Visualizing the Variance of a Random Variable

2011 ◽  
Vol 18 (01) ◽  
pp. 71-85
Author(s):  
Fabrizio Cacciafesta
Keyword(s):  
Stochastic Dominance ◽  
Mean Absolute Error ◽  
Random Variable ◽  
Absolute Error ◽  
Second Order ◽  
Taylor Formula ◽  
Order Stochastic Dominance ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Options Theory

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

scholarly journals Second-Order Stochastic Dominance, Reward-Risk Portfolio Selection, and the CAPM

2008 ◽  
Vol 43 (2) ◽  
pp. 525-546 ◽  
Author(s):  
Enrico De Giorgi ◽  
Thierry Post
Keyword(s):  
Stock Returns ◽  
Portfolio Selection ◽  
Stochastic Dominance ◽  
Risk Model ◽  
Second Order ◽  
Order Stochastic Dominance ◽  
Market Portfolio ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Mean Variance

AbstractStarting from the reward-risk model for portfolio selection introduced in De Giorgi (2005), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. In contrast to the mean-variance model, reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on a few basic principles, including consistency with second-order stochastic dominance. With complete markets, we show that at any financial market equilibrium, reward-risk investors' optimal allocations are comonotonic and, therefore, our model reduces to a representative investor model. Moreover, the pricing kernel is an explicitly given, non-increasing function of the market portfolio return, reflecting the representative investor's risk attitude. Finally, an empirical application shows that the reward-risk CAPM captures the cross section of U.S. stock returns better than the mean-variance CAPM does.

scholarly journals Whale Optimization Algorithm for Multiconstraint Second-Order Stochastic Dominance Portfolio Optimization

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Q. H. Zhai ◽  
T. Ye ◽  
M. X. Huang ◽  
S. L. Feng ◽  
H. Li
Keyword(s):  
Portfolio Optimization ◽  
Optimization Algorithm ◽  
Stochastic Dominance ◽  
Optimization Model ◽  
Second Order ◽  
Whale Optimization Algorithm ◽  
Order Stochastic Dominance ◽  
Whale Optimization ◽  
Portfolio Optimization Model ◽  
Second Order Stochastic Dominance

In the field of asset allocation, how to balance the returns of an investment portfolio and its fluctuations is the core issue. Capital asset pricing model, arbitrage pricing theory, and Fama–French three-factor model were used to quantify the price of individual stocks and portfolios. Based on the second-order stochastic dominance rule, the higher moments of return series, the Shannon entropy, and some other actual investment constraints, we construct a multiconstraint portfolio optimization model, aiming at comprehensively weighting the returns and risk of portfolios rather than blindly maximizing its returns. Furthermore, the whale optimization algorithm based on FTSE100 index data is used to optimize the above multiconstraint portfolio optimization model, which significantly improves the rate of return of the simple diversified buy-and-hold strategy or the FTSE100 index. Furthermore, extensive experiments validate the superiority of the whale optimization algorithm over the other four swarm intelligence optimization algorithms (gray wolf optimizer, fruit fly optimization algorithm, particle swarm optimization, and firefly algorithm) through various indicators of the results, especially under harsh constraints.

Sign in / Sign up

Export Citation Format

Share Document