Suppose an investor placed $5 million into three investment funds at the beginning of the year. All investment earnings were reinvested. One million dollars were invested in a commercial real estate fund and produced a performance of 6.91% by the end of the year. Another three million dollars were invested in a common stock fund and produced a total return of 12.72%. The remaining one million dollars were invested in T-Bills and produced a return of 3.30% by year end.
Using the simple average to calculate the total return produces a misleading measure of financial performance. If we simply add up the three percentage gains and divide them by three that would leave us with a simple average of 7.64% on the rates of return. That doesn't take into account the fact that common stock accounted for 60% of the entire portfolio, while real estate and T-Bills combined accounted for the other 40%. The real performance of this portfolio is 9.76% and is calculated as follows:
WA = (1,000,000 * 6.91% + 3,000,000 * 12.72% + 1,000,000 * 3.3%) / (1,000,000 + 3,000,000 + 1,000,000) = (69,100 + 381,600 + 33,000) / 5,000,000 = 483,700 / 5,000,000 = 9.67%.
That’s 2.03 percentage points more than the simple average—a big difference.