Modified Dietz method: Difference between revisions

Revision as of 04:14, 30 October 2017

Revision as of 02:58, 6 December 2017

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So which is the correct return, 1 percent or 366 percent?

===Adjusted Timetime Intervalinterval===

The only sensible answer to the example above is that the holding period return is unambiguously 1 percent. This means the start date should be adjusted to the date of the initial external flow. Likewise, if the portfolio is empty at the end of the period, the end date should be adjusted to the final external flow. The end value is effectively the final external flow, not zero.

The return annualized using a simple method of multiplying-up 1 percent per day by the number of days in the year will give the answer 366 percent, but the holding period return is still 1 percent.

===Example Correctedcorrected===

The example above is corrected if the start date is adjusted to the end of the day on 30 December, and the start value is now 8.1m HKD. There are no external flows thereafter.

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:{{nowrap begin}}{{sfrac|{{link if exists|gain or loss}}|{{link if exists|average capital}}}} = {{sfrac|81,000|8.1m}} = 1 %{{nowrap end}}

===Second Exampleexample===

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?

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:{{nowrap begin}}{{sfrac|{{link if exists|gain or loss}}|{{link if exists|average capital}}}} = {{sfrac|-2,738|1,128,728}} = -0.24 % 2 d.p.{{nowrap end}}

===Contributions - Whenwhen Notnot Toto Adjustadjust the Holdingholding Periodperiod===

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. When the investment belongs inside a portfolio, and the weight of the investment in the portfolio, and the contribution of that return to that of the portfolio as a whole is required, it is necessary to compare like with like, in terms of a common holding period.

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To measure returns net of fees, allow the value of the portfolio to be reduced by the amount of the fees. To calculate returns gross of fees, compensate for them by treating them as an external flow, and exclude accrued fees from valuations.

==Comparison with Timetime-Weightedweighted Returnreturn and Internalinternal Raterate of Returnreturn==

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. The [[internal rate of return]] method shares this practical advantage with the modified Dietz method.

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so in this case, the modified Dietz return is noticeably less than the unannualized IRR. This divergence between the modified Dietz return and the unannualized internal rate of return is due to a significant flow within the period, and the fact that the returns are large.

==Annual Raterate of Returnreturn==

Note that the Modified Dietz return is a holding-period return, not an annual rate of return, unless the period happens to be one year. Annualisation, which is conversion of the holding-period return to an annual rate of return, is a separate process.

==The Simplesimple Dietz Methodmethod==

Note also that the [[simple Dietz method]] is a special case of the Modified Dietz method, in which external flows are assumed to occur at the midpoint of the period, or equivalently, spread evenly throughout the period, whereas no such assumption is made when using the Modified Dietz method, and the timing of any external flows is taken into account.

==Money-Weightedweighted Returnreturn==

The modified Dietz method is an example of a money (or dollar) weighted methodology. In particular, if the modified Dietz return on two portfolios are <math>R_1</math> and <math>R_2</math>, 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:

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:<math>W_i = \frac{\text{average capital}_i}{\text{average capital}_1+\text{average capital}_2}</math>

==Linked Returnreturn versus Truetrue Timetime-Weightedweighted Returnreturn==

An alternative to the modified Dietz method is to link geometrically the modified Dietz returns for shorter periods. The linked modified Dietz method is classed as a time-weighted method, but it does not produce the same results as the [[time-weighted return|true time weighted]] method, which requires valuations at the time of each cash flow.

==Issues==

===Problems with Timingtiming Assumptionsassumptions===

There are sometimes difficulties when calculating or decomposing portfolio returns, if all transactions are treated as occurring at a single time of day, such as the end of the day or beginning of the day. 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.

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The problem only arises because the day is treated as a single, discrete time interval.

===Negative or Zerozero Averageaverage Capitalcapital===

In normal circumstances, average capital is positive. When an intra-period outflow is large and early enough, average capital can be negative or zero. Negative average capital causes the Modified Dietz return to be negative when there is a profit, and positive when there is a loss. This resembles the behaviour of a liability or short position, even if the investment is not actually a liability or a short position. In cases where the average capital is zero, no Modified Dietz return can be calculated. If the average capital is close to zero, the Modified Dietz will be large (large and positive, or large and negative).

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::<math>= -50 \text { dollars}</math>

The Modifiedmodified Dietz return in this case goes awry, because the average capital is negative, even though this is a long position. The Modified Dietz return in this case is:

:<math>\frac {\text {gain or loss}}{\text {average capital}} = \frac {50}{-50} = -100 \%</math>

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</source>

==Java Methodmethod for Modifiedmodified Dietz Returnreturn==

<source lang="java">

private static double modifiedDietz (double emv, double bmv, double cashFlow[], int numCD, int numD[]) {