Modified Dietz method: Difference between revisions

Revision as of 17:38, 14 November 2018

Revision as of 17:47, 14 November 2018

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so

:{{nowrap begin}}{{link if exists|average capital}} = {{link if exists|start value}} = $10,000 {{link if exists| USD}}{{nowrap end}}

so the return is:

Line 154:

This 9% portfolio return breaks down between 8 percent contribution from the $800 earned on the shares and 1 percent contribution from the $100 interest earned on the cash account, but how more generally can we calculate contributions?

The first step is to calculate the average capital in each of the cash account and the shares over the full year period. These should sum to the $10,000 average capital of the portfolio as a whole. From the average capital of each of the two components of the portfolio, we can calculate weights. The weight of the cash account is the average capital of the cash account, divided by the average capital ($10,000 USD) of the portfolio, and the weight of the shares is the average capital of the shares over the whole year, divided by the average capital of the portfolio.

For convenience, we will assume the time weight of the outflow of $8,000 cash to pay for the shares is exactly 1/4. This means that the four quarters of the year are treated as having equal length.

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:{{nowrap begin}}{{link if exists|average capital}}{{nowrap end}}

::{{nowrap begin}}= {{link if exists|start value}} - {{link if exists|time weight}} × {{link if exists|outflow amount}}{{nowrap end}}

::{{nowrap begin}}= 10,000 - {{sfrac|1|4}} × $8,000 {{link if exists| USD}}{{nowrap end}}

::{{nowrap begin}}= 10,000 - $2,000 {{link if exists| USD}}{{nowrap end}}

::{{nowrap begin}}= $8,000 {{link if exists| USD}}{{nowrap end}}

The average capital of the shares over the last quarter requires no calculation, because there are no flows after the beginning of the last quarter. It is the $8,000 invested in the shares. However, the average capital in the shares over the whole year is something else. 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:

:{{nowrap begin}}{{link if exists|average capital}}{{nowrap end}}

::{{nowrap begin}}= {{link if exists|start value}} - {{link if exists|time weight}} × {{link if exists|outflow amount}}{{nowrap end}}

::{{nowrap begin}}= 0 + {{sfrac|1|4}} × $8,000 {{link if exists| USD}}{{nowrap end}}

::{{nowrap begin}}= $2,000 {{link if exists| USD}}{{nowrap end}}

We can see immediately that the weight of the cash account in the portfolio over the year was:

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To calculate the gain or loss over the two-year period,

:<math>\text {gain or loss} = B - A - F = 300 - 100 - 50 = $150 \text{ USD.}</math>

To calculate the average capital over the two-year period,

:<math>\text {average capital} = A + \sum \text {weight} \times \text {flow} = 100 + 0.5 \times 50 = $125 \text{ USD,}</math>

so the modified Dietz return is: