Mean-variance analysis holds exactly when investors are risk averse; when they choose investments to maximise expected utility or satisfaction; and when either (assumption 1) returns are normally distributed or (assumption 2) investors have quadratic utility functions (a concept used in economics for a mathematical representation of risk and return trade-offs).
Safety-first rules focus on shortfall risk, the risk that portfolio value (or portfolio return) will fall below some minimum acceptable level over some time horizon.
If returns are normally distributed, the safety-first optimal portfolio maximises the safety-first ratio (SFRatio), as follows:
The quantity is the distance from the mean return to the shortfall level. Dividing this distance by gives the distance in units of standard deviation.
Two steps:
- Calculate each portfolio’s SFRatio.
- Choose the portfolio with the highest SFRatio.
