6.13.2005

Q&A: What's the difference between discretely and continuously compounded rates of return?

A: A discretely compounded rate of return measures the rate of changes in the value of asset over a period under the assumption that the number of compounding periods is countable. Most standard deposit and loan instruments are compounded at discrete and evenly spaced periods, such as annually or monthly. For example, suppose that the holding period return on a stock over a year is 50%. If the rate of return is compounded on a quarterly basis, the compounded quarterly rate of return on the stock is ( 1 + 0.5)^(1/4) - 1 = 10.67%.

The continuously compounded rate of return assumes continuously compounding. It is the natural logarithm of 1 plus the holding period return, or equivalently, the natural logarithm of the ending price over the beginning price. From t to t+1: r(t, t+1) = ln( S(t+1)/S(t) ) = ln(1 + R(t, t+1)), where S is stock price.

Category: C++ Quant > Valuation

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