A bank has two loans A & B, valued $20,000 and $30,000 respectively that have the following characteristics: Loan A has an expected return of 12 per cent and a standard deviation of returns of 10 per cent. The expected return and standard deviation of returns for loan B are 8 per cent and 6 per cent, respectively. If the correlation between loans A and B is -0.15, what are the expected return and standard deviation on this portfolio? (1 mark)Question 16Answera.10.4% and 5.24%b.9.6% and 4.96%c.9.6% and 6.87%d.10.4% and 6.87%e.10.4% and 4.96%

To solve this problem, we first need to calculate the weights of the two loans in the portfolio. The total value of the portfolio is $20,000 +$30,000 = $50,000. Therefore, the weight of loan A is$20,000 / $50,000 = 0.4 and the weight of loan B is$30,000 / $50,000 = 0.6.

Next, we calculate the expected return of the portfolio. This is done by multiplying the expected return of each loan by its weight and then adding the results together. So, the expected return of the portfolio is (0.4 * 12%) + (0.6 * 8%) = 4.8% + 4.8% = 9.6%.

Finally, we calculate the standard deviation of the portfolio. This is a bit more complex and involves the weights, standard deviations, and correlation of the loans. The formula is:

sqrt[(wA^2 * σA^2) + (wB^2 * σB^2) + (2 * wA * wB * ρAB * σA * σB)]

where wA and wB are the weights of loans A and B, σA and σB are the standard deviations of loans A and B, and ρAB is the correlation between loans A and B.

Substituting the given values into the formula gives:

sqrt[(0.4^2 * 10%^2) + (0.6^2 * 6%^2) + (2 * 0.4 * 0.6 * -0.15 * 10% * 6%)]

= sqrt[(0.016) + (0.0216) - (0.00432)]

= sqrt[0.03328]

= 0.1824 or 18.24%

However, this value seems too high for a standard deviation. There might be a mistake in the calculation. The standard deviation should be lower than the individual standard deviations of the loans, given that they are negatively correlated. Let's try calculating it again, but this time remember that we need to convert the percentages to decimals before squaring in the formula:

sqrt[(0.4^2 * 0.1^2) + (0.6^2 * 0.06^2) + (2 * 0.4 * 0.6 * -0.15 * 0.1 * 0.06)]

= sqrt[(0.0016) + (0.001296) - (0.000216)]

= sqrt[0.00268]

= 0.0517 or 5.17%

So, the expected return and standard deviation of the portfolio are 9.6% and 5.17%, respectively. This doesn't match any of the given options exactly, but it's closest to option b. 9.6% and 4.96%.