Consider the results of three investment strategies:

Investor X who put K1 in 30 day treasury bills on December, 31, 1925 and always rolled over all proceeds into 30 day treasury bills, would have ended on December 31, 2003, 78 years later, with K17.56.

Investor Y, who put K1 in large stocks (the S & P 500 portfolio) on December 31, 1925, and re-invested all dividends in that portfolio, would have ended on December 31, 2003, with K1992.80.

Suppose we define perfect market timing as the ability to tell with certainty at the beginning of each whether stocks will outperform bills. Investor Z, the perfect timer shifts all funds at the beginning of each year into either bills or stocks, whichever is going to be better. Beginning at the same date, how much would investor Z have ended up with 78 years later? 

What are the annually compounded rates of return for the X, Y and perfect-timing strategies over the 78 year period?