Expected shortfall

So do we need more sophisticated tools?

There are plenty more, such as C-VaR, Delta, Gamma, Vega, sigma, Vanna, Rho, Expected Shortfall, and the list goes on.

But what matters is to understand the psychology of markets and the pricing of risks in times of fear versus greed or bull versus bear markets.

You mean swings between too much or too little risk aversion?