Real Versus Nominal Returns.

A foreign stock market provided a rate of return of 95 percent. The inflation rate in this country during the year was 80 percent. In the United States, in contrast, the stock market return was only 12 percent, but the inflation rate was only 2 percent.
Which country's stock market provided the higher real rate of return?

The real return in the first country was
1.95/1.80 - 1 = 8.3%

In the US is was 1.12/1.02 -1 = 9.8%

So the US stock market performed better in real terms than the foreign market.

Note that I used division rather than subtracting the inflation % from the rate of return %. That is the correct way to adjust for inflation. Subtracting gives an approximate answer that is not accurate at high inflation rates. It would have resulted in 15% for the foreign stock market and 10% for the US.

ok, thanks.
So if the rate was lower, would it then be ok to subtract it, or is it best to use division no matter the scenerio?

It is best to always use division.

Using division to calculate the real rate of return is the more accurate and reliable approach, regardless of the magnitude of the rates involved. This is because dividing the nominal return by the inflation rate accounts for the impact of inflation on the actual purchasing power of the investment.

Subtracting the inflation rate from the nominal return may provide an approximate estimate when the inflation rate is low, but it becomes increasingly unreliable as inflation rates rise. In the example you provided, subtracting the inflation rate from the nominal return would have resulted in inaccurate calculations.

By dividing the nominal return by the inflation rate, you are essentially adjusting the nominal return to reflect the changes in the purchasing power of the investment. This approach gives a more precise indication of the real rate of return, allowing for proper comparison between different investments or stock markets.

Therefore, regardless of the scenario or the magnitude of the rates involved, it is best practice to always use division when calculating the real rate of return to ensure accuracy and consistency in your calculations.