1

Given that

Real Rate of Return = (1 + nominal rate) / (1 + inflation rate) -1

If my nominal rate equals the inflation rate I get 0, meaning that my money is worth the same no matter the inflation rate.

If my nominal rate is greater than the inflation I get positive values, meaning my money is worth more the longer I leave in this investment. And vice-versa.

But something weird happens when the nominal rate is 0%, such as when I leave my money in my wallet. In that case the real rate will be

RR = (1 + 0%)/(1 + 5%) -1 = -4.76%

Am I missing something? How do I interpret that? Shouldn't it be -5%?

EDIT: Also, is there anything wrong with the following formula?

Fake Real Rate of Return = ((1 + inflation rate) / (1 + nominal rate) -1 ) * - 1

In that case when the nominal rate is 0% we get the inflation rate, and when the inflation rate equals the nominal rate we get 0%.

3
  • 2
    Percentages aren't additive. 1.05/1.04 - 1 isn't 0.01, either: it's 0.009615.... – chepner Jun 3 at 18:04
  • Maybe I'm not understading it corretly but the thing is, I'm not changing anything when I put my money on a 'investment' that has no nomial rate, by being very loose about the term investment, the money will devalue by the inflation rate, but when I compute it I get a different result, as if by 'investing it' in a zero nominal rate I changed the real rate of return to be less than the inflation rate. – f.rodrigues Jun 3 at 18:59
  • I think the discrepancy has something to do with the exact Fisher equation vs its approximation. – Flux Jun 3 at 20:44
5

If inflation was 100%, would you expect your money to lose 100% of its value?

Say you have $1000 cash. Widgets cost $1. You can currently buy 1000 widgets with your cash.

After 5% inflation, widgets now cost $1.05, but you still have the same $1000 cash. You can now only buy $1000/$1.05 = 952.38 widgets. Your money only has 952.38/1000 = 95.238% of the buying power it had previously, a loss of 4.762%. This is consistent with the value calculated by the formula.

4

Percentages are multiplicative, not additive.

If you make a 5% gain, and then have a 5% loss, you are not back to where you started, because 1.05 * 0.95 = 0.9975. The loss that balances out a 5% gain is a (1-1/1.05) ~= 4.76% loss, because 1.05*0.9524 ~= 1.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.