I got stuck on practice question 4. in the study notes for Chapter 3 of Dowd.

4. Portfolios (X) and (Y) each have volatility of 20%, but portfolio (Y) has a higher return and therefore its absolute VaR is lower; i.e., Absolute VaR = - return * T + deviate * volatility * SQRT(T). Which coherence property does this illustrate?

a) Monotonicity

b) Subadditivity

c) Positive Homogeneity

d) Translational invariance

The given answer is a), but I don't understand why. Just because Y has a higher return than X doesn't mean Y > X a.s. which I thought is the condition for monotonicity.

I would appreciate it, if somebody can point me in the right direction here.