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Reading 14_Capital Market Expectations_Financial Market Equilibrium Models

I am a bit confused by such Financial Market Equilibrium Models.

On p.15-16 of the Schweser notes or the bit just after Equation 10 but before Equation 11, both notes state that if we assuming a full segmentation, the correlation between the local market and the global portfolio ρi,m is considered to be 1.0. The rationale for that is because the local market is used as the reference market instead of the global market. In other words, the local market and the reference market portfolio are the same. (For example, if Canadian equities were a completely segmented market, the reference market portfolio and the individual market portfolio would each be a broad-based index for Canadian equities, and the correlation of such an index with itself would of course be 1.) 

As a result, the equity risk premium for such fully segmented market = σi*(RPMM). That is where I get confused. Since the market that we are studying is identical to the reference market, shouldn’t its equity premium equal to excess of its expected return over the risk-free rate? (Let’s put it in this way, if Canadian equities were a completely segmented market, the equity risk premium of the Canadian equities should be equal to the expected return from Canadian equities less the risk-free rate.) I am confused because as we are assuming the two markets are actually the same thing, but then we estimate its equity risk premium by multiplying statistics from two things, i.e. the standard deviation from one market σ; and the Sharpe ratio of a different market RPMM

To put it simply, if the segmented market is correlating with itself, then why would the global portfolio has any sort of influence on calculating the equity risk premium of the segmented market?

I just can’t get the logic here. Anyone have a different view on this and  willing to share their views?

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beta = ρ * σim

RPi = ρ * σim * (RPm

if fully segmented market. ρ is one, then RPi = σi  * RPmm