# When is the VAR equal to the CVAR

After running an optimisation using a quadratic utility (CRRA) function I calculate an CVAR that is equal to the VAR especially for very small risk-aversion levels ($$\gamma$$=1 and $$\gamma$$=2 e.g.). What is the intuition behind this finding? I would think that the skewness and kurtosis are approximately normal and these approach one another? Is it even an informative finding?

• Can you give a specific example with some numbers? – phdstudent Jul 26 '20 at 20:40

The way to see this is to remember that the $$\alpha$$% CVaR/ES/TCE is defined as:
$$CVaR(r,\alpha) = E(r|r\leq Var(r,\alpha))$$.
Thus getting an $$\alpha$$-CVaR equal in magnitude to $$\alpha$$-VaR would imply there are no returns below the $$\alpha$$-VaR level.