# Computation of Risk Premium with Real Rate retur

Hi everyone,

I have a problem with Practice Questions 13 and 14 of Reading 39 (regarding computation of risk premium) and the errata published by the CFA. I don’t understand why they change the numerator with (1 + 0.080) whereas the formula in the curriculum seemed more consistent with the previous answer. All the info are below (related to question 13)

Note: in the previous questions (11 and 12), the student is asked about the real return of equities and the real return of corporate bonds and the correct answers were 5,8 % for real return of equities and 4,3 % for real restrung of corporate bonds.

—-

An analyst had the following geometric returns

equities —- > 8%

Corporate bonds —-> 6,5%

Treasury Bills —-> 2,5%

Inflation —-> 2,1 %

Question 13:

The risk premium for equities is :

A 3,2% (erratum : A 5,4%)

B 3,4% (erratum: B 5,5%)

C 3,6% (erratum C 3,6%)

Answer before erratum: A is correct (1 + 0.058) / (1+0.0250) - 1 = 3,2 %

Answer after erratum: A is correct (1 + 0.080)/ (1+0,

.0250) - 1 = 5,4%

i don’t understand the answer after erratum: is it not consistent with the curriculum formula :

(1+r) = (1+r rf) * (1+pi) *(1+RP)

(1+r real) = (1+r rf) * (1+RP) or

(1+r real) = (1+r) / (1+pi)

pi = inflation

RP= risk premium

r rf= real risk return

Any insights ?

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Return on Equity and risk free return (Tbill return) both are nominal return.

So either you adjust both for Inflation or you use nominal return for both. Answer will be 5.4%.

The previous answer user real return for eq and nomnial for Tbill thats why it was incorrect.

Studying With

Thank you for answer.

I am not sure I completely understand. Could you illustrate with the formulas given in the curriculum that I just cited above ?

Equity risk premium using nominal returns(1+nominal return on equities) /(return on T-bills) - 1= 1.08 / 1.025 - 1= 0.053658 ≈5.40%

Equity risk premium using real returnsReal return on equities

(1+nominal return on equities)/(1+inflation) - 1 = 1.08/ 1.021 - 1=0.05778 ≈5.8%

Real return on T-bills

(1+nominal return on T-bills) / (1+inflation) - 1= 1.025 / 1.021 - 1=0.003917 ≈ 0.39%

Equity risk premium

(1+real return on equities) / (1+real return on T-bills) - 1= 1.05778 / 1.003917 - 1=0.053658 ≈5.4%

Hope this helps!