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Compare two stocks. Both have earned 8% per year on average. However, stock A has oscillated between 6% and 10%. Stock B has oscillated between 3% and 13%. (For simplicity, say that they alternated.) If you had purchased $500 in each stock, how much would you have had 10 years later?
Solution
Stock A –
Rannual =
= 7.98%
Stock B –
Rannual =
= 7.88%
Hence 10 years later the value of stock A was
500*(1.0798) ^10 = $1,077.47
While the value of stock B was
500*(1.0788) ^10 = $1,067.53
Instead if this stock had a constant return of 8% per year it would have returned 500*(1.08) ^10 = $1,079.46
This is because the annualized (geometric average) rate of return is always lower than the simple arithmetic average.
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