Aug 01

Empirical probability (Quant: Stat)

by David Harper, CFA, FRM, CIPM

FRM |

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Learning objective: Explain the relative frequency or the empirical definition of probability

Think of a single six-sided die. What is the probability of rolling a six (6)? The classic or a priori probability is 1/6 or 16.67%.

Instead, assume yesterday you rolled a single die 100 times and observed the following frequencies:

 freq_small_1

Based only on this historical (actual) dataset, the empirical probability of rolling a six is 15%.

Like classic probabilities correspond to parametric distributions, empirical probabilities correspond to empirical distributions. As we see in the FRM assigned reading “LDA at work,” Deutsche Bank employs an empirical distribution for the body of the operational loss distribution. (Specifically, they “mix” in piece-wise fashion an empirical body with a parametric tail).

Financial Risk Manager (FRM) Tip: 

  • We always prefer more data to less. Both parametric and empirical distributions rely on data. The parametric approach uses the data as an excuse to find a mathematical function; once the distribution is selected and calibrated (e.g., “the shape param equals ?”), the data is discarded.
  • From a risk standpoint, the singular advantage of empirical distributions is that we might avoid parametric traps, specifically the dreaded heavy- or fat-tails.

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