Risk premium calculation

[neptunhiker]

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?

 

[naren]

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).

 

[S2000magician]

Risk premia – like inflation – compound with the risk-free rate.
#1 is correct; #2 is an approximation.

 

[S2000magician]

naren_ wrote: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).

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

 

[Would You Look]

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).

 

[S2000magician]

Would You Look at That wrote: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).

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.

 

[Would You Look]

I believe you more often than not, S2000.

 

[Gurifissu]

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

 

[naren]

I should qualify ( / backtrack ) - 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.

 

[tickersu]

naren_ wrote:
I should qualify ( / backtrack ) - 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.

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