LOS B requires us to:
compare the money-weighted and time-weighted rates of return and evaluate the performance of portfolios based on these measures
1. Money-weighted Rate of Return
a. The money-weighted rate of return (MWRR) is a measure of the performance of an investment in the portfolio.
b. The MWRR is the internal rate of return of the portfolio i.e., it is the rate of discount at which the present value of all the cash outflows equals the present value of all the cash inflows.
PVOutflows = PVInflows
c. While calculating the value of inflows, we consider the initial and final fund values and the intermediate cash inflows.
d. The cash outflows include:
i. The beginning value or the purchase of an asset,
ii. Dividends and interests reinvested, and
iii. All the withdrawals made.
e. The cash inflows include:
i. The final value of the fund or proceeds of investments sold,
ii. Dividends and interests received, and
iii. Contributions.
Example
If you invest in a mutual fund of $ 1,000 at the beginning of the year and sell the same at $ 1,100 at the end. There is also an annual dividend of $ 10.
So, the inflows = $ 1,000
And outflows = $ 1,100 + $ 10
We can calculate the MWRR by calculating the cash flow of this cash stream.
Or,
[(10) / (1 + r)] + [(1,100) / (1 + r)] = 1,000
If we calculate, the value of IRR is 11%.
1.1. Limitations of Using MWRR
a. MWRR considers all cash flows during its calculations including the intermediate contributions and withdrawals. Thus, they give more weightage to the performance of the fund when it is at its largest.
b. If the investor invests money just before the performance rise, there is a positive effect on the value. Whereas if the investor withdraws the money just before the performance surge, it has a negative impact on the performance of the fund manager.
2. Time-Weighted Rate of Return
a. The time-weighted rate of return (TWRR) is a measure of the compound rate of growth in a portfolio.
b. This is considered a better measure of an investment manager’s performance because it does not consider the biased effect of inflows and outflows on the return, as in the case of MWRR.
2.1. How to calculate Time-Weighted Rate of Return
a. Divide the total holding period into sub-periods. This could be done based on a fixed interval (monthly, quarterly, annually, etc.) or on the basis of major inflows and outflows.
b. Once the sub-periods have been assigned, calculate the holding period return (HPR) for each period.
c. Add 1 to each HPR and multiply each (1 + H) term.
d. Subtract 1 from the final product. The resulting value is compounded TWRR.
So, to sum up the formula for calculating TWRR is: Compounded TWRR = [(1 + HPR1) × (1 + HPR2) × (1 + HPR3) × … … … (1 + HPRn)] – 1 |
e. To annualize the above compounded TWRR, we add it with one and take its nth root and subtract one from the resulting figure. That is,
Annual TWRR = (1 + Compounded TWRR)1/n – 1 |
Example
Suppose we invest $ 1,000 in a unit stock ABC at the beginning of the year. The company pays a dividend of $10 per year at the end of the year. And at the end of the year, we again purchase an additional unit of the stock for $ 1,100. Suppose we sell both the units at the end of the second year at $ 1,200. What will be our TWRR?
Solution:
To do the same we first break the two-year period into two one-year periods.
Second, we calculate the holding period return of each periods, as follows
Particulars |
Year 1 |
Year 2 |
Beginning Value |
$ 1,000 |
$ 2,200 |
Dividends Received |
$ 10 |
$ 20 |
Ending Value |
$ 1,100 |
$ 2,400 |
HPR |
11% |
10% |
1 + HPR |
1.11 |
1.1 |
Lastly, we calculate the TWRR:
(1 + TWRR)2 = 1.11 × 1.10
TWRR = 0.1050 = 10.50 %
3. MWRR vs TWRR
a. Unlike MWRR, TWRR is not sensitive to the major outflows and inflows of funds, which is quite unfair in evaluating the fund manager’s performance. TWRR does not take into account the distorting effects of the major fund transfers.
b. MWRR is only considered a better option if the fund manager has control over the flow and timing of the fund transfers.