Mutual fund unlocked: Time-weighted vs money-weighted rates of return
The time-weighted rate of return is the most common way to measure your rate of return in the investment industry. The other method is known as the money-weighted rate of return. Before getting into details, let us first understand what they are and how are they defined.
Time-Weighted Rate of Return
The time-weighted rate of return is the most commonly used and is defined as the compounded growth rate of every rupee invested over the period being measured. The time-weighted formula is essentially a geometric mean of a number of holding-period returns that are compounded over time. This method of calculating return does not include the effect of an individual’s contributions or withdrawals. This method is useful to calculate the performance of broad market indices or mutual funds because contributions and withdrawals – activities that can impact performance but are not in the fund manager’s control – are not taken into account in this calculation method.
Example:
Consider the following table which lists the market value of a mutual fund portfolio at the end of each quarter.
| Date | Market Value (Rs) |
| 31-Dec-16 | 200000 |
| 31-Mar-17 | 196500 |
| 30-Jun-17 | 200000 |
| 30-Sep-17 | 243000 |
| 31-Dec-17 | 250000 |
On December 31, 2017, the annual fee of Rs. 2,000 was deducted from the account. On July 30, 2017, the contribution of Rs. 20,000 was received, which boosted the account value to Rs. 2,22,000 on July 30. How would we calculate a time-weighted rate of return for 2017?
The calculation is done below: As there is a significant inflow in July, we need to add one extra period in addition to the normal four quarters.
Period 1 (Dec 31, 2016, to Mar 31, 2017):
Return= (Rs 196500 – Rs 200000)/Rs 200000 = -3500/200000 = -1.75%.
Period 2 (Mar 31, 2017, to June 30, 2017):
Return = (Rs 200000 – Rs 196500)/Rs 196500 = 3500/196500 = +1.78%.
Period 3 (June 30, 2017, to July 30, 2017):
Return = ((Rs 222000 - Rs 20000) - Rs 200000)/Rs 200000) = 2000/200000 = +1.00%.
Period 4 (July 30, 2017, to Sept 30, 2017):
Return = (Rs 243000 - Rs 222000)/Rs 222000 = 2100/222000 = +9.46%.
Period 5 (Sept 30, 2017, to Dec 31, 2017):
Return = ((Rs 250000+ Rs 2000) - Rs 243000)/Rs 243000 = 900/243000 = +3.70%
Now the time weighted return is calculated as following
2017 return = [(1 + (-.0175)) x (1 + 0.0178) x (1 + 0.01) x (1 + 0.0946) x (1 + 0.0370)] - 1
=[(0.9825) x (1.0178) x (1.01) x (1.0946) x (1.0370)] – 1
=14.64%
Money-weighted returns
In contrast to time-weighted, money-weighted method calculates the rate of return including the impact of contributions to, or withdrawals from, the portfolio. For example, if an investor contributes a significant sum to their portfolio just prior to the portfolio’s performance rising, intuitively, this is a positive action. The calculation of the money-weighted returns is a little bit involved and needs a calculator as it is like calculating the internal rate of return (IRR). In the above case, the return comes out to be 14.4 per cent, which is slightly less than time-weighted returns.
If there are no cash flows, the two methods will produce the same rate of return.
While time-weighted return calculations are useful for assessing the performance of fund manager relative to market benchmarks, money-weighted calculations help you assess your personal performance relative to your individual financial plans and projections.