Assume a Portfolio Manager Holds $2 Million (Par Value) of 9

Question

Examlex · Accepted Answer

The Answer is Solution: (a) Since the manager is long in the cash market, the correct hedge is a short futures position.
This problem ignores weighted hedges. The

\$ 2

million face value represents

\$ 2,000,000 / \$ 1000=2000

bonds, which at a current price of 77 is worth

\$ 1,540,000

.
The manager sells 20 contracts at a current price of 67 , for a total transaction value of

20(\$ 67,000)=\$ 1,340,000

. Repurchasing the futures three months later at a price of 60 results in a total cost of

20(\$ 60,000)=\$ 1,200,000

.

\begin{array}{llll} ext { Beginning sale } \quad \$ 67,000 imes 20 & = & \$ 1,340,000 \ ext { Ending purchase } \quad \$ 60,000 imes 20 & = & \underline{1,200,000} \ ext { Gain from short futures } & = & \$ 140,000\end{array}

(b) As noted in (a), there are 2000 bonds. If the bonds are priced at 68 three months later, the cash market position is:

\begin{array}{llll} ext { Beginning: } & \$ 770 imes 2000 & = & \$ 1,540,000 \ ext { Ending: } & \$ 680 imes 2000 & = & \underline{\$ 1,360,000} \ ext { Loss from long bonds }& & = & \$ 180,000\end{array}

ext { (c) The net effect of this hedge is a loss of } \$ 40,000 ext {. }

\begin{array}{lll} ext { Gain from short futures } & = & \$ 140,000 ext { from part (a) } \ ext { Loss from long bonds } & = & \underline{180,000 ext { from part (b) }}\ ext { Net loss }&&{\$ 40,000}\end{array}

Assume a Portfolio Manager Holds $2 Million (Par Value) of 9

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