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The best measure is the standard deviation of the difference between the portfolio and index returns. Many portfolios are managed to a benchmark, typically an index. Some portfolios, notably index funds , are expected to replicate, before trading and other costs, the returns of an index exactly, while others ' actively manage ' the portfolio by ...
R M = return on the market portfolio σ M = standard deviation of the market portfolio σ P = standard deviation of portfolio (R M – I RF)/σ M is the slope of CML. (R M – I RF) is a measure of the risk premium, or the reward for holding risky portfolio instead of risk-free portfolio. σ M is the risk of the market portfolio. Therefore, the ...
The MPT is a mean-variance theory, and it compares the expected (mean) return of a portfolio with the standard deviation of the same portfolio. The image shows expected return on the vertical axis, and the standard deviation on the horizontal axis (volatility). Volatility is described by standard deviation and it serves as a measure of risk. [7]
If Portfolio A has an expected return of 10% and standard deviation of 15%, while portfolio B has a mean return of 8% and a standard deviation of 5%, and the investor is willing to invest in a portfolio that maximizes the probability of a return no lower than 0%: SFRatio(A) = 10 − 0 / 15 = 0.67, SFRatio(B) = 8 − 0 / 5 = 1.6
In modern portfolio theory, the efficient frontier (or portfolio frontier) is an investment portfolio which occupies the "efficient" parts of the risk–return spectrum. 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 ...
In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measures generalize the concept of standard deviation .
Downside risk was first modeled by Roy (1952), who assumed that an investor's goal was to minimize his/her risk. This mean-semivariance, or downside risk, model is also known as “safety-first” technique, and only looks at the lower standard deviations of expected returns which are the potential losses.
Elliptical distributions are important in portfolio theory because, if the returns on all assets available for portfolio formation are jointly elliptically distributed, then all portfolios can be characterized completely by their location and scale – that is, any two portfolios with identical location and scale of portfolio return have ...
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