10 votes
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Why stochastic dominance is "stochastic"?

In the below figure, CDF $F(\cdot)$ is first-order stochastically dominated by $G(\cdot)$. But $X_1$ and $X_2$ fall within the support of both distributions. So it would be possible to draw $X_1$ from ...
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9 votes

An agent's expected utility depends only on mean and variance

In order to understand this problem, I will work through the generic case. Say that a user had generalized quadratic (Bernoulli) utility, similar to your problem: $$u(x) = \beta x^2 + \gamma x$$ and ...
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  • 6,409
8 votes
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An agent's expected utility depends only on mean and variance

\begin{eqnarray*} \displaystyle U(L) & = &\sum_{s=1}^{S}\pi_s U(Y_s) = \sum_{s=1}^{S} \left(-\frac{1}{2}\pi_s(\alpha - Y_s)^2\right) = -\frac{1}{2}\sum_{s=1}^{S} \left(\pi_s(\alpha^2 + Y_s^2-2\...
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  • 5,257
7 votes
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What is the equation $\mathbb{E}[mR]=1$?

This is an important result in financial economics (asset pricing) but not trivial to explain intuitively. I do my best to give you the big picture and get you started on your research. R is the ...
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  • 826
7 votes

Prove that variance of a portfolio cannot exceed variance of individual assets

Let $P = \alpha A + (1-\alpha) B$ where $A$ and $B$ are returns (random) from the two assets, and $P$ is their portfolio. Variance of portfolio $P$ can therefore be written as \begin{eqnarray*} \...
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  • 5,257
6 votes

Unintended consequences from "fixing" the US financial system

1) Would lead to the return of general panic led bank runs, and introduce additional instability to the system. It´s not generally appreciated, that 19th century bank runs were not just a symptom of ...
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  • 2,720
6 votes
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Financial Economics Textbooks

The recommended books are decent. From these two I'd go with Bailey first and if you're comfortable with that, then LeRoy & Werner. The latter requires some background in linear algebra and ...
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  • 1,218
6 votes
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Good Europe focused economics blogs

With a European view: The CEPR VOX EU: an economics blog created by the Centre for Economic Policy Research, which promotes research excellence and policy relevance in European economics. It covers a ...
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  • 6,652
6 votes
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Are no arbitrage models and equilibrium models equivalent?

...no-arbitrage models (such as Black-Scholes and HJM) are equivalent to equilibrium models (such as CAPM or C-CAPM). Short Answer Yes, for models where asset prices are assumed to be Ito ...
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  • 2,569
6 votes
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Is it common to see hedge funds go bankrupt?

Have any hedge funds gone bankrupt as a consequence of the "GameStop scandal"? This is very difficult, almost virtually impossible to say as events unfold. In order to understand why ...
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  • 43.5k
6 votes

Most notable papers in Economics in 2021

This is an opinion question, but I'll give my opinion. In terms of methods, I like Arkhangelsky et al.'s synthetic diff-in-diff. In terms of applied economics, I liked Goncalves and Mello's study of ...
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6 votes

Most notable papers in Economics in 2021

I think the randomized trial of mask effectiveness is one of the most notable economic papers in 2021. This is not a pure economics paper and it is published in science that does not specialize in ...
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  • 1,425
6 votes

Most notable papers in Economics in 2021

Some papers that interested me this year (in game theory): Subgame-perfect equilibrium in games with almost perfect information: Dispensing with public randomization They show the seminal result of ...
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5 votes
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Risk Premia in Continuous Time

The easiest way to model short-term but risky debt in continuous time is to have your $\psi$ be the increment of a compound Poisson process. Jumps in this process correspond to events that might or ...
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5 votes
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Dealing with Missing Data when Testing the CAPM

Easiest fix: if you're worried about it you should value weight your results. This is suggest by, for instance, Kothari, Shanken and Sloan (1995). Firms that are delisted tend to have extremely small ...
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  • 2,006
5 votes
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Deriving the Modigliani--Miller Theorem

The first equation can be written as: $$ r_E(Levered) = \frac{E+D}{E}r_E(Unlevered) - \frac{D}{E}r_D $$ Then, isolating the unlevered return gives: $$ r_E(Unlevered) = \frac{E}{E+D}r_E(Levered) + \...
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  • 714
5 votes

When a support function is found to be more profitable than the primary business

The Aerobie Sports company mostly makes odd-ball equipment for having a catch. But they made a coffee maker called the Aeropress as a side project and now it makes up more than half of their sales. ...
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  • 15.9k
5 votes
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Prove that variance of a portfolio cannot exceed variance of individual assets

Let $w$ denote the weight on $A$ so that $1-w$ is the weight on $B$. Recall from the properties of variance that $\sigma_p^2 = w^2\sigma_A^2 + 2w(1-w)\sigma_A\sigma_B \rho_{AB}+ (1-w)^2\sigma_B^2$ ...
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  • 826
5 votes
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Who invented these key notions in Finance?

Net Present Value (NPV) as a soft concept existed probably even in antiquity but it was formalized and made popular by Irving Fisher in his book the Rate of Interest. Internal rate of return is ...
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5 votes
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Properties of Financial Markets in Real Life

Equilibria: in the macroeconomic sense of aggregate equilibrium where all markets clear, markets are most likely never in any equilibrium but rather in constant flux between different equilibria, ...
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5 votes
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Elasticity of demand functions

In the case of linear demand $d_i=a_i-x_iP$ (assuming $d_i$ is quantity demanded by individual $i$), the price elasticity of demand at point $(d_i,P)$ is \begin{equation} \epsilon_i(d_i,P)=x_i\cdot \...
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  • 14.6k
5 votes

Most notable papers in Economics in 2021

Despite the fact that I am tired of reading paper's on natural experiments, there is one contribution in this field that captured my attention. Not only the topic is fascinating (Switzerland offered ...
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  • 2,692
4 votes

What is the significance of the Hansen-Jagannathan bound?

Fundamental theorem of asset pricing tells us that if there is no arbitrage, there must exist a positive random variable $M$ (also called stochastic discount factor) such that for any return $R$, we ...
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  • 1,036
4 votes
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Black-Litterman---in what way are expected returns hard to estimate?

Your question relates more broadly to modern portfolio theory, and can be illustrated via mean-variance analysis of a univariate time-series. The extension to the multi variate (normal) setting, is ...
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  • 311
4 votes

Capital in a credit frictions model

The paper is assuming that some form of "law of large numbers" (LLN) applies for the continuum. The expected value of capital for an individual agent is $$\mathbb{E}[R\cdot 1_{R\geq R^*}]=\int_{R^*}^1 ...
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4 votes

When a support function is found to be more profitable than the primary business

Microplane graters grew out of a company that was manufacturing dot-matrix printer parts, using a process that created extremely sharp metal bands— which was, at the time, more of a liability than a ...
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4 votes
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Show that $W_t - \int_0^t \xi_s ds$ is forward-measure-Brownian

(Looking at the question and notation used more closely, the formulation seems to be problematic in couple places.) General Fact Let $W$ be standard Brownian motion with respect to filtration $( \...
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  • 2,569
4 votes
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Difference between double auction and continuous double auction?

So, if a distinction is made, as continuous double auctions are usually just called double auctions, then the difference has to do with frequency. It is easier to have an example. The New York Stock ...
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  • 1,986
4 votes

A trillion dollar invention

Sure, because dollars are nominal goods. Perhaps a ticket to Star Wars Episode CXVIII will cost one trillion dollars. If you meant today, without huge changes in the price level: Yes, there is way ...
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  • 26.7k
4 votes
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Implication of first-order stochastic dominance

We are given two CDFs $F$ and $G$, such that $F$ FOSD $G$ i.e. $F(x) \leq G(x)$ $\forall x$. Consider the random variables $X\sim F$ and $Y\sim G$. Also, suppose $X$ and $Y$ take non-negative values. ...
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  • 5,257

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