For a two-asset portfolio, the risk of the portfolio, σp, is: 2222p1122112212222p11221212121212σ=wσ+wσ+2wσwσρorσ=wσ+wσ+2wwcovcov since ρ=σσ where σi is the standard deviation of asset i's returns, ρ12 is the correlation between the returns of asset 1 and 2, and cov12 is the covariance between the returns of asset 1 and 2. Problem What is the portfolio standard deviation for a two-asset portfolio comprised of the following two assets if the correlation of their returns is 0.5? Asset A Asset B Expected return 10% 20% Standard deviation of expected returns 5% 20% Amount invested $40,000 $60,000
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"Risk probability" does not quite make sense, perhaps you mean just how to calculate risk. There are many formulas and methods, a lot of them highly complex mathematical models. Risk calculation is an important subset of portfolio theory. For the simplest cases, consider some of the following definitions: * the greatest dive that a stock took over a given historical time period. For example, if stock A dropped 30% maximum over past 5 years before rebounding, and stock B dropped 40% maximum over the same period - then by this metric you can see that stock B is riskier. * standard deviation of the returns over a historical time period. Take as your data set the prices a stock assumed over the last 5 years daily. You can calculate the standard deviation of this data set. The standard deviation is a measure of risk.
The CAPM is a model for pricing an individual security (asset) or a portfolio. For individual security perspective, we made use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio
The Sortino Ratio is the actual return minus the target return, all divided by the downside risk. The downside risk is either calculated by the semi standard deviation, or the 2nd order lower partial moment. The related link "Calculate the Sortino Ratio with Excel" provideds an Excel spreadsheet to calculate the Sortino Ratio