# Real vs nominal rate of return

An analyst observes the following historic geometric returns:

Equities 8.0%

Corporate Bonds 6.5%

Treasury Bills 2.5%

Inflation 2.1%

The risk premium for equities is closest to:

A) 5.4%

B) 5.5%

C) 5.6%

Why is the answer is A? Surely we need to obtain the real rate of return for equities which is 5.8% (1.08/1.021) and then divide this by the treasury bill (risk-free) rate of 1.025. Yet the book uses the nominal return in the top half of the fraction (1.08/1.025)?

In the book it says that the REAL RATE of interest is equal to (1+Rf)x(1+Rp) NOT the nominal rate of interest so I’m confused as to why they’ve used the nominal rate to compute the risk premium. Any ideas?

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Both the equity return and the Treasury return will include inflation; it cancels.

Ah right! That makes sense, thanks!

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My pleasure.

Hey, Could you pls explain this? I’m still struggling with it.

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Risk premia compound.

\left(1 + r_f\right)\left(1 + ERP\right) = 1 + r_{eq}
1 + ERP = \frac{1 + r_{eq}}{1 + r_f} = \frac{1.08}{1.025} = 1.0537
ERP = 1.0537 - 1 = 0.0537 = 5.37\%
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