Mr. Smith is a busy entrepreneur. A financial advisor decides where to invest Mr. Smith’s stock portfolio worth several million dollars. After a few years, Mr. Smith hires two consultants to independently evaluate the performance of his stock portfolio. These consultants were given daily data on the total dollar value of portfolio, as well as the data on the episodic infusions of cash from Mr. Smith. “I can’t trust these guys”, says Mr. Smith. “It is true they found the same return, but the risk‐adjustment calculations don’t match.” Consultant 1 reports that Mr. Smith’s stock portfolio had an annual Sharpe Ratio of 0.43, and while “a broad stock market index” had an annual Sharpe Ratio of 0.39. He also found an annual CAPM alpha of 1.54% per year. In contrast, Consultant 2 reports annual Sharpe Ratios of 0.41 and 0.40 for Mr. Smith’s portfolio and for a market index, respectively, and an annual CAPM alpha of 0.12%. Can both consultants have correct calculations? Explain in detail.
Impact Of The Use Of Time Weights And Dollar Weights On The Capm And Sharpe Ratios
Length: 1 pages (342 Words)
Impact of the Use of Time Weights and Dollar Weights on the CAPM and Sharpe Ratios
The disparity over the observations by the two consultants is possible if they adopted different formulas of adopting returns. There are two methods of deriving returns; time based returns and dollar based returns. Fabozzi (2001) argues that the difference in the CAPM return rates and the annual Sharpe ratios in the example could have caused by weighting differences. He argues that dollar weighted return method assigns more weight to periods where money is invested while time based allocates weight on average.
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