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Backtest of a 60 / 30 / 10 portfolio rebalanced once a year with 100 added every month: time-weighted against money-weighted return

Tool	Portfolio Backtest
Source	Illustrative data: 120 months of synthetic prices from a random-number generator (numpy, seed 348), not market data. Return definitions: CFA Institute (2010). GIPS Guidance Statement on Calculation Methodology. Not a printed example; checked against an independent numpy / scipy implementation.
Level	Undergraduate

Problem

Three assets are held at target weights of 60, 30 and 10 % over 120 months. The portfolio starts with 10,000, 100 is added at the end of every month and the weights are restored at the end of every twelfth month. Follow the portfolio month by month and find the ending value, the time-weighted and money-weighted yearly returns, the volatility, the maximum drawdown, the turnover, and the result of the other rebalancing rules with the same money.

Inputs to Enter

Prices of three assets at 121 month ends (the tool's default, illustrative); weights 60 / 30 / 10 %; 12 periods a year
Starting amount 10,000; 100 added at the end of each of the first 119 months; rebalanced every 12 months; no costs or fees

Open the Portfolio Backtest tool (loaded with this example)

Answers

Month 1: stock fund 6,000 · (1 − 0.0277) = 5,833.80; portfolio 5,833.80 + 2,992.80 + 992.80 = 9,819.40; return 9,819.40 / 10,000 − 1 = −1.806 %
Month 2 starts with 9,819.40 + 100 = 9,919.40 and reaches 9,305.51 before the next addition: return 9,305.51 / 9,919.40 − 1 = −6.189 %
Linking the 120 monthly returns: growth of 1 = 1.6967; time-weighted return 1.6967^(1/10) − 1 = 5.43 % a year
Ending value 34,958.09 on 10,000 + 119 · 100 = 21,900 put in; gain 13,058.09; money-weighted return (internal rate of return of the flows) 6.35 % a year
Volatility 2.959 % · √12 = 10.25 % a year; maximum drawdown 1.3325 / 1.7166 − 1 = −22.37 %; best 12 months 37.46 %, worst −17.43 %
9 rebalancings, total turnover 39.8 % of the portfolio (4.0 % a year)
Same money under the other rules: never 33,214.93; every month 34,280.48; when a weight drifts more than 5 points 34,588.93
Gain added by each asset 9,024.21 + 2,509.81 + 1,524.06 = 13,058.09, and 10,000 + 11,900 + 13,058.09 = 34,958.09

Notes

The tool's default inputs are this case; press Submit. The money-weighted return is above the time-weighted one because the later months, when more money was invested, were the better ones in this sample. The order of the rebalancing rules belongs to this made-up history and says nothing about another period. A backtest describes the past sample only. A calculator for education and analysis, not investment advice.