Would you be happy if the value of your investments grew by 10% in a year? It turns out that the answer depends on a few factors. One of the main factors (we'll discuss others in future tutorials) is the inflation rate. To understand why we need to know the inflation rate when evaluating our investment performance, we have to think about why we invest in the first place.
In the very first tutorial, we argued that we invest in order to boost our future consumption. The example we gave was saving from your income now in order to enjoy a better life when you retire in future. How does this relate to assessing whether 10% per year is a good or bad rate of return on investment? Suppose that last year you invested $500. Let's say you could spend this money to buy 20 meals in a restaurant @ $25/meal. Now, since your investment grew by 10%, you have $550, which you can use to buy 22 meals, if (and that's a big if) the meal price did not change. But, suppose all prices in the economy went up by 10% during the year. In other words, the inflation rate was 10%. Then, a meal costs $27.5 and with $550 you can purchase $550 / $27.5 = 20 meals.
Therefore, even though the value of your investments went up by 10%, because the prices also went up by the same amount, you are unable to consume more. This is where the distinction between nominal and real rate of return becomes important. The real rate of return is the rate of return that is net of the inflation rate. The 10% return on your investment is the nominal rate of return. Intuitively, the real rate of return is high if the inflation rate is low and vice versa. To be exact, the real rate of return
RRt over a period t is:
RRt = [( 1 + Rt ) / ( 1 + It )] - 1
where Rt is the total return (also the nominal rate of return) and It is the inflation rate.
In the discussion above, we had Rt = 10% and It = 10%, so the real rate of return is [(1 + 10%) / (1 + 10%)] - 1 = 0%. If the inflation rate was lower, say 5%, the real rate of return would be 4.76%. On the other hand, if the inflation rate was higher, say 15%, the real rate of return would be -4.35%. In other words, when prices rise faster than the value of your investments (i.e., It > Rt), in real terms, you realize a loss.
To sum up, whether 10% per year is a good return on investment or not depends, among other factors, on the rate of inflation. When the inflation rate is very low, we can ignore it in calculations, since in such circumstances nominal rates approximately equal real rates (i.e., Rt ≈ RRt). But, when the inflation rate is high, we have to explicitly account for it using the equation provided above.
Next tutorial: Single- vs multi-period returns
Previous tutorial: Inflation rate
In the discussion above, we had Rt = 10% and It = 10%, so the real rate of return is [(1 + 10%) / (1 + 10%)] - 1 = 0%. If the inflation rate was lower, say 5%, the real rate of return would be 4.76%. On the other hand, if the inflation rate was higher, say 15%, the real rate of return would be -4.35%. In other words, when prices rise faster than the value of your investments (i.e., It > Rt), in real terms, you realize a loss.
To sum up, whether 10% per year is a good return on investment or not depends, among other factors, on the rate of inflation. When the inflation rate is very low, we can ignore it in calculations, since in such circumstances nominal rates approximately equal real rates (i.e., Rt ≈ RRt). But, when the inflation rate is high, we have to explicitly account for it using the equation provided above.
Next tutorial: Single- vs multi-period returns
Previous tutorial: Inflation rate
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