Question

Portfolio Return At the beginning of the month, you owned $12,000 of Ford Motor, $18,000 of Netflix, and $20,000 of Wayfair. The monthly returns for Ford Motor, Netflix, and Wayfair were 1.50 percent, 1.0 percent, and − 1.50 percent. What is your monthly portfolio return? What is your effective annual portfolio return? To solve, first you must calculate each stock’s weight of the total portfolio. Times that weight for the stock’s contribution to the portfolio return, then sum all three stocks. See P7-1 from Week 3 for the annual return (EAR).

Answer 1

Value of Ford motor in the portfolio = 12000

Value of Netflix in the portfolio = 18000

Value of Wayfair in the portfolio = 20000

The total value of the portfolio = 12000+18000+20000 = 50000

Ford Motor

Weight of Fordmotor in the portfolio = W_F = 12000/50000 = 24%

Monthly Return on Ford Motor = r_F = 1.5%

Netflix

Weight of netflix in the portfolio = W_N = 18000/50000 = 36%

Monthly Return on Netflix = r_N = 1%

Wayfair

Weight of Wayfair in the portfolio = W_W = 20000/50000 = 40%

Monthly Return on Wayfair = r_W = 1%

	Weights	Monthly Return
Ford Motor	24%	1.50%
Netflix	36%	1%
Wayfair	40%	-1.50%

Monthly portfolio return

E[R_monthly] = W_F*r_F+W_N*r_N+W_W*r_W =(24%*1.5%)+(36%*1%)+(40%*(-1.5%)) = 0.12%

Annual Portfolio return

E[R_Annual] = (1+E[R_monthly])¹²-1 = (1+0.12%)¹²-1 = 1.44954211884061%

Answer

Monthly portfolio return = 0.12%

Annual portfolio return = 1.44954211884061% or 1.45%