Study Session 3
Learning Outcome Statements
9.p. distinguish between discretely and continuously compounded rates of return, and calculate and interpret a continuously compounded rate of return, given a specific holding period return;
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Exam: Dec. 2014 Level 1 > Study Session 3. Quantitative Methods: Application > Reading 9. Common Probability Distributions > Subject 11. Discretely and continuously compounded rates of return.
Subject 11. Discretely and continuously compounded rates of return.
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 measures the rate of change in the value of an asset associated with a holding period under the assumption of 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:
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