Question

State of                               Prob. of the                        Rate of return if state occurs

the economy                      state of economy                    Stock A         Stock B

Boom                                            0.40                             0.12               0.04

Bust                                               0.60                             0.02               0.04

You MUST use 4 digits in every calculation you do in order for your answer to be the same as the one in the system. Enter answer using 4 decimals. Do not use or enter the %. For example, if your answer is 3.48% enter 0.035; if your answer is 0.12013 then enter 0.1201

What is the expected return of a portfolio with 70% in asset A and 30% in Asset B?

What is the variance of the portfolio with 70% in asset A and 30% in Asset B?

Answer 1

• Probability Weighted Return = Return x Probability
  • bust Probability Weighted Return = 40% x 12% = 4.8%
  • Boom Probability Weighted Return = 60% x 2% = 1.2%
• Mean or Expected Return = sum of Probability Weighted Return      
  • Expected Return = 4.8%+1.2%= 6.00%

To calculate variance and standard deviation we need to calculate the probability weighted squared deviations or P(X - Expected return of R)^2

• Boom Probability weighted squared deviations = 0.40(0.12-0.06)2=0.144%
• Boom Probability weighted squared deviations = 0.60(0.5-0.175)2=0.096%

Variance = Sum of Probability weighted squared deviations

• Variance = 0.144+0.096
• Variance = 0.24%

Standard deviation = Square root of variance

• Standard deviation = Square root of 0.24%
• Standard deviation = 4.899%

Similarly all value for B are also calculated

So the portfolio expected return is 5.4% or 0.0540 As answers are required in decimal format

To calculate the portfolio variance we need to first calculate the covariance and correlation of the two assert:

Both assets are uncorrelated

So the variance is 0.0343 rounded to 4 decimal places.