Reading 39 : Equity Risk Premium in integrated markets (International CAPM)

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 ?

.