A Second-Order Upper Bound on the Expected Value of a Convex Function - Revisited - A Geometric Proof

We propose a new proof of a second-order upper bound on the expected value of a convex function of a random variable. The bound is called the Dula bound on finite support (DBFS). The original proof is based on a relaxation of the Generalized Moment Problem. We now present a proof based on a geometric construction. In numerical applications, we apply the upper bound as a second-order upper bound approximation. The expected portfolio return shortfall function is approximated by the bound for developing daily trading signals. The uncertainty is captured by the random variable that represents the portfolio return. DBFS is minimized instead of the expected portfolio return shortfall function, which is non-differentiable, while DBFS is a smooth function. Numerical results for trading signals are presented for a portfolio containing 29 crypto-currency ETFs (Exchange Traded Funds) over an 18-month period on the NASDAQ market.