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Suppose a mutual fund maintains a portfolio with 2/3 of the investment weight in in the S&P 500 and 1/3 of the investment weight in a riskless investment with constant daily return of 1%. Letting Rt denote day-t fund return, and RtS&P the day-t S&P 500 return, the fund return each day t therefore satisfies Rt = 1/3×1% + 2/3× RtS&P Suppose you regress the daily fund returns (the Y-variable) on daily S&P 500 returns.
Hint: You should be able to answer the following questions without doing any calculations.
a) What should the R-squared of the regression be? Why?
b) What should the slope of the regression line (i.e., the beta) be?
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