Risk Premium

[ckyeh]

Dear David:
On webnair 2010-8-a-Investment, page 5:
E{Rn}=1+iF+βn*μB+βn*ΔfB+αn
βn*μB is Risk Premium.

And On webnair 2010-7-a-Operational, page 18:
Equity risk premium (ERP) = 5%
equity beta = 1.2
Riskless rate = 4%, Market return = 9%.
So I concluded:
Equity risk premium (ERP) = equity beta*{ Market return- Riskless rate}
5%=1.2*{9%-4%}=6% ???
Do we need to put ALPHA here? So Alpha=-1%?
Then 5%=-1% +1.2*{9%-4%}

But If we do so, 5%couldn’t be the Equity risk premium, right?
Because based on the definition of Equity risk premium:
The excess return that an individual stock or the overall stock market provides over a risk-free rate.
Equity risk premium = { Equity return- Riskless rate}=equity beta*{ Market return- Riskless rate}
Compared to webnair 2010-8-a-Investment, page 5:
E{Rn}=1+iF+βn*μB+βn*ΔfB+αn
βn*μB is Risk Premium, right? The meaning of { Equity return- Riskless rate}、equity beta*{ Market return- Riskless rate} andβn*μB seems all the same, right?

Thanks for your help!

 

[David Harper CFA FRM]

Hi ckyeh,

In regard to RAROC (p 18 of 7a), the ERP (aka, market risk premium) of 5% is just the 9% - 4%.
Note this is incorrect: Equity risk premium (ERP) = equity beta*{ Market return- Riskless rate}
Rather: ERP = { Market return- Riskless rate}, such that
CAPM says: excess return (i) = beta*ERP
Alpha does not need to enter except it may implicitly impact the 11% RAROC; e.g., please note:
ARAROC = (RAROC - Rf)/beta and project passes if ARAROC > ERP
(RAROC - Rf)/beta > ERP, such that
(RAROC - Rf) > ERP * beta, and
RAROC > Rf + ERP * beta
… note similarity to CAPM/Jensen's alpha: pass the project if it returns equal to our better than implied by its beta

You are absolutely correct to draw a line to Grinold. As you know, he is basically generalizing the CAPM into APT. In this case.
E{Rn}=1+iF+βn*μB+βn*ΔfB+αn, is equal to:
E{Rn}=1+iF+βn*(μB+ΔfB) +αn

And this is analogous to CAPM:
E(R) = riskfree rate + beta*ERP
… where (i) is his "time premium" = riskfree rate
… beta matches βn as factor EXPOSURE
… and the CAPM matches/parses into a long-term risk premium + short-term variation (whereas CAPM is single-period and does not make room for a short- versus long-run difference)

So, when you say, "μB is Risk Premium, right?" that is absolutely correct, only Grinold has "broken out" the long-run ERP/MRP, then added another "exceptional" term for short-run variation

David