The Markowitz Bullet underlies the best-known and most widely-used portfolio optimization approach. We provide a guided tour using a 3-asset portfolio.
In the risk business one is not so much concerned with the probability of loss as the expected size of the loss. We explore this idea for various probability distributions by looking at the expected loss given that the loss exceeds a certain threshold. We see for fat tails that the expected loss exceeds the threshold itself.
Resolving a discrepancy between my results and Taleb’s in Taleb’s favor, naturally! I had made an assumption that was not implied in his narrative.
In the real world we generally have only the data and no information about what generated the data. We can go far astray if we make the wrong assumptions.