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  2. Modern portfolio theory - Wikipedia

    en.wikipedia.org/wiki/Modern_portfolio_theory

    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]

  3. Markowitz model - Wikipedia

    en.wikipedia.org/wiki/Markowitz_model

    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 ...

  4. Post-modern portfolio theory - Wikipedia

    en.wikipedia.org/wiki/Post-modern_portfolio_theory

    Downside risk (DR) is measured by target semi-deviation (the square root of target semivariance) and is termed downside deviation. It is expressed in percentages and therefore allows for rankings in the same way as standard deviation. An intuitive way to view downside risk is the annualized standard deviation of returns below the target.

  5. Efficient frontier - Wikipedia

    en.wikipedia.org/wiki/Efficient_frontier

    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 ...

  6. Sharpe ratio - Wikipedia

    en.wikipedia.org/wiki/Sharpe_ratio

    In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for its risk.

  7. Standard deviation - Wikipedia

    en.wikipedia.org/wiki/Standard_deviation

    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.

  8. Tracking error - Wikipedia

    en.wikipedia.org/wiki/Tracking_error

    Under the assumption of normality of returns, an active risk of x per cent would mean that approximately 2/3 of the portfolio's active returns (one standard deviation from the mean) can be expected to fall between +x and -x per cent of the mean excess return and about 95% of the portfolio's active returns (two standard deviations from the mean) can be expected to fall between +2x and -2x per ...

  9. Monte Carlo methods in finance - Wikipedia

    en.wikipedia.org/wiki/Monte_Carlo_methods_in_finance

    In finance, the Monte Carlo method is used to simulate the various sources of uncertainty that affect the value of the instrument, portfolio or investment in question, and to then calculate a representative value given these possible values of the underlying inputs. [1] ("Covering all conceivable real world contingencies in proportion to their ...