CFA Practice Question

There are 227 practice questions for this study session.

CFA Practice Question

An investor bought a bond (par value: $1,000) when it was originally issued with a maturity of 30 years. The bond pays semi-annual coupons of $60. The first coupon occurs 181 days after issue, the second 365 days, the third 547 days, the fourth 730 days, and so. 120 days later he entered into a forward contract that would allow him to sell the bond in 612 days (from the contract initiation date) at a then no-arbitrage price of $875.44. Now, 365 days since he entered into the forward contract, the risk-free rate is 7% and the new price of the bond is $1,034.75. What's the value of the forward contract for the investor?
A. $81.84
B. $74.26
C. $93.79
Explanation: Now it is the 485th day of the bond's life (120 + 365). There are two coupons to go, one occurring in 547 - 485 = 62 days, and the other in 730 - 485 = 245 days. The present value of the coupons is now: $60/1.0762/365 + $60/1.07245/365 = $116.65.

There are 612 - 365 = 247 days now remaining until the contract's expiration. The value of the forward contract is then: $1,034.75 - $116.65 - $875.44/1.07247/365 = $81.84.

This positive value represents a loss to the investor, as his position is "short."

User Contributed Comments 4

User Comment
danlan2 Use stat with following data:
X1=1034.75, Y1=1
X2=-60, Y2=1.07^(-62/365)
X3=-60, Y3=1.07^(-245/365)
X4=-875.44, Y4=1.07^(-247/365)

We will get sigma(XY)=81.84
wollogo Danlan - its 120 days since purchasing the bond that he enters into the futures contract.

Ree2 - The coupon on day 730 is before he sells the bond which is on day 732 (120 days after purchasing the bond + 612 days after purchasing the forward)
Rotigga Orig Length of contract = 612 days
Now at t=365 or 120+356=485 days since investor bought the bond
Remaining days in contract = 612-365 = 247 days
Contract ends from POV of orig = 120+612 = Day 732
PV(Coupons) = 60/(1.07)^[(547-485)/365] + 60/(1.07)^[(730-485)/365] = 116.65
Value = 1,034.75 - 116.65 - 875.44/(1.07)^[(612-365)/365] = 81.84
janis36 managed to calculate this in 89 seconds.
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