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# GARP 2021 Pre Study Pack Q2 (Repo)

#### rohinjain

##### Member
Hi all,

Here is the question from the pre study pack (2021):

A bank buys a bond on its coupon payment date. Three months later, in order to generate immediate liquidity, the bank decides to repo the bond. Details of the bond and repo transaction are as follows:
Notional value (USD) 100,000
Coupon (semi-annual) 6%
Current bond price 97
Repo haircut 10%
Repo interest rate 4%

If the repo contract expires 6 months from now, what is the bank’s expected cash outflow at the end of the repo transaction?
A. USD 89,046
B. USD 90,423
C. USD 93,177
D. USD 100,470

Correct Answer: B
Explanation: A. Incorrect. Left out the accrued interest of 6%*0.25 in the correct equation for cash inflow.
B. Correct. Cash inflow at beginning of repo: (100,000)*(97%+6%*0.25)*(1-10%) = 88,650; Cash outflow at end of repo: 88,650*(1+4%*0.5)=90,423
C. Incorrect. Used 1 instead of 97% for price in the correct equation for cash inflow.
D. Incorrect. Left out haircut of 10% in the correct equation for cash inflow.

The only question I have is why is the price in 3 months time not equal to 97 + 6*0.25*DF where DF is the discount factor from the next coupon date to today (i.e. when the repo was executed). I assume that the DF must be using the current YTM rate.

It's also a bit confusing that they say the current price is 97 (why does this not include the coupon already?). I assume they meant to say that it was the clean price.

Thanks!

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @rohinjain This is another question pattern that created confusion along the way due to GARP's imprecise language. See here for discussion on the 2020 instance of same question (albeit with different inputs https://www.bionicturtle.com/forum/threads/garp-2020-practice-exam-part-2-q74.23268/ i.e.,
Hi @lincoln40113 I think your question is excellent, in no small part because, let's notice: this bond will pay a coupon while the bank's counterparty (aka, the lender of cash, or "buyer" of the repo who is the "reverse repo" counterparty). The coupon pays 5.0% per annum semi-annually and the bank bought the bond three months ago; so the next coupon is paid in three months, while the repo contract matures in six months. So there will be a coupon three months after opening/first leg.

A few initial reactions:
• I have learned not to assume GARP's practice questions are correct (given a 30+ % error rate)
• However, let's make an inference from the solution to the correct answer: the repo here is sold at the full (aka, cash, invoice, dirty) price because the accrued interest is added to 98.00 (which we can infer is the flat/quoted/clean although the question would be helpful to include that term). As the repurchase does occur per the 3.0% repo rate--i.e., $94,288 * (1 + 3.0%/2)^(0.5*1) =$95,702--without further adjustments, I infer that the bank's counterparty keeps the coupon. That's implied by the full price upon sale: it can't be returned to the bank, in this example, because then the bank would be paying less than 3.0% on the repo! Put another way, imagine the coupon was returned to the bank during the repo: then instead of paying 95,702/94,288 - 1 = 1.5% interest (over six months), the bank would only be effectively paying (95,702 - $1,250 coupon to fund the repurchase) / 94,288 - 1 = 0.174% interest. So that's just a deduction based on the solution ... • This shows how either/any treatment of the coupon can be addressed by way of an adjusted repurchase price. The repurchase price can always be changed to enforce the 3.0% repo rate. Nevertheless, according to (the Repo Handbook, which I happen to own), emphasis mine: "5.2.1 Illustration of Classic Repo: There will be two parties to a repo trade, let us say Bank A (the seller of securities) and Bank B (the buyer of securities). On the trade date the two banks enter into an agreement whereby on a set date, the value or settlement date Bank A will sell to Bank B a nominal amount of securities in exchange for cash. The price received for the securities is the market price of the stock on the value date. The agreement also demands that on the termination date Bank B will sell identical stock back to Bank A at the previously agreed price; consequently, Bank B will have its cash returned with interest at the agreed repo rate. In essence a repo agreement is a secured loan (or collateralised loan) in which the repo rate reflects the interest charged on the cash being lent. On the value date, stock and cash change hands. This is known as the start date, on-side date, first leg or opening leg, while the termination date is known as the second leg, off-side leg or closing leg. When the cash is returned to Bank B, it is accompanied by the interest charged on the cash during the term of the trade. This interest is calculated at a specified rate known as the repo rate. It is important to remember that although in legal terms the stock is initially “sold” to Bank B, the economic effects of ownership are retained with Bank A. This means that if the stock falls in price it is Bank A that will suffer a capital loss. Similarly, if the stock involved is a bond and there is a coupon payment during the term of the trade, this coupon is to the benefit of Bank A, and although Bank B will have received it on the coupon date, it must be handed over on the same day or immediately after to Bank A [dharper note: Choudrhy is saying that the repo "buyer" or "lender" who is the "reverse repo" counterpary will receive the coupon per holding title but must send it back to the repo "seller" or "buyer" who is the "repo" counterparty and who is the bank in the question above]. This reflects the fact that although legal title to the collateral passes to the repo buyer, economic costs and benefits of the collateral remain with the seller. A classic repo transaction is subject to a legal contract signed in advance by both parties. A standard document will suffice; it is not necessary to sign a legal agreement prior to each transaction. We discuss this further in a later chapter." --- page 117, Moorad Choudhry, The Repo Handbook (https://amzn.to/2LUFbVd) I hope that's helpful, thanks, It's not productive to draw certain precise inferences from imprecise questions (I'm always amazed at how many candidates assume the practice questions are rigorous when we know that >30% have been problematic), so let's just operate from the solution: • Re: why not 97 + 6*0.25*DF: well, we would not do that because the question reads, "A bank buys a bond on its coupon payment date. Three months later, in order to generate immediate liquidity, the bank decides to repo the bond." ...to me, this aspect is not confusing: the bond is sold three months from today (not today). • Re: current price: yes, absolutely that is confusing. In fact, the question is incomplete to not specify. It should read "Current quote (aka, flat, clean) price is$97.00." There are other language improvements that should be made. This question has enough calculations, a good question does not cause the candidate delays trying to interpret assumptions. I hope that's helpful,

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#### rohinjain

##### Member
Thanks David! Very helpful thread

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