Hey everyone, I stumbled upon a question that said something like the following :
Country A is moving toward perfect integration with the world. Beta of country A relative to world is 0.9.
Equity risk premium (A) = 5%, Risk-free (A) = 4%, Risk-free (World) = 7%.
_ The question is to find the Equtiy Risk Premium for the World and which risk-free rate to use in the international CAPM to estimate the required return ? _
The answer was ERP (world) = ERP (A) / Beta (A to world) = 5% / 0.9, and use the country A risk-free rate.
I haven’t found anything clear and close to this in the curriculum, so my guess is the following :
Given that markets are integrated : Return A = Return World
where : Return_(A)_ = Rf_(A)_ + Beta_(A,A)_ * ERP_(A)_ where Beta_(A,A)_ = 1 (beta of country A with itself)
and Return_(world)_ = Rf_(A)_ + Beta_(A,world)_ * ERP_(world)_
So we have :
=> Rf_(A)_ + Beta_(A,A)_ * ERP_(A) =_ Rf_(A)_ + Beta_(A,world)_ * ERP_(world)_
=> ERP_(A) =_ Beta_(A,world)_ * ERP_(world)_
=> ERP_(world) =_ ERP_(A) /_ Beta_(A,world)_ (same as answer of the question)
Does this formula exist somewhere and do you think it is correct ?