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In-line exercise: real returns, solution

If inflation is running at 1%/month, what are the real rates of return to Ursidae Corp for the three months examined in the previous in-class exercise? Recall that the nominal returns were 10%, -20%, and 5%.

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approximate:

Rreal_1 ~ 10% - 1% = 9%; Rreal_2 ~ -20% - 1% = -21%; Rreal_3 ~ 5% - 1% = 4%

exact:

Rreal_1 ~ (1 + 10%)/(1 + 1%) - 1 ~ 8.911%; Rreal_2 ~ (1 - 20%)/(1 + 1%) - 1 ~ -20.79%; Rreal_3 ~ (1 + 5%)/(1 + 1%) ~ 3.96\%

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Phil Dybvig
Using the approximate equation, we subtract 1% from the nominal returns of 10%, -20%, and 5%, to obtain real returns of 9%, -21%, and 4%, respectively. Using the exact equation, we divide 1 plus the return by 1 plus inflation and subtract 1. As is usual for computations over short periods, the approximation works very well. The precision of the approximation is much better than the precision of inflation measurement.

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