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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 ...
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.
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 }} .
The problem is then to devise a way of combining the experience of the group with the experience of the individual risk to calculate the premium better. Credibility theory provides a solution to this problem. For actuaries, it is important to know credibility theory in order to calculate a premium for a group of insurance contracts. The goal is ...
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions , such as banks and insurance companies, acceptable to the regulator .
Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice.An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility.