Question

Portfolio A has $65 million in stock and $45 million in bonds.

Portfolio B has $40 million in stock and $70 million in bonds.

Portfolio manager A makes a swap with portfolio manager B to exchange stock for bonds with a notional principal of $25 million.

Year-end returns are as follows.

Stock return         4%                   Bond return            6%

A. Show the asset allocation for each portfolio before the swap here; Identify as A or B.

Portfolio A		Portfolio B
Dollars	Weights	Dollars	Weights
Stock Bonds
Total

B. Show the asset allocation for each portfolio after the swap here; Identify as A or B.

Portfolio A		Portfolio B
Dollars	Weights	Dollars	Weights
Stock Bonds
Total

C. Show the year-end results without the swap for portfolio A here.

Portfolio A	Portfolio B
Return=	Return=

Which portfolio performed better?

D. Show the year-end results for portfolio A with the swap here.

Portfolio A	Portfolio B
Return=	Return=

Which portfolio performed better?

E. Does portfolio manager A gain or lose from this swap and show the dollar amount here.

Show the same results for the year-end values for portfolio B.

Answer 1

A) Allocation before swapping

	Portfolio A	Portfolio B
	Dollars	Weights	Dollars	Weights
Stock	65	59%	40	36%
Bonds	45	41%	70	64%
Total	110	100%	110	100%

B) Allocation after swapping

	Portfolio A	Portfolio B
	Dollars	Weights	Dollars	Weights
Stock	40	36%	65	59%
Bonds	70	64%	45	41%
Total	110	100%	110	100%

C) Returns before swapping

Return of Portfolio A = 0.59*4% + 0.41*6% = 4.82%

Return of Portfolio B = 0.36*4% + 0.64*6% = 5.28%

Portfolio B did better.

D) Returns after swapping

Return of Portfolio A = 0.36*4% + 0.64*6% = 5.28%

Return of Portfolio B = 0.59*4% + 0.41*6% = 4.82%

Portfolio A did better.

E)

Portfolio Manager A gains by swapping.

Year end value of A before swapping = 110*(1+4.82%) = 115.302

Year end value of A after swapping = 110*(1+5.28%) = 115.808

So manager A gains by 115.808-115.203 = $0.605 million

Year end value of B before swapping = 110*(1+5.28%) = 115.808

Year end value of B after swapping = 110*(1+4.82%) = 115.302

So manager B loses by 115.808-115.203 = $0.605 million