The modified Dietz method[1][2][3] is a measure of the ex post (i.e. historical) performance of an investment portfolio in the presence of external flows.
(External flows are movements of value such as transfers of cash, securities or other instruments in or out of the portfolio, with no equal simultaneous movement of value in the opposite direction, and which are not income from the investments in the portfolio, such as interest, coupons or dividends.)
To calculate the modified Dietz return, divide the gain or loss in value, net of external flows, by the average capital over the period of measurement.
The GIPS are intended to provide consistency to the way portfolio returns are calculated internationally.
[5] The original idea behind the work of Peter Dietz was to find a quicker, less computer-intensive way of calculating an IRR as the iterative approach using the then-quite-slow computers that were available was taking a significant amount of time; the research was produced for BAI, Bank Administration institute.
If the flow happens at the beginning of the day, the flow is in the portfolio for an additional day, so use the following formula for calculating the weight: The modified Dietz method has the practical advantage over the true time-weighted rate of return method, in that the calculation of a modified Dietz return does not require portfolio valuations at each point in time whenever an external flow occurs.
[6] The modified Dietz method is based upon a simple rate of interest principle.
Note that in the example above, the flow occurs midway through the overall period, which matches the assumption underlying the simple Dietz method.
Suppose we are calculating the 2016 calendar year return, and that the portfolio is empty until a transfer in of EUR 1m cash in a non-interest bearing account on Friday 30 December.
However, blindly applying the modified Dietz formula, using an end-of-day transaction timing assumption, the day-weighting on the inflow of 8.1m HKD on 30 December, one day before the end of the year, is 1/366, and the average capital is calculated as: and the gain is: so the modified Dietz return is calculated as: So which is the correct return, 1 percent or 366 percent?
The corrected gain or loss is the same as before: but the corrected average capital is now: so the corrected modified Dietz return is now: Suppose that a bond is bought for HKD 1,128,728 including accrued interest and commission on trade date 14 November, and sold again three days later on trade date 17 November for HKD 1,125,990 (again, net of accrued interest and commission).
Assuming transactions take place at the start of the day, what is the modified Dietz holding-period return in HKD for this bond holding over the year to-date until the end-of-day on 17 November?
The answer is that firstly, the reference to the holding period year to-date until the end-of-day on 17 November includes both the purchase and the sale.
There are no flows, so the gain or loss is: and the average capital equals the start value, so the modified Dietz return is: This method of restricting the calculation to the actual holding period by applying an adjusted start or end date applies when the return is calculated on an investment in isolation.
Suppose that at the beginning of the year, a portfolio contains cash, of value $10,000, in an account which bears interest without any charges.
At the beginning of the fourth quarter, $8,000 of that cash is invested in some US dollar shares (in company X).
At the end of the year, the shares have increased in value by 10% to $8,800, and $100 interest is capitalized into the cash account.
The first step is to calculate the average capital in each of the cash account and the shares over the full year period.
For convenience, we will assume the time weight of the outflow of $8,000 cash to pay for the shares is exactly 1/4.
The start value of the shares at the beginning of the year was zero, and there was an inflow of $8,000 at the beginning of the last quarter, so: We can see immediately that the weight of the cash account in the portfolio over the year was: and the weight of the shares was: which sum to 100 percent.
The modified Dietz method is an example of a money (or dollar) weighted methodology (as opposed to time-weighted).
, measured over a common matching time interval, then the modified Dietz return on the two portfolios put together over the same time interval is the weighted average of the two returns: where the weights of the portfolios depend on the average capital over the time interval: An alternative to the modified Dietz method is to link geometrically the modified Dietz returns for shorter periods.
Whatever method is applied to calculate returns, an assumption that all transactions take place simultaneously at a single point in time each day can lead to errors.
Some such problems are resolved if the modified Dietz method is further adjusted so as to put purchases at the open and sales at the close, but more sophisticated exception-handling produces better results.
There are sometimes other difficulties when decomposing portfolio returns, if all transactions are treated as occurring at a single point during the day.
The problem only arises because the day is treated as a single, discrete time interval.
Then in this case, use the simple return method, adjusting the end value for outflows.
The Modified Dietz return in this case is: Instead, we notice that the start value is positive, but the average capital is negative.
It is not ideal, for two further reasons, which are that it does not cover all cases, and it is inconsistent with the Modified Dietz method.