A friend tips you off on a hot stock: Sure Thing Mines Ltd.You only have $10,000 to invest but you want to invest more.Assume that you can borrow an additional $5,000 by short-selling the risk free asset (issuing T-Bills).You purchase $15,000 worth of shares in Sure Thing Mines Ltd.
The expected returns and standard deviations of the two assets are outlined in the table below:

What is the beta of the portfolio?
A) 1.50
B) 1.70
C) 2.50
D) 2.55
E) 2.70

Question

A friend tips you off on a hot stock: Sure Thing Mines Ltd.You only have $10,000 to invest but you want to invest more.Assume that you can borrow an additional $5,000 by short-selling the risk free asset (issuing T-Bills).You purchase $15,000 worth of shares in Sure Thing Mines Ltd.
The expected returns and standard deviations of the two assets are outlined in the table below:

What is the beta of the portfolio?
A) 1.50 
B) 1.70 
C) 2.50 
D) 2.55 
E) 2.70

Quizplus · Accepted Answer

Step 1 - Compute the weights of each asset in the portfolio. You issued $5,000 of T-Bills, so you are short T-Bills. Short positions are represented by negative portfolio weights. w_i = 11ea7fdb_fc09_d77e_a768_57ce0b7221c1_TB2902_11 11ea7fdb_fc09_d77f_a768_b19e418c6f0e_TB2902_11 = 11ea7fdb_fc09_d780_a768_6b553762c986_TB2902_11 = -0.50 11ea7fdb_fc09_fe91_a768_e93e6015ff9d_TB2902_11 = 11ea7fdb_fc09_fe92_a768_2716dff596e6_TB2902_11 = 1.50 Step 2 - Use the weights to compute the beta for the portfolio. β_p = w₁β₁ + . . . + w_nβ_n Recall that the beta of the risk free asset is 0 β_p = -0.50 × 0 + 1.50 × 1.70 = 2.55

A Friend Tips You Off on a Hot Stock: Sure