G. H. Hardy, the legendary mathematician, once claimed that his greatest disappointment in life was learning that someone had discovered an application for one of his theorems. Although Hardy's disinterest in practical matters was a bit extreme, it sometimes seems that scholars view the real world as an uninteresting special case of their models. This disinterest in real‐world complexity, unfortunately, often brings unpleasant consequences. In this chapter, we address two simplifications about risk that often lead investors to underestimate their portfolios' exposure to loss. First, investors typically measure risk as the probability of a given loss, or the amount that can be lost with a given probability, at the end of their investment horizon, ignoring what might occur along the way. Second, they base these risk estimates on return histories that fail to distinguish between calm environments, when losses are rare, and turbulent environments, when losses occur more commonly. In this chapter, we show how to estimate exposure to loss in a way that accounts for within‐horizon losses as well as the regime‐dependent nature of large drawdowns.

We measure the likelihood that a portfolio will experience a certain percentage loss at the end of a given horizon by computing the standardized difference between the percentage loss and the portfolio's expected return, and then converting this ...

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