Investing in a Portfolio: Two-Asset Comparison and Risk Analysis

Comparison of Investment in Two Different Portfolios

1. You are deciding which of two portfolios to invest $50,000 in. The first portfolio has equal amounts of these eight stocks: Microsoft and Apple, Bristol Myers Squibb and Humana, Amazon and Ford, and JP Morgan Chase and Bank of America.  (This is the 8-asset portfolio from Assignment A.)  The second portfolio has two assets:  the market portfolio, M, and one-year Treasury bills, a risk-free asset (F).  Here are some relevant facts (note: E(R) is expected return, σ2 is return variance, σ is return standard deviation, RF is risk-free return, XF and XM are the portfolio weights of F and M, σFM is the covariance of the returns on F and M): 

i) Suppose you want the two-asset portfolio to have the same expected return as the 8-asset portfolio. What XM and XF make E(RP) = 0.106?  What is σP for this portfolio? How does it compare with σP for the 8-asset portfolio?  Based on your numbers which of these two portfolios should you invest in and why?

ii) Suppose instead that you want the two-asset portfolio to have the same standard deviation as the 8-asset portfolio. What XM and XF make σP = 0.307?  What is E(RP) for this portfolio? How does it compare with E(RP) for the 8-asset portfolio? Based on your numbers, which of these two portfolios should you invest in and why?

iii) What is the capital market line (CML)? Why is it significant to investors? How do your answers to i) and ii) relate to the CML? 

2. (Round your calculations to 4 decimal places.) You are curious about how the stocks of two companies – Bank of America (BAC) and Bristol Myers Squibb (BMY) – affect the risk of the market portfolio, M:  Do they make M riskier or safer? Both companies have outstanding stock valued at around $150b (i.e., Vi = $0.15t). Let M-O be the market portfolio without either stock and let M-N be the market portfolio including one of the stocks. The value of M-O, VM-O, is about $53.85t.  Here are some relevant facts (note: σ2 is return variance; σi M-O is the covariance of the returns on BAC and M-O or BMY and M-O; Xi and XM-O  are portfolio weights):  

i) Suppose you add BAC stock to M-O.  What is the return variance of M-N, σM-N2?  Is σM-N2 > σM-O2 or < σM O?  What role does BAC’s unique risk play in this change? What role does BAC’s market risk play? Does adding BAC raise, lower or leave unchanged the average of the covariances in σM-N2?  What is the beta of BAC stock?

ii) Suppose you add BMY stock to M-O instead of BAC stock. What are the answers to the same questions as in i) but for BMY stock?

iii) Based on your answers to i) and ii), how would you describe beta as a risk measure? What does it measure, and how?