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The risk-free asset has zero variance in returns if held to maturity (hence is risk-free); it is also uncorrelated with any other asset (by definition, since its variance is zero). As a result, when it is combined with any other asset or portfolio of assets, the change in return is linearly related to the change in risk as the proportions in ...
(A portfolio is mean-variance efficient if there is no portfolio that has a higher return and lower risk than those for the efficient portfolio. [1]) Mean-variance efficiency of the market portfolio is equivalent to the CAPM equation holding. This statement is a mathematical fact, requiring no model assumptions.
Resampled efficient frontier is a technique in investment portfolio construction under modern portfolio theory to use a set of portfolios and then average them to create an effective portfolio. This will not necessarily be the optimal portfolio, but a portfolio that is more balanced between risk and the rate of return.
Risk premium is the product of the market price of risk and the quantity of risk, and the risk is the standard deviation of the portfolio. The CML equation is : R P = I RF + (R M – I RF)σ P /σ M. where, R P = expected return of portfolio I RF = risk-free rate of interest R M = return on the market portfolio σ M = standard deviation of the ...
However, in this case the value at risk becomes equivalent to a mean-variance approach where the risk of a portfolio is measured by the variance of the portfolio's return. The Wang transform function (distortion function) for the Value at Risk is g ( x ) = 1 x ≥ 1 − α {\displaystyle g(x)=\mathbf {1} _{x\geq 1-\alpha }} .
This model provides a rapid update of market variance which is incorporated into the update of F, resulting in a more dynamic model of risk. In particular it accounts for the convergence of asset returns and consequent loss of diversification that occurs in portfolios during periods of market turbulence.
Bootstrapping is a procedure for estimating the distribution of an estimator by resampling (often with replacement) one's data or a model estimated from the data. [1] Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates.
It is a variant of MAPE in which the mean absolute percent errors is treated as a weighted arithmetic mean. Most commonly the absolute percent errors are weighted by the actuals (e.g. in case of sales forecasting, errors are weighted by sales volume). [ 3 ]