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The standard form of the Omega ratio is a non-convex function, but it is possible to optimize a transformed version using linear programming. [4] To begin with, Kapsos et al. show that the Omega ratio of a portfolio is: = [() +] + The optimization problem that maximizes the Omega ratio is given by: [() +], (), =, The objective function is non-convex, so several ...
The market portfolio is unobservable: The market portfolio in practice would necessarily include every single possible available asset, including real estate, precious metals, stamp collections, jewelry, and anything with any worth. The returns on all possible investments opportunities are unobservable.
The rate of return on a portfolio can be calculated indirectly as the weighted average rate of return on the various assets within the portfolio. [3] The weights are proportional to the value of the assets within the portfolio, to take into account what portion of the portfolio each individual return represents in calculating the contribution of that asset to the return on the portfolio.
Portfolio return is the proportion-weighted combination of the constituent assets' returns. Portfolio return volatility is a function of the correlations ρ ij of the component assets, for all asset pairs (i, j). The volatility gives insight into the risk which is associated with the investment.
For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().
Risk-weighted asset (also referred to as RWA) is a bank's assets or off-balance-sheet exposures, weighted according to risk. [1] This sort of asset calculation is used in determining the capital requirement or Capital Adequacy Ratio (CAR) for a financial institution.
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If portfolio weights are largely a function of estimation errors, then Ex-post performance of a growth-optimal portfolio may differ fantastically from the ex-ante prediction. Parameter uncertainty and estimation errors are a large topic in portfolio theory. An approach to counteract the unknown risk is to invest less than the Kelly criterion.