Cumulative Return

finance - a la shmoop how do you calculate rates of return? well invest a dollar get

more than a dollar back right? well yeah you hope so anyway in in finance land [dollar bill on table]

and Wall Street and any other professional gig. well rates of return

from financial investments are generally stated as annual returns, so calculating

a rate of return revolves around the one year at a time thing. there are a ton of

curveballs that get thrown into these calculations. here's a big one,

dividends. well guess what clueless financial journalists with little to no [dividends defined]

real schooling in finance quote stock market returns all the time. let's say

that shares in random example industries traded at the same price at the

beginning of the 1970s as they did at the end of the decade. prices for random

example industries were totally flat from 1970 to 1980. that's what one of

those journalists might say. and they don't even get fired for making such a [man reports news]

narrow statement .no nothing happened at all. and wrong. had they taken this course

they'd have realized that monster-sized dividends were paid out during that time

period. five six seven eight percent a year, each year. yet the journalists

ignored them when they stated that the stock market was in fact flat for a

decade and maybe shares of that company were also flat for a decade. but it

implied that they got no return from their investment which is absolutely [icons of stock market and a stock deflate]

wrong. did readers get their money back for that bad journalistic work? yeah we

doubt it - well what about zero coupon bonds? that is their bonds that pay no

dividends or interest along the way and they sell at a discount to par. what does

that mean? that is $1,000 par value bond pays you a grand in seven years. well how

do you calculate the annualized rates of return there? well today that bond sells

for six hundred forty two dollars. like you buy it today for six hundred forty

two you get a thousand bucks in seven years. well what's the rate of return on [zero coupon bond rates of return listed]

that bond? hmm. well vanilla bonds like these we're a whole lot easier to

calculate. because like you got the interest rate right there on the thingy.

yeah so the question is really what interest rate will accrue and then

compound for this bond such that in exactly seven years you get a thousand

bucks? well if it compounded at ten percent a year the compounding would

look like this. you see the table right there and whoa we've already passed the

grand way ahead of seven years. so the compound rate must be less than ten

percent right well what if it compounded at five percent a year well then the [compound rate listed]

rates of return would look like this and basically we're just multiplying 1.0

five times a 6.2 and we take that compound totally multiply 1.05 again and

so on and so on. much closer .well here's the formula you'll want to remember.

where f is the face value PV is the present value and n is the number of

periods. well in our example the face values a thousand bucks, the present

value is 642 dollars and the number of periods is the number of years or seven

years. all right well then we just you know put our handy-dandy calculator to [mathematical formula shown]

work and get a yield of well right around here. so here's the key idea rates

of return are an annual thing when quoted among finance professionals. among

fun dance professionals well and maybe a different story. [three stooges pictured]