_{i}}{S_{i}}$. I have seen solutions for the standard GBM model however I suspect that the ...
61 views

### How do I maximize my expected utility of wealth?

Suppose I have a utility function say $U(p)=p^{1/2}$ and I bet on a basketball game. I have my initial investment, payouts and probabilities of winning, how can I determine the maximum I need to bet ...