(Round your calculations to 4 decimal places.) (Note: If you invest equal dollar amounts in the 4,400 stocks traded publicly in the US, the X_i of any stock is 1/4400 or 0.000227.) 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., V_i = $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, V_M-O, is about $53.85t. Here are some relevant facts (note: σ² is return variance; σ_{i M-O} is the covariance of the returns on BAC and M-O or BMY and M-O; X_i and X_M-O are portfolio weights):

Metrics:	p 2	σi M-O	V	X
M-O	0.039	----------	$53.85t	0.9972
BAC	0.264	0.0605	$00.15t	0.0028
BMY	0.038	0.0263
M-N	see below	----------	$54.00t	1.0000
Equations for a two-asset portfolio with M-O and i:
σM-N2 = Xi2 σi2 + 2 Xi XM-O σiM-O + XM-O2 σM-O2
Note: Xi2 + 2 Xi XM-O + XM-O2­ = 1 because Xi + XM-O = 1

i) Suppose you add BAC stock to M-O. What is the return variance of M-N, σ_M-N²? Is σ_M-N² > σ_M-O² or < σ_M‑O²? 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 M-N? 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?