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Chapter 18 - Measuring Net Asset Values ... > 18.13 CONTINUOUS COMPOUNDING

18.13 CONTINUOUS COMPOUNDING

It is relatively easy to calculate simple net and simple gross returns over a single holding period return. However, it is tiresome to take into account compounding effects using multiplications and powers as soon as we have more than one period – see, for instance, equation (18.5). Things would be much simpler if we could just add and subtract simple returns rather than multiply and divide simple gross returns.
This has motivated an alternative approach to measuring returns, which produces continuously compounded returns or log returns. The continuously compounded return 272on a fund between any time T1 and T2 = T1 is defined as the natural logarithm of its simple gross return187:
273
As an illustration, Table 18.4 shows the calculation of a series of continuously compounded returns from a series of monthly net asset values. We intentionally express the result with three decimals to show that simple returns and continuously compounded returns are in fact slightly different.

  

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