What's the compound annual rate of return on stocks?

Question

all the charts don't show what it should be after dividends are reinvested so are not what I want.

Answer 1

This is a slightly involved answer. Assume the stocks are bought at low price and you sell at high price during the course of the year, dividend states are easily covered up after the ex dividend date days, so it is not taken into consideration. Suppose the L is the lowest price and H the highest price reached and it happens in time t days, then,
H=L x e^r x t/365. then,
r the return for the stock = Natural log (H/L)x 365/t.
Assume you don't trade after the high price is reached and you sell at that point. Anyway this will give the average annual return for the stock since you will be buying and selling many times as the prices hits lows and highs. For modelling purpose only a single transaction is taken into account to average out the effects of individual sale. So if you know the low and high prices this is the method. These prices are published. This will most of the time equivalent to the Capita Asset Pricing model (CAPM) required rate of return Ks= Krf+beta(km - krf) where krf is the risk free rate, Km the market return, beta is the volatility of the stock with respect to the market.