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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
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.
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
Cumulative probability of a normal distribution with expected value 0 and standard deviation 1. In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. [1]
These are the expected value (or mean) and standard deviation of the variable's natural logarithm, (), not the expectation and standard deviation of itself. Relation between normal and log-normal distribution.
An estimation of the CAPM and the security market line (purple) for the Dow Jones Industrial Average over 3 years for monthly data.. In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.
Formally, it is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected return but with the same standard deviation of return (i.e., the risk). [1] The efficient frontier was first formulated by Harry Markowitz in 1952; [2] see Markowitz model.
The slope of the capital allocation line is equal to the incremental return of the portfolio to the incremental increase of risk. Hence, the slope of the capital allocation line is called the reward-to-variability ratio because the expected return increases continually with the increase of risk as measured by the standard deviation.