Consider the following transactional information for the inventory account of an institutional bond house:
1st Quarter
Ending portfolio value: $400,500,000
Total amount invested: $396,000,000
2nd Quarter
Ending portfolio value: $401,900,000
Total amount invested: $400,500,000
3rd Quarter
Ending portfolio value: $406,500,000
Total amount invested: $400,000,000
4th Quarter
Ending portfolio value: $409,800,000
Total amount invested: $400,000,000
Using this information, what is the annual time-weighted rate of return for this portfolio? Assume no taxes or transaction charges.
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A. B. C. D. E. F.B
The time-weighted rate of return is the preferred method of return calculation in the investment management industry, primarily because this method is not sensitive to significant additions and withdrawals of funds from portfolios under examination. The calculation of the time-weighted rate of return involves three steps, which are illustrated as follows:
Step 1:
Price the portfolio immediately prior to any significant additions or withdrawals. Separate the portfolio into a series of subperiods based on the dates of cash inflows and outflows.
Step 2:
Calculate the holding period return for each subperiod.
Step 3:
Determine the annualized holding period return by linking or compounding the holding period return of each subperiod. If the investment is for more than one year, use the geometric mean of the annual returns as the time-weighted rate of return. If the investment is for less than one year, compound the subperiod returns to obtain an annualized measurement.
To begin the process of determining the time-weighted rate of return, we would break the portfolio up into the subperiod series of cash flows. However, in this example, the cash flows are already aggregated for us and we can move on to the next step: determining the holding period return for each subperiod. This process is detailed as follows:
Quarter 1 holding period return = [($400,500,000 ending value - $396,000,000 invested) / $396,000,000 invested] = 1.13636%
Quarter 2 holding period return = [($401,900,000 ending value - $400,500,000 invested) / $400,500,000 invested] = 0.34956%
Quarter 3 holding period return = [($406,500,000 ending value - $400,000,000 invested) / $400,000,000 invested] = 1.625%
Quarter 4 holding period return = [($409,800,000 ending value - $400,000,000 invested) / $400,000,000 invested] = 2.450%
Now that the holding period return for each subperiod has been determined, we must annualize the return measure by taking the product of all four quarterly returns. This process is illustrated below:
[(1 + .0136) * (1 + .0035) * (1 + .0163) * (1 + .0245) - 1] = .05905 or 5.905%
When calculating the time-weighted rate of return, remember that the total amount invested is the relevant figure, not the beginning portfolio value. Notice that during the third quarter, the total amount invested does not equal the ending amount for the second quarter. (A similar situation exists in the fourth quarter).
This differential could be explained by numerous phenomena. Perhaps the difference is due to a cash withdrawal from the account. Maybe it was used to pay expenses or meet an outstanding margin call.
What is important to note is the fact that this money (the difference between the total amount invested and the ending portfolio value for the previous subperiod) was not invested, and should not be included in the holding period return for the fourth quarter. So said, whenever possible you should use the total amount invested rather than the beginning portfolio value in the calculation of the subperiod holding period return.
If you chose 5.79%, remember that in the calculation of the time-weighted rate of return, it is the geometric average that is used, not the arithmetic average.