Question

Consider a portfolio with $3,697 invested in Asset A and $4,421 invested in Asset B with the following returns and probabilities. What is the rate of return on the portfolio pay when a LOSS occurs? (round the the nearest whole percentage ##%, include a negative sign if appropriate )

State

Probability Asset A Asset B

WIN 0.7 24% 39%

TIE 0.2 7% 6%

LOSS 0.1 -3% -9%

Answer 1

invested in A= $3,697
+ invested in B= $4,421

Total amount invested in all stocks= $8118

Weights of the portfolio( proportion of portfolio)

Asset A =( 3,697 / 8118) *100
= 45.54% or 46% i.e. 0.46

Asset B = 1 - 0.46
= 0.54 or 54%

When a loss occurs:

Pi= 0.1
Return of Asset A= ( -3%)
Return of Asset B= (-9%)

Return on Portfolio: [ R_A * W_A + R_B * W_B ] * P_i
=[ (-3) * 0.46 + (-9) * 0.54 ] * 0.1
= [-1.38 + (-4.86) ] * 0.1
= - 6.24 * 0.1
= (- 0.624 %) or Approximately ( - 0.62 % )

[Note: Answer can not be rounded off to whole percentage]