For problems 4 through 8, consider the data set available in this quiz. In this data set, you find the monthly returns of seven popular exchange traded funds (ETFs): S&P 500 (SPY), Russell 2000 (IWM), Dow Jones (DIA), MSCI Germany (EWG), MSCI China (MCHI) and MSCI Emerging Markets (EEM). When loading the data into your Jupyter notebook, make sure to pass the arguments index_col=0 and parse_dates=True to instruct pandas to properly read the index containing the dates. What is the shape of the resulting data frame df, accessed as df.shape? Write your answer in the format (x, y), where x and y are the numerical outputs you get.

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We are going to first focus on the column IWM and the returns in it. What is the average return over the entire time period covered in the data frame? Round your answer to five decimals.

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What is the maximum return observed in the years 2016 through 2018 for IWM? (Hint: Use loc to first access the records, and then use the max() function to find the maximum value.) Round your answer to five decimals.

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As an investor, we are not only concerned with the returns of our holdings; we also care about the risks involved. Compute the standard deviation for all seven ETFs for the years 2016 and 2017. To this end, apply the function std() to the data frame. Because they are so broadly diversified, SPY and DIA usually have the lowest standard deviation. Then, which ETF has the third lowest standard deviation? Type in the name of the corresponding column.

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Now, let us compute to how much a dollar invested into the IWM ETF in the beginning of 2016 would have grown to by end of March 2020. To find this answer, first add 1 to the returns and then apply the cumprod() function to the result. Then read out the value for March 2020. This is the value of an investment of one dollar in the beginning of 2016. Round your answer to the nearest cent.

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