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nism-series-xa-exact-real-return-fisher-equation-11-3-percent-nominal[ INVESTMENT ADVISER (LEVEL 1) ]

An investment adviser projects a nominal portfolio return of 11.30% per annum over the next decade. If the expected annual inflation rate is 6.00%, what is the exact real (inflation-adjusted) annual rate of return?

[ A ]5.30%

[ B ]5.00%[ CORRECT ]

[ C ]6.78%

[ D ]4.50%

Takeaway

Using the exact Fisher equation, the real rate of return is 5.00% p.a. after adjusting the 11.30% nominal return for 6.00% expected inflation.

Derivation

Step 1: Fisher equation: r_real = [(1 + r_nominal)/(1 + r_inflation)] - 1. Step 2: Substitute: [(1.1130)/(1.0600)] - 1. Step 3: 1.1130/1.0600 = 1.0500. Step 4: 1.0500 - 1 = 0.0500 = 5.00%. The exact compound formula differs from the commonly-used linear approximation (nominal minus inflation = 11.30% - 6.00% = 5.30%), which slightly overstates the true real return because it ignores the cross-term interaction between the nominal rate and inflation rate. The exam specifically asks for the 'exact' figure to test whether candidates know and can apply the full Fisher formula rather than defaulting to the simpler but less accurate approximation.

Why the others fail

A — 5.30%

5.30% is the simple linear approximation (11.30% - 6.00%) rather than the exact compound Fisher equation result, which correctly divides (1+nominal) by (1+inflation) before subtracting 1.

C — 6.78%

6.78% does not follow from either the exact Fisher equation or the linear approximation applied to these inputs — it appears to result from a division or computational error.

D — 4.50%

4.50% subtracts an unexplained additional margin beyond the correct inflation adjustment; it does not match either the exact Fisher equation result or the simple linear approximation for these.