Stochastic Dominance and Risk Measures

9.5 Summary

In Chapter 1, we saw that it is very hard to quantify risk. R&S (1970) establish-several equivalent definitions of risk (and variance is not one of them!) that enable us to define one variable as “more risky” than another for equal means distributions. According to these definitions, risk is not quantified, but ranking investments by their risk is enabled.

Where E_f(x) ≠ E_G(x), R&S’s definition still holds and it is possible to establish two sets of mixes of the random variables with the riskless asset such that G_β is more risky than F_α. Finally, the addition of a DARA assumption may enable the ranking of investments by their risk in U_d when it is impossible to do so in U₂: While G is riskier than F in U₂ if G = F + MPS, G will be riskier than F in U_d if G = F + MPSA where MPSA denotes mean preserving spread antispread.