Quantitative Analysis, use STAT software analysis Finance "S and P 500" data for 4 questions.

timer Asked: Oct 17th, 2018
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Question Description

Most important thing, Be sure you have Stata software and know how to use it, otherwise, if you do not have the software and don't how to use it, please do not bid this question!!!! (I will check it first)

Put screen shot form STATA to word document and answer each question(tables, graphs, charts).

Must have Do-file(s) showing the commands used to answer the questions.

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Page 1 of 7 FIN-665 Quantitative Analysis Instructions: Answer the following questions by performing the appropriate analysis. Please use this document inserting space where necessary. When finished, email the completed exam in Microsoft Word.docx (DO NOT CONVERT TO AND SEND AS AN ADOBE PDF FILE) format and attach the following: • Do-file(s) showing the commands used to answer the questions. FIN-665 Quantitative Analysis Page 2 of 7 For this exam you will analyze the performance of eight of the most popular S&P 500 tracking funds. The SP500.dta file contains the daily returns of the S&P 500, returns of the eight tracking funds, the 1-month Treasury bill rate, the three Fama and French factors, the Carhart factor, and an indicator variable that takes the value of one (1) when the economy is in recession. Variable date SP500 SPY IVV VFIAX FUSVX SWPPX PREIX DFUSX RYSOX rf mktrf smb hml umd USRECD Label Date Return of the S&P 500 SPDR S&P 500 iShares Core S&P 500 Vanguard 500 Index Fidelity 500 Index Premium Class Schwab S&P 500 Index T. Rowe Price Equity Index 500 DFA U.S. Large Company Portfolio Rydex S&P 500 Risk-Free Return Rate (1-Month Treasury Bill Rate) Excess Return on the Market Small-Minus-Big Return (size) High-Minus-Low Return (growth vs value) Up-Minus-Down Return (momentum) NBER based Recession Indicators for the United States from the Period following the Peak through the Trough FIN-665 Quantitative Analysis Page 3 of 7 1. An analyst friend states that since June 2006, the economy has been in recession 5 percent of the time and when it is in a recession the market experiences a statistically significant lower average return than when it is in expansion (not in recession). You claim he is understating the time in recession; that it is closer to 12.5% and there is no significant difference in average returns during recession and expansion. A. Perform the appropriate test(s) to determine who is correct regarding the proportion of time the economy is in recession and post the results below. B. Perform the appropriate test(s) to determine who is correct regarding the average returns while in and not in recession and paste the results below. C. Perform a regression of the market return using the recession indicator and paste below. Do the results support the results of the test(s) in B? D. Who is correct? Use the results from the tests above to support your conclusion. FIN-665 Quantitative Analysis Page 4 of 7 2. Calculate and analyze the performance of 1-month Treasury bill, stock portfolio of S&P 500 firms, and funds that track the S&P 500. A. Calculate the following: (1) arithmetic mean daily return; (2) standard deviation of daily returns; (3) mean annualized return using 252 days in a year; (4) rank the mean annualized returns from best to worst (1=best); (5) the daily Sharpe ratio = (mean return of fund – risk free return) / standard deviation of fund for the funds only; and (6) rank the Sharpe ratio from best to worst (1=best) for the funds only and fill in the results in the following table. See the following link for an explanation of the Sharpe Ratio. (report daily mean return, std. dev., and Sharpe ratio In decimal form to 6 decimal places; annual mean return as a percentage to 2 decimal places) https://www.investopedia.com/terms/s/sharperatio.asp Security/Portfolio/Fund Treasury Bill S&P 500 SPY IVV VFIAX FUSVX SWPPX PREIX DFUSX RYSOX Daily Return Mean Std. Dev. Annual Return Mean Rank Sharpe Ratio Ratio Rank B. Calculate the tracking error of each of the tracking funds. One way to calculate the tracking error is to calculate the standard deviation of the difference in the fund and benchmark returns over time. Fill in the following table for each fund and rank their performance by tracking error from best to worst (1=best). See the following link for an explanation of tracking error. (report mean and std. dev. To 6 decimal places) http://www.investopedia.com/terms/t/trackingerror.asp Fund SPY IVV VFIAX FUSVX SWPPX PREIX DFUSX RYSOX Daily Return Difference Mean Std. Dev. Rank FIN-665 Quantitative Analysis Page 5 of 7 C. Explain the results from parts A & B above. How did the funds perform against their benchmark? Which funds have the best/worst total performance? Which funds have the highest/lowest total risk? Which funds have the best/worst Sharpe ratio? What does the Sharpe ratio measure? Which funds have the best/worst tracking error? What does the tracking error measure? FIN-665 Quantitative Analysis Page 6 of 7 3. Another way to calculate the tracking error is to perform a t-test of the performance between each fund and the returns of the portfolio of S&P 500 stocks (SP500). A. Perform a t-test of the daily performance of each fund with the S&P 500. For each fund in the following table fill in: (1) the mean difference between the daily returns of the fund and the daily returns of the S&P 500; (2) standard deviation of the daily return difference; (3) the pvalue of the t-test; (4) the excess return ratio = (mean return – mean S&P 500 return) / standard deviation of fund; and (5) rank the excess return ratio from best to worst (1=best). (report mean, std. dev., and ratio to 6 decimal places; p-value to 3 decimal places) Daily Return Difference Fund SPY IVV VFIAX FUSVX SWPPX PREIX DFUSX RYSOX Mean Std. Dev. Excess Return p-value Ratio Rank B. Using the results from your answers in Question 2 and A above, which funds have the best/worst excess return performance compared to the benchmark? What is causing different funds to be selected as the best performing fund using the techniques in questions 2 and 3? Which fund would you recommend? Why? FIN-665 Quantitative Analysis Page 7 of 7 4. Perform a factor analysis of the Fidelity 500 Index Premium Class (FUSVX) fund’s performance using the CAPM, Fama & French 3-factor, and Carhart 4-factor models and complete the following questions. A. Calculate the risk adjusted performance of FUSVX using the CAPM, Fama & French 3-Factor, and Carhart 4-Factor models. Report the coefficient estimates to four decimal places and the p-value to three decimal places. Factor Alpha Market factor Size factor Value vs. growth factor Momentum factor CAPM Coef. p-value Fama & French 3-Factor Model Coef. p-value Carhart 4-Factor Model Coef. p-value B. Calculate the annualized alpha as a percentage with 2 decimal places for each of the models using 252 days in a year and complete the following table. Model CAPM Fama & French Carhart Annualized Alpha Significant? (yes/no) C. Determine which factor(s) are significant in describing the performance and interpret their meaning. Include an analysis of Alpha. D. Which model would you choose as the best model to evaluate performance? Why? ...
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