Suppose you observed the following data on two securities: Mars and Venus:

You short sold 200 shares of Mars at $20 per share and purchased 400 shares of Venus at $25 per share to increase the possible return on the portfolio.The correlation between the securities is 0.30.What is the standard deviation of the portfolio?
A) 7.06%
B) 26.56%
C) 32.45%
D) 56.96%

Question

Suppose you observed the following data on two securities: Mars and Venus:
  
You short sold 200 shares of Mars at $20 per share and purchased 400 shares of Venus at $25 per share to increase the possible return on the portfolio.The correlation between the securities is 0.30.What is the standard deviation of the portfolio? 
A) 7.06% 
B) 26.56% 
C) 32.45% 
D) 56.96%

Quizplus · Accepted Answer

Portfolio weight in Mars,WM = (-200*$20)/(-200*$20+400*$25)= -$4,000/$6,000 = -0.6667 Portfolio weight in Venus w_V = 1-(-0.6667)= 1.6667 σ_P = √[(w²_M)(σ²_M)+(w²_V)(σ²_V)+2(w_M)(w_V)(σ_M)(σ_V)(ρ_MV)] = √(0.002844+0.340278-0.018667 = 56.96%

Suppose You Observed the Following Data on Two Securities: Mars