A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing

by Burton G. Malkiel

We assumed that only two outcomes were possible after one year. But suppose we consider a two-stage (six-month) binomial model. After the first six months, the stock can go up or down. After the second six months, again two outcomes are possible. This leads to three possible outcomes at the end of one year. The stock can go up in both periods or down in both. Alternatively the stock could rise (fall) in the first period and fall (rise) in the second. Thus, three outcomes are possible. We could also do a four-stage binomial model where each quarter the stock price could rise or fall and several different outcomes would be possible. Or we could do a daily binomial or even an hourly or minute-by-minute model. As we break the binomial model into finer and finer subperiods, the binomial model and the Black-Scholes model converge.