# Statistical Significance of the Small Value Advantage

Whenever you spot a market trend, you should try to determine whether it's statistically significant or just the result of random noise. After all, every game of chance has its lucky winners; and past luck tells you absolutely nothing about likely future results.

To help you decide, this simulator creates four possible outcomes for the number of years you specify. Each outcome is calculated the same way: each year it grows by an amount determined by a random process using the same expected annualized return and standard deviation as the stock market (inflation adjusted). You should run the simulation several times; since it's random, you'll get a different result each time.

Years:

 Four Random Outcomes: % % % % Expected: %

Each run will produce winners and losers; but it's very unusual to get any winner that beats the expected value by as much as Small Value has historically beaten the Total Stock Market:

for 1927-2005
 Value Growth Large Cap 9.21% 6.17% Small Cap 12.13% 5.77% TSM: 6.72%

This is a strong indication that the Small Value advantage really is statistically significant. It doesn't look like it was based on luck or noise; it looks like the result of some economic or market factor that really made Small Value better than the market. (Of course that still doesn't guarantee that the trend will continue in the future.)

## Two Notes about the Simulator

1.   Over the long run the simulator probably overstates the ability of randomness to create winners. That's because it assumes that each year's result is independent of all past results; but in reality the market seems to show mean reversion, meaning that a great year increases the likelihood of a future poor year. (In other words, the market is like a coin that knows how many times it has come up heads, and keeps making an effort to get the average back to 50/50.) This means that the Small Value advantage is even more statistically significant than the simulator implies.

2.   If you set the time frame to five years, you can see lots of HUGE winners. That's why trying to spot a trend from recent events doesn't work. In the short run "noise" dominates, and meaningful trends are invisible (or inaudible!)

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