This one always trips me up: Over a period of one year, an investor’s portfolio has declined in value from 127,350 to 108,427. What is the continuously compounded rate of return? A) -16.09%. B) -13.84%. C) -14.86%. (108,427-127,350)/127,350=-14.86% I already know the answer isn’t C right off the bat. By process of elimination I know the answer is A due to the compounding nature of a negative return. What’s the next step in the process. e^?
For some reason this just sticks in my head: LN(1+Annual Rate) = Continuous Rate
ooooh, but the first time I did it, I used (1+.1486) It’s actually (1+(-.1486)) methinks!
Yep, thanks. Ln(1-.1486) = -16.09%
A cheap way to do it is to just divide by 100 and then add 1 and exponent it to 100. The difference between numbers after 20 or so become so small that it’s essentially the same number. LN(1+HPY) is the real formula though, as mentioned above.