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It makes sense that we use the same Sharpe for the GIM, since it is one global market. This piece from the CFAI curriculum might help:
(equation 10 is: RPasset = SD of asset x correlation of asset and world market x sharpe ratio of world market)
pg 43, Volume 3
“Equation 10 requires a market Sharpe ratio estimate. Singer and Terhaar (1997, pp. 44–52) describe a complete analysis for estimating it. As of the date of their analysis, 1997, they recommended a value of 0.30 (a 0.30 percent return per 1 percent of compensated risk). Goodall, Manzini, and Rose (1999, pp. 4–10) revisited this issue on the basis of different macro models and recom- mended a value of 0.28. For this exposition, we adopt a value of 0.28. In fact, the Sharpe ratio of the global market could change over time with changing global economic fundamentals.
(Level III Volume 3 Capital Market Expectations, Market Valuation, and Asset Allocation, 4th Edition. Pearson Learning Solutions p. 44). “

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Footnote on page 45. “For simplicity, we are assuming that the Sharpe ratios of the GIM and the local market portfolio are the same”

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then its settled. they are NOT the same portfolio. Thanks.

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bump
Anyone else having problem with understanding their approach?

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