Assume an FI holds three different positions.The following DEAR information is available for the positions.Position 1 is five-year zero-coupon bonds with DEAR of $12 500, position 2 is a CHF spot contract with DEAR of $9500 and the third position are Australian equities with DEAR of $34 500.The five-year zero-coupon bonds and the CHF spot position have a negative correlation of 0.5, the correlation between the zero-coupon bonds and the Australian equities is positive 0.5 and the correlation between the CHF spot contract and the Australian equities is positive 0.2.What is the DEAR of the portfolio? A)12,500 + 9500 + 34,500 = $56,500 B)12,500(-0.5) + 9500(0.5) + 34,500(0.2) = $5400 C)[12,500² + 9500²+ 34,500² - 2(-0.5)(12,500)(9500) - 2(0.5)(12,500)(34,500) - 2(0.2)(9500)(34,500)]^1/2 = $31 514 D)[$12,500² + $9500² + $34 500² + 2(-0.5)(12,500)(9500) + 2(0.5)(12,500)(34 500) + 2(0.2)(9500)(34,500)]^1/2 = $43,363

Question

Quizplus · Accepted Answer

We need to use the formula for calculating the DEAR of a portfolio with three positions: DEAR = ²(position 1) + ²(position 2) + ²(position 3) + 2(r12)(w1)(w2) + 2(r13)(w1)(w3) + 2(r23)(w2)(w3) where: - S: the standard deviation of each position - U: the currency exchange rate for each position (if needed) - P12: the correlation coefficient between positions 1 and 2 - P13: the correlation coefficient between positions 1 and 3 - P23: the correlation coefficient between positions 2 and 3 - r: the expected return of each position - w: the weight of each position (sum of weights should equal 1) Plugging in the values given in the question, we get: DEAR = ($12,500)(²) + ($9,500)(²) + ($34,500)(²) + 2(-0.5)(0.5)(0.1) + 2(0.5)(0.5)(0.2) + 2(0.2)(0.1)(0.5) DEAR = $43,363 Therefore, the answer is choice D.

Assume an FI Holds Three Different Positions