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Investment / Financial Markets Old Exam MFE Forum

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  #1  
Old 04-20-2017, 02:27 AM
NoobGingrich NoobGingrich is offline
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Default MFE 10th Ed. 1.4

Hi All,

Going back to some of the earlier questions in my manual and I can't seem to make heads or tales of this question.

"A 3-year zero-coupon bond with maturity value 1000 has an annual effective interest rate of 6%. The bond is short-sold, with collateral of 110% of its value. After one year, the position is closed: the bond is bought back. At that time, the annual effective interest rate of the bond is 7%. There are no commissions paid when buying or selling the bond, and no cost in providing the collateral. Net profit at the end of one year is 12.36. Determine the repo rate."

Their solution is:
"The original price of the bond is 1000/1.06^3=839.62 and the ending price is 1000/1.07^2=873.44. Thus 873.44-839.62=33.82 was the net amount spent repurchasing the bond. Total interest on the collateral must be 33.82+12.36=46.18. The collateral is 1.1(839.62)=923.58, so the repo rate is 46.18/923.58=0.05"


I can't rationalize this answer. If our net profit is 12.36, we should be able to solve for the repo rate using:
12.36=839.62*1.1*(1+i)-873.44
But when you do so, you get i=-0.04091 which makes no sense. What am I misunderstanding here?
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Old 04-20-2017, 10:45 AM
Academic Actuary Academic Actuary is offline
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With a repo, the repurchase price is specified in the agreement so the whole question has nothing to do with repos.
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Old 04-20-2017, 11:21 AM
NoobGingrich NoobGingrich is offline
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Well I think the question is assuming that we're buying the bond back from a third party that has nothing to do with the short sale, such that purchase price is dictated by the market. So the proceeds from the short sale and the haircut need to earn a repo rate while they're posted as collateral.

What I don't get is how that repo rate is 0.05.
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Old 04-20-2017, 12:27 PM
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The Disreputable Dog The Disreputable Dog is offline
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Quote:
Originally Posted by NoobGingrich View Post
I can't rationalize this answer. If our net profit is 12.36, we should be able to solve for the repo rate using:
12.36=839.62*1.1*(1+i)-873.44
But when you do so, you get i=-0.04091 which makes no sense. What am I misunderstanding here?
It looks like they're saying the following: Our net profit is made up of two pieces. One is the interest we receive from our posted collateral. The other is the profit/loss we make on the short sale.

total profit = interest + short sale profit

12.36 = 839.62*1.1*repo + (839.62 - 873.44)
12.36 = 839.62*1.1*repo + -33.82
(12.36 + 33.82)/923.582 = repo = 0.05

It looks like the problem with your formula might be the (1+i). If you multiply this through you've got 839.62*1.1 + 839.62*1.1*i. These two pieces are the proceeds you receive when you short sell the bond and the interest you receive from your collateral, respectively. The issue is that your proceeds aren't 839.62*1.1, they're just 839.62.

Last edited by The Disreputable Dog; 04-20-2017 at 12:30 PM..
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Old 04-20-2017, 11:34 PM
NoobGingrich NoobGingrich is offline
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You're right, that's what it was. I was including the haircut into the profit calculations, but if I posted the haircut with my own money it wouldn't be considered profit. If you subtract the 83.962 from the leftover funds after buying the bond back, you get 12.36.

Thanks dog!
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Old 11-16-2017, 05:30 PM
Patbaker12 Patbaker12 is offline
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I'm breaking this down a different way and getting a different answer. I think this question may be defective because the profit doesn't account for the market rate of 6% that can be earned on the haircut. I get a repo rate of 5.5% even though the books says 5%.

Net Investment= 83.962
AV(Net i) = 83.962(1.06) = 89
At 1, receive: 839.62*1.1*(1+repo) - 873.44
Profit = 12.36 = What we recieved at 1 - AV(Net i)
which breaks down to: 923.58(1+repo) - 873.44 - 89 = 12.36 and the repo rate is 5.5%.
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Old 01-11-2018, 04:39 PM
BartimaeusOfUruk BartimaeusOfUruk is offline
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Default Accounting market interest rate lost

I tried to account for the interest the collateral would’ve earned had that money been invested instead.

Time 0: Collateral paid. I.E. lose market interest rate for period of time money was loaned:

1000/1.06^3=839.62
(839.62)(1.06)(1.1) - 839.62(1.1) = 979- 923.58 = 55.42

Net cashflow at time 0: -55.42

Time 1:
- Buy back bond: 1000/1.07^2= 873.44
+Receive collateral: (1.1)(839.62)(1+repo rate)

Net cash flow at time 1:
-873.44 + (1.1)(839.62)(1+repo rate)

12.36 = -55.42 - 873.44 + 898.39(1+ repo rate)

941.22 = 898.39(1+ repo rate)

Repo rate= 4.77%
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