Real vs nominal rate of return

CFA Level I Portfolio Management
#1

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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#2

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

#3

Ah right! That makes sense, thanks!

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#4

My pleasure.

#5

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

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#6

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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#7

what i dnot understand about this question why in 1 we are using treasuary bill as denominator and in the other one the inflation?

#8

What do you mean by, “the other one”?

Which other one?

#9

some question ask for The real rate of return of equity instead of risk premium for equities
i guess the real rate is calculated with the infaltion in the denominator and the risk premiun with the closest one to a risk free investment in the denominator but i’m not sure on why though.

#10

On a $1 equity investment you would receive an extra 0.055 (1.08-1.025) in premium vs the tbill investment. This premium is 5.366% (0.055/1.025) more than you would receive over and above the tbill.

OR the long way
prem
= (1.08-1.025) / 1.025
= 1.08/1.025 - 1.025/1.025
= 1.05366 - 1
= 0.05366

No formula required. Just use basic math to calculate a % gain. If you purchase a stock for 102.5 and sell for 108. Your 5.5 gain (premium) is 5.366% more than your original purchase price.

108/102.5 -1 = 0.05366

or

5.5/102.5 = 0.05366