Skip to main content
11 votes
Accepted

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 ...
Ubiquitous's user avatar
  • 16.9k
10 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 ...
Kitsune Cavalry's user avatar
  • 6,638
9 votes
Accepted

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\...
Amit's user avatar
  • 8,881
7 votes
Accepted

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 ...
farnsy's user avatar
  • 836
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*} \...
Amit's user avatar
  • 8,881
6 votes
Accepted

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 ...
John L.'s user avatar
  • 1,228
6 votes
Accepted

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 ...
emeryville's user avatar
  • 6,945
6 votes
Accepted

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 ...
Michael's user avatar
  • 2,619
6 votes
Accepted

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 ...
1muflon1's user avatar
  • 56.8k
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 ...
Michael Gmeiner's user avatar
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 ...
WilliamT's user avatar
  • 1,819
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 ...
Walrasian Auctioneer's user avatar
5 votes
Accepted

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 $\sigma_p^2 = w^2\sigma_A^2 + 2w(1-w)\sigma_A\sigma_B \rho_{AB}+ (1-w)^2\sigma_B^2$ ...
farnsy's user avatar
  • 836
5 votes
Accepted

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 ...
1muflon1's user avatar
  • 56.8k
5 votes
Accepted

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, ...
1muflon1's user avatar
  • 56.8k
5 votes
Accepted

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 \...
Herr K.'s user avatar
  • 15.4k
5 votes
Accepted

Unresolved paradoxes or puzzles in financial economics

Merger paradox from industrial organization: I believe a fairly good overview is here: Garcia, F, Paz y Miño, JM, Torrens, G. The merger paradox, collusion, and competition policy. J Public Econ ...
RegressForward's user avatar
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 ...
Bertrand's user avatar
  • 3,371
5 votes
Accepted

Can a single dummy variable be made to meet multiple criteria?

"Dummy variables" are binary variables, i.e. indicator functions. The indicator function takes the value $1$ if the associated event happens: $$I\{A\}= \begin{cases} 1 & A\; {\rm happens}...
Alecos Papadopoulos's user avatar
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 ...
Giskard's user avatar
  • 29.2k
4 votes
Accepted

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 ...
Dave Harris's user avatar
  • 2,006
4 votes
Accepted

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 $( \...
Michael's user avatar
  • 2,619
4 votes
Accepted

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. ...
Amit's user avatar
  • 8,881
4 votes
Accepted

Growth in dividends will equal growth of earnings

The textbook probably means growth rate and not absolute growth. Given your assumptions $$ \frac{\frac{d}{dt}Div_t}{Div_t}= \frac{\frac{d}{dt}\text{Earnings}_t}{\text{Earnings}_t} $$ does hold.
Giskard's user avatar
  • 29.2k
4 votes
Accepted

What accounts for the high GDP of the United States?

Looking at gross output (which includes using the outputs of other industries) and value-added (largely wages and profits) by industry you get numbers like this for 2017 in USD trillion. Adding up ...
Henry's user avatar
  • 4,765
4 votes
Accepted

Volatility and the stock market

There seems to me no relationship between the general direction of price movements and market volatility. Clearly the market disagrees with you. As the saying goes, "markets go up in an escalator ...
Michael's user avatar
  • 2,619
4 votes
Accepted

What would happen if we eliminated fractional reserve banking while expanding the money supply?

You are actually not the first person to wonder about this, there is a whole literature on this topic (although most of it is now out of date). What you describe is called “the Chicago Plan”. It was ...
1muflon1's user avatar
  • 56.8k
3 votes

Financial Economics Textbooks

ASSET PRICING THEORY: Cochrane, Asset Pricing is a good book in that it displays the way that hard-core asset pricers see the world. Huang and Litzenberger, Foundations for Financial Economics is ...
Fix.B.'s user avatar
  • 2,666
3 votes
Accepted

A trillion dollar invention

A trillion dollars is nominal, there's no indication of when this invention is going to be worth a trillion dollars. Maybe in 100 years, this question would be worth a trillion dollars, but a Coke ...
olliek's user avatar
  • 46
3 votes

Given fractional banking and the multiplier effect, for every dollar in circulation, how many dollars in spendable money exist?

The initial statements about fractional reserve banking are not a question. The simplified example you give does not reflect the complexity of bank lending. The article "Money Creation in the Modern ...
Brian Romanchuk's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible