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Volatility (finance) In finance, volatility (usually denoted by "σ") is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price ...
The variance is the square of differences of measurements from the mean divided by the number of samples. The standard deviation is the square root of the variance.The standard deviation of the continuously compounded returns of a financial instrument is called volatility.
Modern portfolio theory. Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is ...
Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. [1][2] Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the ...
The amount of information (the covariance matrix, specifically, or a complete joint probability distribution among assets in the market portfolio) needed to compute a mean-variance optimal portfolio is often intractable and certainly has no room for subjective measurements ('views' about the returns of portfolios of subsets of investable assets ...
Expected shortfall (ES) is a risk measure —a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst of cases. ES is an alternative to value at risk that is more sensitive to the shape of the ...