Risk premium calculation

CFA Level I Equities
#1

Hi,

let’s say we have the following geometric returns: Equities (8%) and Treasury Bills (2.5%). What is the risk premium for equities?

1.) 1.08/1.025-1=5.37%

2.) 8%-2.5%=5.5%

What is the correct solution and why?

#2

2

I have never seen risk premia being multiplied. e.g. bond nominal rates = real rate + inflation risk premium + default risk premium + maturity risk premium + liquidity risk premium.

Never seen (1 + nominal rate) = (1 + real rate) * (1 + inflation risk premium) * (1 + default risk premium) * (1 + maturity risk premium) * (1 + liquidity risk premium).

#3

Risk premia – like inflation – compound with the risk-free rate.

#1 is correct; #2 is an approximation.

#4

I’m surprised that you’ve never seen it; it’s the way it’s always (properly) calculated.

#5

I happened to be on the page discussing the equity risk premium in this year’s Morningstar Ibbotson SBBI Classic Yearbook looking up something for work, they define it, as S2000 suggests,

(1+Equity Total Return) / (1+Treasury Bill Total Return).

2 Likes
#6

The biggest problem with not having the slightest clue is that on those rare occasions when I’m actually right (by accident), nobody believes me.

#7

I believe you more often than not, S2000.

#8

Answer 1 for sure. Same for the real return: (1+total return)/(1+inflation rate). The differences are quick (and accurate) approximations.

#9

I should qualify ( / backtrack smiley) - I don’t think I saw #1 in CFA L1 textbook. Obviously #2 is the real deal and #1 is an approximation.

I missed that the question is a giveaway - geometric returns. So they are probably expecting (1+x)/(1+y) - 1. My bad.

#10

But it is in the L1 book… and #1 is the real deal, #2 is the approximation.

#11

hi -sorry i know this is going back a bit, but to the original question, why is inflation not included in the denominator? treasury bill is the rf rate and equity return is the nominal rate, don’t we need the inflation number as well?

many thanks

#12

The Treasury rate is a nominal rate.

#13

ah ok i had that wrong. so then what’s the equites rate - is that the real rate?

im just trying to figure which numbers i plug in to the below formula.

using the equation (1+r) = (1+rf)(1+inflation)(1+risk premium)

again many thanks… only a few days to go.

cheers

#14

ah i think ive got it, the rf rate * inflation is = nominal rate = treasury rate

thanks mate

#15

Also nominal.

Thus, in the division the inflation premia cancel each other.