Mean-adjusted S&P 500 real return data set:
TIP$TER performs what is known as an "exploratory simulation" of historical S&P 500 real returns. TIP$TER stores the real monthly returns (including dividends) of the S&P 500 from January 1871 through Dec. 2011 (at later, depending on the version).
The use of historical S&P 500 returns, without any adjustment for present-day realities, is potentially misleading. Between 1871 and 2011, the S&P 500 experienced an annualized real return (including reinvested dividends) of 6.6%. It is unrealistic to assume that future stock market returns will be anywhere nearly as generous. After all, in the infinitely long run, it is mathematically impossible for the stock market to return more than its dividend yield plus the long term growth rate of the economy it represents.
So TIP$TER scales its set of historical S&P 500 return data to yield an annualized return equal to the user-specified expected annualized return on stocks. The expected annualized return on stocks is equal to the sum of the risk-free rate (in TIP$TER's interface, the "Real return on TIPS") and the expected equity risk premium (in TIP$TER's interface, the "extra expected return for stocks"). If the user keeps TIP$TER's default inputs of 2% for TIPS plus an "extra" 1.5% for stocks, TIP$TER scales its set of historical S&P 500 return data to yield an annualized return of 3.5%.
For every month of its mean-adjusted 1600+ month historical data set, TIP$TER calculates the 12-month return going forward. (For the last 11 months of the data set, TIP$TER wraps back to the beginning of its data set – i.e., 1871 – to calculate the 12-month return going forward).
To simulate a portfolio, TIP$TER tests a user's portfolio against every available start date in the modified data set. For example, one simulation iteration would test the user's portfolio against an interval of modified S&P 500 data starting with Jan. 1871. The next simulation iteration would test the user's porfolio against an interval that started with Feb. 1871. And so on and so on. And for intervals starting more recently, TIP$TER wraps back to the beginning of its data set (1871) after simulating the last return in its historical data set. This way, every TIP$TER simulation samples every modified historical data point equally. Also, because there are over 1600 months in TIP$TER's historical data set, every TIP$TER simulation is tested against over 1600 intervals of rolling annualized returns.
Technical Notes: By default, TIP$TER's mean-adjusted historical data set has the same volatility as the original data set (i.e., 19.7% standard deviation for rolling annual returns from Jan. 1871-Dec. 2011). However, TIP$TER can scale its set of historical S&P 500 return data to have a volatility (standard deviation) equal to the user-specified volatility. To keep the interface simple for most users, TIP$TER mostly conceals the "annualized standard deviation of returns" input behind a "Reserved" comment when the "exploratory simulation" option is selected. Sophisticated users who wish to adjust the volatility of the data set, however, can still access the standard deviation input spinners (by zooming on this section of the spreadsheet or by unprotecting the spreadsheet and closing or moving the comment).
TIP$TER's exploratory simulation is insensitive to any changes a user makes to the "Expected reversion-to-the-mean time (yrs)" input spinners. Those spinners only affect simulations using a normal, lognormal, or double lognormal model of returns.