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:<math>20 \times 12.50 - 100 \times 10 + 80 \times 15</math>
::<math>= 250 - 1,000 + 1,200</math>
::<math>=
There is a gain, and the position is long, so we would intuitively expect a positive return.
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The modified 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 {
Instead, we notice that the start value is positive, but the average capital is negative. Furthermore, there is no short sale. In other words, at all times, the number of shares held is positive.
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