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
8
votes
Does my research prove market inefficiency?
The efficient market hypothesis does not imply that there are no patterns!
As Eugene Fama pointed out decades ago, any test of market efficiency is a joint test of market efficiency and an asset ...
- 906
7
votes
Accepted
Quadratic utility: monotonicity and risk aversion
Quadratic utility is given by
$$u(w) = w - b w^2$$
which has derivative
$$u'(w) = 1- 2b w$$
such that for high levels of $w, u'(w)<0$. That is, the utility is not everywhere increasing. This may be ...
- 5,291
5
votes
Accepted
5
votes
Utility theory and portfolio optimization: utility of what exactly?
In mean-variance optimisation I have typically seen the below quadratic utility function where $𝐸[𝑅]$ is the expected return (or mean return) of a possible portfolio, $\sigma^{2}$ is the return ...
- 1,097
4
votes
The efficient frontier in mean variance criterion
Using $\mathbb E$ for the expected value symbol, $E_R$ and $V_R$ for the mean and the avriance of returns $R$, for a utility function of the form
$$U(R) = \ln(1+R)$$
the second-order Taylor expansion ...
- 33.9k
3
votes
Can data be created using Monte Carlo Simulation
The library TensorFlow Probability is designed for this purpose. In fact, the first example currently at the web site involves the creation of synthetic data which is then used for a regression ...
- 131
3
votes
Budget line for mean variance utility
For example, considering the allocation between two identical assets with identical mean and variance but independent correlation. Then, the allocated portfolio reduces the variance but keeps the mean ...
- 29.6k
3
votes
Accepted
Optimal consumption in Merton-like portfolio choice model with constant wage
$\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\E}{\mathbb{E}}
%short command for inseting abbreviated "such that" in a ...
- 9,355
2
votes
given someone's past investing history, is there a way to calculate his risk aversion?
adding to the previous answer, i found this paper here where the authors just did that. They controlled for other effects and the shape of the utility function so i guess its possible..
https://papers....
- 303
2
votes
Accepted
Short call in binomial option pricing model
One reason why you might want to do this, and perhaps is the motivation for this example, is that it gives you a simple example for thinking about option pricing.
Under some assumptions, the value of ...
- 2,156
2
votes
risk aversion and convexity of indifference curve
This seems to be specific to the CFA exam and is a badly formulated question. First, an indifference curve for some fixed utility level can be viewed as a function mapping $\sigma$ to $\mu$. At any ...
- 7,119
2
votes
risk aversion and convexity of indifference curve
It would seem that both options are correct given the specific mean-variance utility function.
Use $\mu$ to denote the expected value. In the $(\sigma,\mu)$-plain, an indifference curve representing a ...
- 15.8k
1
vote
Implications for the economics literature of possible mistakes in Black-Scholes-Merton option pricing?
You can derive the Black-Scholes formula just by assuming (a) stocks obey a lognormal distribution and (b) this distribution has a risk neutral expectation. I don’t see how that can be ‘wrong’ due to ...
- 1,358
1
vote
Negative Risk Free Rate Sharpe Ratio
You should be fine to use negative interest rates for the risk-free rate when calculating a Sharpe ratio. If rates are negative, they are negative. That does not change the calculation of excess ...
- 410
1
vote
Does my research prove market inefficiency?
The latest Freakonomics podcast topic Stupidest money may shed some light.
I just quote part of the conversation from John Bogle:
The markets are highly efficient — although, importantly, not
...
- 381
1
vote
Accepted
Estimated betas and optimal portfolio
Let me begin with noting that models such as the CAPM have been extensively falsified, beginning with Mandelbrot in 1963 and ending with the Fama-MacBeth testing in 1973. Other falsifications ...
- 2,006
1
vote
Accepted
How to calculate standard deviation of a portfolio?
You could say the return on Johnson & Johnson is a random variable $R_J$ with expected value $\mu^{\,}_J$ and variance $E[(R_P-\mu^{\,}_P)^2] = \sigma^2_J$, and on Ford is $R_F$ with expected ...
- 4,765
1
vote
log returns in finance
Why are log returns used in finance?
It really is about compactness when devising models. The mathematical property of logarithms $$log(S_{t+n}/S_t)=log(S_{t+n})-log(S_t)$$ makes log returns more ...
- 1,807
1
vote
A question about Lagrange multiplier(when $\lambda=0$)
A $\lambda = 0$ means that the objetive function's derivative with respect to the restriction is zero. In more intuitive terms, one cannot change the expected utility of consumption by relaxing or ...
- 778
1
vote
Flat Term Structure and Immunized Portfolio Strategy
Note: This answer is preliminary, as I am unsure about some components of the question. I will note that it is a very long time since I studied portfolio immunization, and so I am describing how this ...
- 9,907
1
vote
Accepted
Two Funds Separation & CAPM
An equlibrium is a property of an entire market, not of any given investor's portfolio. The CAPM is an equilibrium theory.
In equilibrium, all (nontoxic!) assets must have non-negative prices. Hence, ...
- 420
1
vote
Does my research prove market inefficiency?
By itself, no it does not, at least how I am understanding your post. While I am an opponent of the Efficient Market Hypothesis, what you would need to show is that there is a "free lunch," with your ...
- 2,006
1
vote
How do economists model VNM-rationality violation?
It appears you are looking for literature on Ambiguity Aversion and/or "Uncertainty Aversion".
You can start by looking up the work of L.G Epstein, I. Gilboa, and D. Schmeidler.
It is an attempt to ...
- 33.9k
Only top scored, non community-wiki answers of a minimum length are eligible