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The Capital Market Line says that the return from a portfolio is the risk-free rate plus risk premium. 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
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 upside and downside risk.
The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. [1] It is calculated by using the following formula: [] = = where
All this can be visualised by plotting expected return on the vertical axis against risk (represented by standard deviation upon that expected return) on the horizontal axis. This line starts at the risk-free rate and rises as risk rises. The line will tend to be straight, and will be straight at equilibrium (see discussion below on domination).
If one makes the parametric assumption that the underlying distribution is a normal distribution, and has a sample set {X 1, ..., X n}, then confidence intervals and credible intervals may be used to estimate the population mean μ and population standard deviation σ of the underlying population, while prediction intervals may be used to estimate the value of the next sample variable, X n+1.
The standard deviation is more amenable to algebraic manipulation than the expected absolute deviation, and, together with variance and its generalization covariance, is used frequently in theoretical statistics; however the expected absolute deviation tends to be more robust as it is less sensitive to outliers arising from measurement ...
The return - standard deviation space is sometimes called the space of 'expected return vs risk'. Every possible combination of risky assets, can be plotted in this risk-expected return space, and the collection of all such possible portfolios defines a region in this space.