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8 votes

Do stock returns show positive skewness?

I think most people agree that aggregate (index) stock returns have negative skewness. However, this does not appear to be the case for individual stock returns. These two papers find that average ...
fes's user avatar
  • 1,727
8 votes

The possible preferences of investors for higher than first 2 moments of return distribution?

Investor preferences for higher level moments are probably most easily explained by behavioral finance. Investors' tendency to overvalue out-sized positive and negative outcomes, such as gamblers' ...
David Addison's user avatar
5 votes
Accepted

Maximum skewness portfolio solution derived from its Lagrangean formulation

Unfortunately, there exist no closed form for this. The Lagrangean reads $$ L(w,\lambda)=w^TM_3(w\otimes w)-\lambda(w^T\mathbf{1}-1) $$ with first order conditions $$ \begin{align} \frac{\partial L }{\...
Kermittfrog's user avatar
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4 votes
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How to add the effect of skewness in the portfolio optimisation objective function?

Let's derive a possible approach from utility theory. Our investor is risk averse and exhibits CARA utility using an exponential utility function with risk aversion parameter $\gamma>0$ (risk ...
Kermittfrog's user avatar
  • 6,737
3 votes

What is better: A negatively skewed return or a positively skewed returns distribution?

The usual answer is that most risk assets tend to exhibit left-skew, with correlations ->1 into the left tail (ie diversification breaks down). And so positively skewed assets have attractive ...
demully's user avatar
  • 5,071
3 votes

Is positive skewness preferences rational or irrational?

I think the usual argument is that if an investor is maximizing expected log wealth, then this implies preference for higher odd order moments (mean return, skew, etc.) and for lower even order ...
steveo'america's user avatar
2 votes
Accepted

Vol skew and spot-vol correlation

Suppose you were to price 2 instruments: a strongly OTM put and a strongly OTM Call. In the standard BS settings, instantaneous volatility is assumed to be constant. Consequently, the implied ...
Quantuple's user avatar
  • 14.7k
2 votes
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Is there a stochastic equation which can model returns according to its four moments?

I suggest you have a look at the paper: Schloegel, Erik (2010) "Option Pricing Where the Underlying Assets Follow a Gram/Charlier Density of Arbitrary Order", Journal of Economic Dynamics and Control,...
LocalVolatility's user avatar
2 votes
Accepted

SABR model: from calibration to mapping the smile/skew in a graph

You would simply calculate the prices of various strike options using your parameters, then calculate the black scholes implied vol of each option. Did I miss the point of your question ?
dm63's user avatar
  • 17.2k
2 votes
Accepted

Are momentum returns negatively skewed?

From Daniel-Moskowitz ("Momentum Crashes") you can see that equity CSMOM has negative skewness. However, this is less clear for other asset classes. From their table 11 you can see that ...
fes's user avatar
  • 1,727
2 votes

How to add the effect of skewness in the portfolio optimisation objective function?

Instead of starting from a CARA utility function like how the other answer does, an alternative for incorporating portfolio skewness in the mean-variance model's objective function, without risk-...
develarist's user avatar
  • 3,030
2 votes

Higher moments arbitrage

I'm not sure if this would qualify as "empirical work" but you should definitely read Dynamic Hedging if you haven't already. Taleb talks a lot about this. To be more specific, have a look at page 264,...
Karan Pillai's user avatar
2 votes
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Modelling Skew when using ARMA Time Series

Conceptually, if you want constant conditional skewness, you could simply choose an error distribution that is skewed for your ARMA model. ARMA only restricts the conditional mean of the time series ...
Richard Hardy's user avatar
1 vote

What is better: A negatively skewed return or a positively skewed returns distribution?

It's a little simplistic to say that positive skew is better, you could for example have a return distribution which is negatively skewed but has a mean of 10%, versus a positively skewed one with a ...
deftfyodor's user avatar
1 vote
Accepted

Alternative low-moment measure of skewness

Pearson 2 skewness, which compares mean and median, lying between $-3$ and $3$ while being zero for symmetric distributions, was introduced by Yule, G. U. and Kendall, M. G. (1950), An Introduction ...
develarist's user avatar
  • 3,030
1 vote

Contribution of an asset's variance, skewness and kurtosis to its portfolio weight?

It is not clear that this allocation would be useful or even possible. Suppose you had a portfolio of two assets and that the optimal weights you had derived, based on a mean-variance approach were 0....
Attack68's user avatar
  • 10.7k
1 vote

The possible preferences of investors for higher than first 2 moments of return distribution?

The argument I have seen for higher order moments follows from an expansion of log wealth: \begin{align} log(W) &= log(W_0 (1+r))\\ &= log(W_0) + log(1 + E[r] + r - E[r])\\ &= log(W_0) + ...
steveo'america's user avatar
1 vote

What are some heurestics you could use to judge if skew is cheap or expensive? If any?

Another example of a thing you can do. Every day I receive a chart showing the skew, i.e the IV versus strike for S&P options. Don't throw all those out the next day, save a few of them and tape ...
nbbo2's user avatar
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1 vote
Accepted

What are some heurestics you could use to judge if skew is cheap or expensive? If any?

For example you could ask yourself what the realized volatility will be if the stock were to be at 80 at some time in the future. If the answer is ‘much higher than the realized volatility when the ...
dm63's user avatar
  • 17.2k
1 vote

Relationship mean variance efficiency and skewness of the return distribution?

Mean-variance efficiency generally only considers the first two moments. Skew and kurtosis are outside of it, and Sharpe is commonly criticized for not accounting for skew and kurtosis (leading to ...
Chris's user avatar
  • 1,643
1 vote
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SKEW Index as parameter in lognormal distribution

The formula in your skew function is one of skew normal distribution. That distribution has a limit on skew parameter, while in the real world there is no such limit. From personal experience, few ...
onlyvix.blogspot.com's user avatar

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