Question

Consider the following information:

State Probability Stock A Stock B Stock C

Boom 0.32 0 0.25 0.19

Bust 0.68 0.25 0.08 0.16

What is the expected return of a portfolio that has invested $9,242 in Stock A, $7,934 in Stock B, and   $7,984 in Stock C? (Hint: calculate weights of each stock first). Enter the answer with 4 decimals (e.g. 0.1234).

Answer 1

Below table shows the calculations and the given information:

		Returns
State	Probability	A	B	C	Total
Boom	0.32	0.00%	25.00%	19.00%
Bust	0.68	25.00%	8.00%	16.00%
Amount invested		9242	7934	7984	25160
Weight		36.7329%	31.5342%	31.7329%
		Probability Weighted Returns
Boom	0.32	0.0000%	2.5227%	1.9294%	4.4521%
Bust	0.68	6.2446%	1.7155%	3.4525%	11.4126%

Weights = amount invested in stock/total amount invested

• Weight for A = 9242/25160 = 36.7329%
• Weight for B = 7934/25160 = 31.5342%
• Weight for C = 7984/25160 = 31.7329%

Probability weighted return = probability of state x weight of stock x return of stock

• Probability Weighted Return for A :
  • Boom = 36.7329% x 0.32 x 0 = 0
  • Bust = 36.7329% x 0.68 x 0 = 0
• Probability Weighted Return for B :
  • Boom = 31.5342% x 0.32 x 0.25 = 2.5227%
  • Bust = 31.5342% x 0.68 x 0.08 = 1.7155%
• Probability Weighted Return for C :
  • Boom = 31.7329% x 0.32 x 0.19= 1.9294%
  • Bust = 31.7329% x 0.68 x 0.16 = 3.4525%
• Portfolio probability weighted return =
  • Boom = 0 + 2.5227%+1.9294% = 4.4521%
  • Bust = 0 + 1.7155%+3.4525% = 11.4126%