Case study: Managing a portfolio and the S&P 500

The S&P 500 is an index fund of 500 of the largest companies in America. The index keeps track of the annualized returns of the entire basket of companies. You are a portfolio manager (stock investor) who is interested in understanding the long term behavior of the index fund before you begin investing.

Part I: Summarizing the data

  1. Open the S&P 500 data provided in google classroom.
  2. The S&P500 Growth variable records the annualized percent growth of the entire index of funds for each year from 1871 to 2015. Create a histogram of this variable move the histogram to a new sheet named S&Pchart.
  3. Does the distribution of annualized returns look approximately normal? Justify your answer.
  4. Calculate the mean of the S&P500 Growth variable and record it in the table provided.
  5. Calculate the standard deviation of the S&P500 Growth variable and record it in the table provided.

Part II: Testing the theorem

We now would like to see if our theorem discussed in class actually holds for a variable describing the stock market.

  1. Create a new variable named standardized that is the standardized version of the S&P500 Growth variable.
  2. Calculate the mean of the *standardized** variable you just created and record it in the table provided.
  3. Calculate the standard deviation of the *standardized** variable you just created and record it in the table provided.
  4. Based on (2) and (3), does the theorem discussed today in class hold? In other words, does the standardized variable have a mean of 0 and a standard deviation of 1?

Part III: Drawing conclusions about the stock market

Now to the interesting part! We want to use the data to draw conclusions about the stock market. This is where the tools discussed in class come in.

  1. As an investor, you would like to know what the probability of losing money is within a given year. Using the z-score method, calculate the probability that the expected growth of the S&P 500 index is negative.
  2. Conversely, you would like to know the probability that the growth of the S&P 500 is positive (in other words this means you make money by investing in the S&P 500). Calculate the probability in a given year that the growth in the S&P 500 is positive. Hint: you can use part I to your advantage!.
  3. As a portfolio manager you would like the returns to your portfolio to be between 6% and 18%. Calculate the probability of this happening in a given year.