Actuarial Outpost ASM Exercise 1.4
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#1
09-28-2018, 06:37 PM
 umites Non-Actuary Join Date: May 2014 Posts: 17
ASM Exercise 1.4

Apparently, I have a long road ahead, because I don't understand the fourth exercise of the first chapter.

Exercise:
A 3-year zero-coupon bond with maturity value 1000 has annual effective interest 6%. The bond is short-sold, with collateral 110% of its value. After one year the position is closed. At that time, the annual effective interest rate for the bond is 7%. There are no commissions paid when buying or selling. The interest rate paid on the loan to provide the collateral is 6%. Net profit at the end of one year is 7.32.
determine the repo rate

What does the bold sentence mean? Here's what I know:
• Short seller sells bond at t=0 for \$839.62, and buys it back at t=1 for \$873.44, losing \$33.82
• Short seller pays 0.06*0.1*\$839.62 = \$5.04 in interest on the 10% haircut
• Collateral is 1.1*\$839.62 = \$923.58

Where does \$7.32 come from? Who is making a net profit of \$7.32 at the end of one year and why? It doesn't seem like the short-seller or the lender gets \$7.32 at the end of the year, so I'm not sure what the question is saying here.
#2
09-30-2018, 03:19 PM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 7,250

The short-seller earns interest on the collateral. At what rate? You know that he made 7.32, so you can back out the rate.
#3
09-30-2018, 06:11 PM
 umites Non-Actuary Join Date: May 2014 Posts: 17

Got it, thanks!