Investments, tenth edition

  Where Is Research on Rates of Return Headed? 

 In order to learn more about the distribution of returns, particularly the behavior of rela-

tively rare extreme events, we need a lot more data. The speed with which we accumulate 

even daily rates of return will not get us there; by the time we have a large enough sample, 

the distributions may well have changed. But it may be that help is on the way. 

 The highest frequency we can obtain for rates of return comes from trade-by-trade data. 

Statistical methods recently developed by astrophysicists can glean from these observa-

tions the essential components of the return distributions. The return process can usefully 

be described as a sum of an instantaneous normal that develops into a lognormal compound