1. (This question requires preliminary computations in Excel before answering.) The Excel file that accompanies this assignment shows variances of annual stock returns for eight firms in the four largest S&P 500 sectors: Microsoft (MSFT) and Apple (AAPL) from the technology sector; Bristol-Myers-Squibb (BMY) and Humana (HUM) from the health care sector; Amazon (AMZN) and Ford (F) from the consumer discretionary sector; and JP Morgan Chase (JPM) and Bank of America (BAC) from the financial sector. Return covariances are also shown. Beneath these data are templates which compute return variances for portfolios (_P²) having from one to eight assets. For example, computes the return variance of an eight-asset portfolio as follows:

Replacing the X_i s, _i² s, and _ij s with numbers causes the template to compute the portfolios return variance. Doing likewise for all eight templates triggers the computation of more metrics at the end of the worksheet.

Instructions: Identify the riskiest asset from among the eight. Use the first template to compute the return variance of a one-asset portfolio invested entirely in this asset. Next, identify the riskiest asset from the remaining seven assets. Use the second template to compute the return variance of a two-asset portfolio invested equally in this asset and the first one. Now, identify the riskiest asset from the remaining six assets. Use the third template to compute the return variance of a three-asset portfolio invested equally in this third-riskiest asset and the other two. Continue this process until all the assets are in the portfolio.

Use the results of this exercise to discuss how diversification (investing in many assets) affects portfolio risk, measured as _P², and why. Include a description how assets unique risks and market risks influence _P². (Answer in 8 - 18 sentences.)

2. (Answer in 8 - 15 sentences.) A portfolio with the stocks of the 500 largest US corporations is safer than a portfolio with the stocks of the 2,000 smallest companies traded on the New York Stock Exchange: historically, the former portfolio has a return variance (_P²) of around 0.039 versus a return variance of around 0.100 for the latter. A possible explanation for this fact is that, individually, large corporations have less unique risk than small corporations. Do you agree with this explanation? Either support or refute this explanation using strongest arguments you can muster. Be precise. (Hint: use the investment theory presented in class and the information given.)