 # 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?

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.

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\%