Final answer:
Guinness' combined portfolio, with 70% invested in Portfolio A and 30% in Portfolio B, should produce returns between approximately -11% and 33% with 95% confidence.
Step-by-step explanation:
To calculate the expected range of returns for the combined portfolio with 95% confidence, we need to compute the expected return and the standard deviation of the combined portfolio. For the expected return, we use the weighted average of the returns of Portfolio A and Portfolio B based on the percentage invested in each. The formula for expected return (E(R)) of the combined portfolio is:
E(R) = wA × RA + wB × RB
Where wA and wB are the weights (percentage of total investment) of portfolios A and B respectively, and RA and RB are the expected returns of portfolios A and B.
The weighted expected return of the combined portfolio is:
E(R) = 0.70 × 14% + 0.30 × 4% = 9.8% + 1.2% = 11%
Next, we calculate the standard deviation (σP) of the combined portfolio using the following formula:
σP = √[wA2 × σA2 + wB2 × σB2 + 2 × wA × wB × σA × σB × ρAB]
σP = √[0.49 × (0.14)2 + 0.09 × (0.07)2 + 2 × 0.7 × 0.3 × 0.14 × 0.07 × 0.5]
σP = √[0.009646 + 0.000441 + 0.002574] = √[0.012661] = 11.25%
To find the range for 95% of the returns, we need to calculate the range within approximately 1.96 standard deviations from the mean (the 95% confidence interval).
Range = [E(R) - 1.96×σP, E(R) + 1.96×σP]
Range = [11% - 1.96× 11.25%, 11% + 1.96× 11.25%]
Range = [-11.075%, 33.075%]
Therefore, 95% of the time, the combined portfolio should produce returns between approximately -11% and 33%. The answer is d) Between -11% and 33%.