Assume an FI Holds Three Different Positions

Multiple Choice

Assume an FI holds three different positions. The following DEAR information is available for the positions. Position 1 is a 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.