Question

Guinness is considering two portfolios: 1. Portfolio A with a return of 14% and a standard deviation of 14% and 2. Portfolio B with a return of 4% and a standard deviation of 7%. Assuming the correlation between A and B is 0.5 and he invests 70% in A and 30% in B, what range of returns should this portfolio produce 95% of the time?

A. Between 0% and 9%.
B. Between 0% and 22%.
C. Between -6% and 26%.
D. Between -11% and 33%.

Answer 1

The range of returns for this portfolio should produce returns between approximately 9.6% and 10.0% 95% of the time.

Step-by-step explanation:

To find the range of returns for the portfolio, we need to calculate the weighted average return and the weighted standard deviation. First, we calculate the weighted average return:

Weighted Return = (Weight of A * Return of A) + (Weight of B * Return of B)

Weighted Return = (0.7 * 14%) + (0.3 * 4%) = 9.8%

Next, we calculate the weighted standard deviation:

Weighted Standard Deviation = sqrt((Weight of A)^2 * (Standard Deviation of A)^2 + (Weight of B)^2 * (Standard Deviation of B)^2 + 2 * (Weight of A) * (Weight of B) * (Correlation between A and B) * (Standard Deviation of A) * (Standard Deviation of B))

Weighted Standard Deviation = sqrt((0.7)^2 * (0.14)^2 + (0.3)^2 * (0.07)^2 + 2 * (0.7) * (0.3) * (0.5) * (0.14) * (0.07)) = 0.096

Now, we can calculate the range of returns:

Range of Returns = Weighted Return ± (Z-Score * Weighted Standard Deviation)

To calculate the Z-Score for a 95% confidence level, we use a standard normal distribution table and find the Z-Score that corresponds to a cumulative probability of 0.975 (since it's a two-tailed test).

The Z-Score for a 95% confidence level is approximately 1.96.

Range of Returns = 9.8% ± (1.96 * 0.096)

Range of Returns ≈ 9.8% ± 0.18816

Therefore, the range of returns for this portfolio should produce returns between approximately 9.6% and 10.0% 95% of the time.