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
9 votes
Accepted

given someone's past investing history, is there a way to calculate his risk aversion?

Generally speaking no. You wouldn't be able to distinguish re-balancing for risk aversion reasons from re-balancing motivated by changes in expected returns or the co-variance of returns. Consider ...
BKay's user avatar
  • 16.3k
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 ...
Matthew Gunn's user avatar
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 ...
Bayesian's user avatar
  • 5,280
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 ...
M3RS's user avatar
  • 1,087
5 votes
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Can data be created using Monte Carlo Simulation

YES I’ll give an example in R. ...
Dave's user avatar
  • 390
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 ...
Alecos Papadopoulos's user avatar
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 ...
Dan Piponi's user avatar
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 ...
Giskard's user avatar
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3 votes
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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 ...
jmbejara's user avatar
  • 9,345
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....
T123's user avatar
  • 303
2 votes
Accepted

Two asset Markowitz Portfolio Optimization and Capital-Market Line construction for a Given Risk Free Rate

The Sharpe ratio tells us the amount of excess return we get for taking on each additional unit of portfolio standard deviation. $$\frac{\mu_p - r_f}{\sigma_p }$$ We are looking for the combination ...
BKay's user avatar
  • 16.3k
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 ...
Theoretical Economist's user avatar
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 ...
VARulle's user avatar
  • 6,725
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 ...
Herr K.'s user avatar
  • 15.4k
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 ...
kurtosis's user avatar
  • 410
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 ...
Dave Harris's user avatar
  • 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 ...
Henry's user avatar
  • 4,755
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 ...
Iñaki Viggers's user avatar
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 ...
Pedro Cavalcante's user avatar
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 ...
Brian Romanchuk's user avatar
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, ...
Mico's user avatar
  • 420
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 ...
mootmoot's user avatar
  • 381
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 ...
Dave Harris's user avatar
  • 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 ...
Alecos Papadopoulos's user avatar

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