Financial Market Equilibrium Models

CFA Level III Economics
#1

I have a question about Level 3 Reading 15 (Capital Market Expectations) - Paragraph 3.1.4 p.40 and after

Equation (10) states that RP(i) = standard deviation(i) * correlation (I,M) * Sharpe Ration(M)

In the case of the Canadian equities and bonds:

  • Fully integrated markets: I fully agree with the calculation
  • Fully segmented markets (p.42): “We must first recognize that if a market is completely segmented, the market portfolio in Equations 9 and 10 must be identified as the individual local market. Because the individual market and the reference market portfolio are identical, ρ_i,M_ in Equation 10 equals 1. (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).”

Then we move on to use formula 11 with correlation = 1 and a Sharpe ratio of 0.28. This is the Sharpe ratio of GIM. GIM is defined on p.40 as “The GIM is a practical proxy for the world market portfolio consisting of traditional and alternative asset classes with sufficient capacity to absorb meaningful investment”.

Shouldn’t the Sharpe ratio in the completely segmented market be the Sharpe Ratio of the broad-based index for Canadian equities and not the Sharpe Ratio of the GIM? The way they implement it, the Canadian market would have a correlation of 1 with the GIM (i.e. the world market portfolio) and this is not the case for a segmented market.

My question also applies to Example 19.

In short, can anyone explain to me why the Sharpe ratio of GIM (world market portfolio) is used with a correlation of 1 for a segmented market? I’d expect to use the Sharpe Ratio of the local market with a correlation of one.

#2

Good point, I was wondering the same.

#3

On p.42, click on footnote 50, it says: “For simplicity, we are assuming that the Sharpe ratios of the GIM and the local market portfolio (used in Equation 11) are the same.”

I hope this helps. Good luck :slight_smile:

#4

It is the same in the mocks exams , they assume it is the same.

Example in " Capital Marcket expectation : Ptolemy" Q5 asks to use the method for an emerging small-cap equities and the text gives the following information:

Sharpe ratio for GIM and emerging small-cap equity: 0.31

#5

Because it is the I CAPM approach, not the CAPM.

WIth that said, the GIM is thought to be the most reliable benchmark historically. Don’t forget that this was mostly done to estimate emerging markets ERP, where historical data remains vauge and biased.

In this case, your global ERP is always the base you start with, then you multiply by the desired county’s standard deviation, netting you a relative risk weighted ERP.

For example, if ERP in the GIM is 5%, the SD is 10%, but the SD (risk) of the emerging market is double that at 20%, then your ERP is simply 5*2=10%.

Using the broad based index for the same market would render the whole equation useless in the first place, since all like terms will cancel out, leaving you with ERP = Ri - Rf, which are the variables we are trying to deduce in the first place.