problem 5: Consider Facebook. Since Facebook is a fairly large company, you can use S&P 500 Index as a proxy for the market portfolio.

(a) Estimate the beta of Facebook using past 5 years of monthly data (60 data points until the end of September 2018, which is from 11/1/2013 to 10/1/2018 in Yahoo Finance) and full length of monthly data (78 data points until the end of September 2018, which is from 5/1/2012 - actually 5/18/2012 - to 10/1/2018 in Yahoo Finance). To get the monthly returns of Facebook and S&P 500 Index, follow the same procedure as described in problem 4. Report your estimates in regression output tables and discuss the statistical significance.

(b) Which beta from (a) would you suggest is a better proxy for the market risk of Facebook? Briefly discuss your reasoning.

problem 4: The Vanguard Index 500 Fund (VFINX) has prices that replicate the S&P 500 Index with dividends reinvested. Use VFINX to estimate the expected return of the S&P 500 Index in two ways: (i) use 1 the historical average monthly return of VFINX over the full sample period (1/1/1980 - 10/1/2018 in Yahoo Finance, 466 data points); (ii) use the historical average monthly return of VFINX over last three years (11/1/2015 - 10/1/2018 in Yahoo Finance, 36 data points). To get the monthly returns of VFINC, first you need to collect price level data (adjusted for dividends and splits) for VFINX from Yahoo Finance.1 Second, you need to transform adjusted prices into returns by the definition of holding period return: rt = (PtPt1)/Pt1 . Report both arithmetic average and geometric average. Present all data and calculations in Excel (hide rows or columns to make your presentation visually appealing). Answer following questions: (a) Why arithmetic average is different from geometric average? (b) Which one of these estimates is representative of all possible economic circumstances for the stock market?

(only answer problem 5)