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). “ |