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 ...
- 17k
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 ...
- 6,658
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\...
- 9,421
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 ...
- 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*} \...
- 9,421
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 ...
- 6,990
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 ...
- 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 ...
- 57.7k
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 ...
- 3,768
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 ...
- 1,914
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 ...
- 1,924
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
$\sigma_p^2 = w^2\sigma_A^2 + 2w(1-w)\sigma_A\sigma_B \rho_{AB}+ (1-w)^2\sigma_B^2$
...
- 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 ...
- 57.7k
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, ...
- 57.7k
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 \...
- 15.8k
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 ...
- 3,477
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 ...
- 3,481
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:
$$I\{A\}= \begin{cases} 1 & A\; {\rm happens}...
- 33.9k
4
votes
Accepted
Show that $W_t - \int_0^t \xi_s ds$ is forward-measure-Brownian
(Looking at the question and notation used more closely, the formulation seems to be problematic in couple places.)
General Fact
Let $W$ be standard Brownian motion with respect to filtration $( \...
- 2,619
4
votes
A trillion dollar invention
Sure, because dollars are nominal goods. Perhaps a ticket to Star Wars Episode CXVIII will cost one trillion dollars. If you meant today, without huge changes in the price level:
Yes, there is way ...
- 29.6k
4
votes
Accepted
Difference between double auction and continuous double auction?
So, if a distinction is made, as continuous double auctions are usually just called double auctions, then the difference has to do with frequency. It is easier to have an example.
The New York Stock ...
- 2,006
4
votes
Accepted
Implication of first-order stochastic dominance
We are given two CDFs $F$ and $G$, such that $F$ FOSD $G$ i.e. $F(x) \leq G(x)$ $\forall x$. Consider the random variables $X\sim F$ and $Y\sim G$. Also, suppose $X$ and $Y$ take non-negative values.
...
- 9,421
4
votes
Accepted
Growth in dividends will equal growth of earnings
The textbook probably means growth rate and not absolute growth. Given your assumptions
$$
\frac{\frac{d}{dt}Div_t}{Div_t}=
\frac{\frac{d}{dt}\text{Earnings}_t}{\text{Earnings}_t}
$$
does hold.
- 29.6k
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 ...
- 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 ...
- 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 ...
- 57.7k
3
votes
An agent's expected utility depends only on mean and variance
I think this may not always be true as stated
You say "$U(y_s) = -\frac{1}{2}(\alpha - Y_s)^2$ for $Y_s < \alpha$" so presumably $U(y_s) = 0$ for $y_s \ge \alpha$ to avoid utilities decreasing as ...
- 4,765
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 ...
- 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 ...
- 9,907
3
votes
What is the No Free Lunch Axiom?
First, to give a little more background to 123's answer, a production set $Y$ is the set of all feasible production values. With $y \in Y$, $y$ is a vector in $\mathbb{R}^L$, where positive elements ...
- 6,658
Only top scored, non community-wiki answers of a minimum length are eligible