{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Auctions","Repo Fin","LTCM Trade"],"not_rendered":{"defined_names":26},"read":"whole","date_system":"1900"}

{"sheet":"Auctions","index":0,"n_rows":88,"n_cols":22,"rows_kept":88}
["Let's consider a new note auction.  For example, the 1 5/8 % August 2029 note.",{"$nulls":6},"Announcement of auction: ",null,null,"This announcement was made at 8:30 am on Wednesday, July 31, 2019."]
[null,"It announces that the US Treasury will conduct a sealed-bid single price auction on Wednesday August 7 at 1:00 pm Eastern time."]
[null,"The New York Federal Reserve Bank will serve as agent to conduct the auction on behalf of the Treasury."]
[null,"The Treasury announces that they are offering $27 billion of the new August 15, 2029 note.  Note the standard terms for 10-year Treasury notes."]
[]
["Bidders place sealed bids with the NYFed.  A bid may be non-competitive or competitive.  If it is non-competitive, it just specifies a par amount.  For example, I place a non-competitive bid through my TreasuryDirect account for $10,000 par."]
["Competitive bids specify a par amount and a (bond-equivalent) yield.  Notice that the new note's coupon rate is not set prior to the auction.  It well be set in increments of 1/8 of 1% at the highest level that makes the bond sell at par or lower."]
[]
["Note that at bid at a lower yield is more competitive, since this will net more money per bond than higher yield bids."]
["As you can see bids must be in increments of one-tenth of a basis point (0.001%)."]
[]
["SOMA refers to the System Open Market Account at the US Federal Reserve.  ",{"$nulls":6},"The Treasury will allot the Fed whatever it wants at the final auction value, and this will increase the size of the issue."]
[]
["Here is the Treasury's announcement on completion of its auction:"]
["https://www.treasurydirect.gov/instit/annceresult/press/preanre/2019/R_20190807_1.pdf"]
[]
["This outcome is consistent with the following bids:"]
[]
[null,"Par Amount","Yield Bid"]
[null,"0.0275 billion","Noncompetitive"]
[null,"1.57 billion",{"v":0.01625,"d":"1.625%"}]
[null,"1.1 billion",{"v":0.01605,"d":"1.605%"}]
[null,"1 billion",{"v":0.0167,"d":"1.670%"}]
[null,"2.6 billion",{"v":0.0164,"d":"1.640%"}]
[null,"4 billion",{"v":0.018,"d":"1.800%"}]
[null,"2.6 billion",{"v":0.01575,"d":"1.575%"}]
[null,"2 billion",{"v":0.0167,"d":"1.670%"}]
[null,"2.8 billion",{"v":0.0163,"d":"1.630%"}]
[null,"1.4 billion",{"v":0.0158,"d":"1.580%"}]
[null,"0.6 billion",{"v":0.0159,"d":"1.590%"}]
[null,"1 billion",{"v":0.0151,"d":"1.510%"}]
[null,"1.2 billion",{"v":0.01765,"d":"1.765%"}]
[null,"0.9 billion",{"v":0.016,"d":"1.600%"}]
[null,"0.3 billion",{"v":0.0155,"d":"1.550%"}]
[null,"2 billion",{"v":0.0167,"d":"1.670%"}]
[null,"1 billion",{"v":0.016,"d":"1.600%"}]
[null,"5 billion",{"v":0.0186,"d":"1.860%"}]
[null,"1.5725 billion",{"v":0.0158,"d":"1.580%"}]
[null,"7 billion",{"v":0.0172,"d":"1.720%"}]
[null,"3 billion",{"v":0.0167,"d":"1.670%"}]
[null,"6 billion",{"v":0.018,"d":"1.800%"}]
[null,"2.2 billion",{"v":0.0161,"d":"1.610%"}]
[null,"4.5 billion",{"v":0.01765,"d":"1.765%"}]
[null,"1.1 billion",{"v":0.0158,"d":"1.580%"}]
[null,"2.2 billion",{"v":0.0155,"d":"1.550%"}]
[]
[]
["So the NYFed's software will subtract the non-competitive bids from the supply, and then rank the bids from lowest to highest yield (combining all bids at the same yield):"]
["Total avaiable supply:",null,null,27]
[null,"Yield ","$ Amt (billions)","Running Total Demand"]
[null,{"v":0.0151,"d":"1.510%"},1,{"$f":"C51","v":1}]
[null,{"v":0.0155,"d":"1.550%"},2.5,{"$f":"D51+C52","v":3.5}]
[null,{"v":0.01575,"d":"1.575%"},2.6,{"$f":"D52+C53","v":6.1}]
[null,{"v":0.0158,"d":"1.580%"},{"$f":"1.1+1.5725+1.4","v":4.0725},10.1725]
[null,{"v":0.0159,"d":"1.590%"},0.6,10.772499999999999]
[null,{"v":0.016,"d":"1.600%"},1.9,12.6725]
[null,{"v":0.01605,"d":"1.605%"},1.1,13.772499999999999]
[null,{"v":0.0161,"d":"1.610%"},2.2,15.9725]
[null,{"v":0.01625,"d":"1.625%"},1.57,17.5425]
[null,{"v":0.0163,"d":"1.630%"},2.8,20.3425]
[null,{"v":0.0164,"d":"1.640%"},2.6,22.942500000000003]
[null,{"v":0.0167,"d":"1.670%"},{"$f":"1+2+2+3","v":8},30.942500000000003,"<---- This is where we have to stop to meet the supply.  So this will be the winning bid.  All buyers at the auction will make this yield."]
[null,{"v":0.0172,"d":"1.720%"},7,37.9425]
[null,{"v":0.01765,"d":"1.765%"},5.7,43.642500000000005]
[null,{"v":0.018,"d":"1.800%"},10,53.642500000000005]
[null,{"v":0.0186,"d":"1.860%"},5,58.642500000000005]
[]
[null,"Price setting:","Treasury sets the coupon at 1/8% increments so that the note sells as close to par as possible -- from below.  "]
[null,null,"This means that the coupon has to be less than or equal to the winning bid.  Nearest 1/8:",{"$nulls":6},{"v":0.01625,"d":"1.625%"}]
[]
["Treasury's price determination (note it is not precise):"]
[null,"T (Yrs):",0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6,6.5,7,7.5,8,8.5,9,9.5,10]
[null,"Cash Flow:",{"$f":"50*$J$69","v":0.8125},{"$f":"50*$J$69","v":0.8125},0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,0.8125,{"$f":"100*(1+0.5*$J$69)","v":100.8125}]
[null,"df (@ytm):",{"$f":"1/(1+$B$62/2)^(2*C72)","v":0.9917191451380968},{"$f":"1/(1+$B$62/2)^(2*D72)","v":0.9835068628334376},0.9753625852466281,0.9672857492404703,0.9592757963410227,0.9513321726989861,0.9434543290514067,0.9356417206836979,0.9278938073919749,0.9202100534457032,0.9125899275506552,0.9050329028121736,0.897538456698739,0.8901060710058403,0.8827352318201419,0.8754254294839511,0.8681761585599752,0.8609869177963755,0.8538572100921062,0.846786542462544]
[null,"PV:",{"$f":"C73*C74","v":0.8057718054247036},{"$f":"D73*D74","v":0.799099326052168},0.7924821005128854,0.7859196712578821,0.7794115845270809,0.7729573903179262,0.7665566423542679,0.7602088980555045,0.7539137185059797,0.7476706684246338,0.7414793161349074,0.7353392335348911,0.7292499960677254,0.7232111826922453,0.7172223758538653,0.7112831614557102,0.7053931288299798,0.699551870709555,0.6937589831998363,85.36666831200522]
[null,{"$f":"SUM(C75:V75)","v":{"v":99.58714936591697,"d":"99.587149"}}]
[]
[null,"continuously compounded ytm:",null,"exp(y) = (1+r/2)^2",null,"(1+r/2)^2 =",{"$f":"(1+B62/2)^2","v":1.0167697225},"==> equivalent continuously compounded yield to maturity:",{"$nulls":4},{"$f":"LN(G78)","v":0.01663066320742757}]
[null,"The Treasury sells roughly 27 billion par at this value, raising:",{"$nulls":4},{"$f":"27.000345*B76/100","v":26.888873904462894}," billion dollars from this auction."]
[null,"Auction allocation:"]
[null,null,"All noncompetitive bids are filled at the auction price."]
[null,null,"All competitive bids at yields less than 1.67% receive the full amount of the bid."]
[null,null,"All competitive bids at yields greater than 1.67% receive no notes."]
[null,null,"Bids at 1.67% are allocated on a pro-rata basis.  There are 8 billion par to buy and 4 billion available.  So the bids at this quote are filled at a rate of 1/2."]
[null,null,"   So, for example, the 3 billion bid at 1.67% receives 1.5 billion par value."]
[]
[]
[null,null,"Note that a single bidder (e.g., Morgan Stanley) may submit multiple bids, but may not receive more than 9.45 billion par at auction.  (This cap is to prevent collusion, or a bidding ring.)"]

{"sheet":"Repo Fin","index":1,"n_rows":77,"n_cols":18,"rows_kept":77}
["Example of Repo financing of an on-the-run Treasury Note."]
["Today:","September 2 2020 (Wednesday)",null,null,"Settlement:","2020-09-03"]
[null,"Note:","2030-08-15",{"v":0.00625,"d":"0.625%"},null,"Acrued Interest:",null,{"$f":"(F2-N3)/(N4-N3)*R3","v":0.03226902173913043},{"$nulls":4},"Dated Date:","2020-08-15","Semi-annual coupon (per 100 par):",null,null,{"$f":"50*D3","v":0.3125}]
[null,null,"Bid","Ask",{"$nulls":8},"Next Coupon:","2021-02-15"]
[null,"Price:","99-1+","99-2"]
[null,"Cash Quotes:",{"$f":"99+1.5/32+H3","v":99.07914402173913},{"$f":"99+2/32+H3","v":99.09476902173913}]
[]
["We put ourselves in the position of a hedge fund, and in this example we are going to purchase this note using repo financing.",{"$nulls":8},"Our hedge fund has a 9% cost of capital on trades."]
["   As soon as we buy the note from the dealer we ``sell'' the note to a repo dealer with the agreement to buy it back at a specified future date plus interest.  The interest that we pay is the repo rate --applied daily on a 360-day basis."]
[null,"Of course, effectively, this amounts to using the note as collateral for a loan.  The repo dealer has posession of the note so if we default the dealer can take full ownership of the note.  (Repo transactions supersede national bankruptcy laws.)"]
["       In our first example we will assume that there is no haircut on Treasury repo collateral, so that we can finance the entire purchase amount using repo finance."]
[]
["We buy $100 million par value of this note, finance with repo and sell it in 2 months."]
["We will ignore the need to mark the repo collateral to market every day, and assume that we roll over our repo every business day until maturity.  Repo over a weekend has 3 days of interest, and over a 3-day weekend, 4 days of interest."]
[]
["Par:",{"v":100000000,"d":"100,000,000.00"}]
["Market Value:",{"$f":"B16*D6/100","v":{"v":99094769.02173913,"d":"99,094,769.02"}}]
["Repo:",{"$f":"B17","v":{"v":99094769.02173913,"d":"99,094,769.02"}}]
[]
["The repo rate (to borrow) is 12 basis points.",null,null,0.0012,null,null,"Bid","Ask",{"$nulls":4},"Settlement:","2020-11-03"]
["We sell the position on November 2, 2020 (Monday), when the Note has quotes:",{"$nulls":5},"98-31","99-00","Accrued Interest:",null,{"$f":"(N20-N3)/(N4-N3)*R3","v":0.1358695652173913}]
[{"$nulls":4},"Cash Quotes:",null,{"$f":"98+31/32+K21","v":99.10461956521739},{"$f":"99+K21","v":99.13586956521739}]
["So when we sell our position we receive:",null,null,{"$f":"G22*B16/100","v":{"v":99104619.5652174,"d":"99,104,619.57"}}," (on the settlement date)"]
[]
["So from holding the note for 2 months we have P&L:",{"$nulls":3},{"$f":"D23-B17","v":{"v":9850.543478280306,"d":"9,850.54"}}]
["    Financing costs:"]
[null,"Number of days:",null,{"$f":"N20-F2","v":61}]
[null,"repo rate:",null,{"$f":"D20","v":0.0012}]
[null,"Repo interest:",null,{"$f":"D28*(D27/360)*B17","v":{"v":20149.269701086956,"d":"20,149.27"}}]
[]
["Trade P&L:",{"$nulls":3},{"$f":"E25-D29","v":{"v":-10298.72622280665,"d":"-10,298.73"}}]
[]
[]
["Next, we consider the phenomenon trading on special in repo."]
[null,"This reflects the fact that there is a market to borrow and lend specific securities.  Most securities, most of the time, are considered general collateral."]
[null,"  And these are eligible for repo transactions in the tri-party repo market."]
[null,"But at times the demand to borrow a security may arise and make the security special."]
[null,"An example is when 3Com spun off Palm, but retained ownership.  For example on March 2, 1999, 3Com had sold 23 million shares and retained 532 million shares of Palm (its subsidiary)."]
[null,"3Com was to spin off its holdings of Palm entirely in 1 year."]
[null,"And the market price of of Palm was $99 per share, and 3Com $81, with a market cap of $28 million."]
[null,"This situation seems inconsistent with the absence of arbitrage.  The market says that Palm is worth:",{"$nulls":6},{"$f":"532+23","v":555},99,{"$f":"I41*J41","v":54945}," -- almost 55 billion."]
[{"$nulls":5},"and that 3Com is worth:",null,null,{"$f":"K42/J42","v":{"v":345.679012345679,"d":"345.7"}},81,28000,"  -- roughly 28 billion."]
[{"$nulls":5},"Yet, the value of 3Com's Palm stock is:",null,null,532,null,{"$f":"I43*J41","v":52668},"  which implies that the rest of 3Com is worth:",{"$nulls":3},{"$f":"K42-K43","v":-24668}," minus 25 billion dollars."]
[]
[null,"So the strategy is obvious:  Buy 3Com and short Palm, and wait for convergence as the full spin off approaches."]
[null,"The demand to borrow Palm shares exceeded the supply, and Palm shares started trading special on repo.  It traded with negative rebate rates of 30%.  In 1999, the risk free rate was around 5%, so a trade that borrowed Palm shares, and sold them, and then deposited the"]
[null,"     proceeds from the sale with the securities lender earned repo interest of ",{"$nulls":4},-0.3]
[null,"This explains why the Palm shares we so valuable.  If you owned 1000 shares at $99 per share, you could lend them to a short seller and earn 30% on the cash that he gives you in exchange."]
[]
[null,"This happens on a much smaller scale in Treasury markets as dealers come into the auction with large short positions (from the when-issued market), and they bid aggressively at the opening auction, often failing to cover their short exposure."]
[null,"  Thus, there is heightened demand to borrow the note to keep the short position open."]
[null,"This has 2 consequences:"]
[null,null,"1. The note trades on special in repo"]
[null,null,"2. The note's price reflects the value of expected future repo specialness, and appears to be too high.  This is the on-the-run premium."]
[]
["To continue with the above example, let's suppose that instead of being general collateral, the on-the-run 10-year note trades on special in repo for 200 basis points.  This means that the effective repo rate is:",{"$nulls":14},"general collateral rate:",null,{"$f":"D20","v":0.0012}]
[{"$nulls":15},"--minus specialness",null,0.02]
[{"$nulls":15},"= applied repo rate",null,{"$f":"R56-R57","v":-0.0188}]
[]
["Let's look at the P&L if the note is trading on special of 200 bps over the holding period:"]
[]
[null,"Holding the note:",null,{"$f":"E25","v":{"v":9850.543478280306,"d":"9,850.54"}}]
[null,"Financing ``cost'':",null,{"$f":"R58*D27/360*B17","v":{"v":-315671.8919836956,"d":"-315,671.89"}}]
[null,"Total Trade P&L:",null,{"$f":"D62-D63","v":{"v":325522.4354619759,"d":"325,522.44"}},"  So you see that owning a security that trades on special in repo is valuable."]
[]
["Next, we consider haircuts in repo."]
["Suppose that conditions in the repo market are such that there is a 2% haircut on US Treasuries."]
["Original example with 2% haircut:"]
[null,"Purchase Note:",{"$f":"B17","v":{"v":99094769.02173913,"d":"99,094,769.02"}}]
[null,"Repo:",{"$f":"0.98*C69","v":{"v":97112873.64130434,"d":"97,112,873.64"}}]
["Tie-up Firm Capital:",null,{"$f":"C69-C70","v":{"v":1981895.3804347813,"d":"1,981,895.38"}}]
[]
["Trade P&L:"]
[null,"Sell note:",{"$f":"D23","v":{"v":99104619.5652174,"d":"99,104,619.57"}}]
[null,"Repo interest:",{"$f":"D27*D28/360*C70","v":{"v":19746.284307065212,"d":"19,746.28"}}]
[null,"Cost of Capital:",{"$f":"(EXP(0.09*D27/365.25)-1)*C71","v":{"v":30014.480467983965,"d":"30,014.48"}}]
[null,"  Trade P&L:",{"$f":"C74-C69-C75-C76","v":{"v":-39910.22129676887,"d":"-39,910.22"}}]

{"sheet":"LTCM Trade","index":2,"n_rows":90,"n_cols":32,"rows_kept":90}
["In the preceding spreadsheet, we took a speculative position in the on-the-run note.  We use the repo market to finance the purchase, so as to avoid tying up valuable firm capital."]
["We saw that when a security, such as the on-the-run note--is trading on special in repo it is cheaper to finance.  This means that it has value in addition to the present value of its future cash flows."]
[]
["Here, we look at a convergence trade, such as discussed by Long Term Capital Management--the first super hedge fund."]
["The premise is that the on-the-run note tends to trade at a premium to other securities for a period following the originating auction."]
["A convergence trade attempts to profit from the expected convergence of the on-the-run note to related securities."]
[]
["Today:","September 2 2020 (Wednesday)",null,null,"Settlement:","2020-09-03"]
[null,"Note:","2030-08-15",{"v":0.00625,"d":"0.625%"},null,"Acrued Interest:",null,{"$f":"(F8-N9)/(N10-N9)*R9","v":0.03226902173913043},{"$nulls":4},"Dated Date:","2020-08-15","Semi-annual coupon (per 100 par):",null,null,{"$f":"'Repo Fin'!R3","v":0.3125}]
[null,null,"Bid","Ask",{"$nulls":8},"Next Coupon:","2021-02-15"]
[null,"Price:","99-1+","99-2"]
[null,"Cash Quotes:",{"$f":"99+1.5/32+H9","v":99.07914402173913},{"$f":"99+2/32+H9","v":99.09476902173913}]
[]
["ytm:",7.232744008990568E-3,"(cc)"]
["Date:","2021-02-16","2021-08-16","2022-02-15","2022-08-15","2023-02-15","2023-08-15","2024-02-15","2024-08-15","2025-02-18","2025-08-15","2026-02-17","2026-08-17","2027-02-16","2027-08-16","2028-02-15","2028-08-15","2029-02-15","2029-08-15","2030-02-15","2030-08-15"]
["T (Yrs):",{"$f":"(B15-$F$8)/365.25","v":0.4544832306639288},{"$f":"(C15-$F$8)/365.25","v":0.9500342231348392},1.4510609171800137,1.946611909650924,2.4503764544832305,2.945927446954141,3.4496919917864477,3.9479808350444903,4.459958932238193,4.947296372347707,5.456536618754278,5.952087611225188,6.453114305270363,6.9486652977412735,7.449691991786447,7.94798083504449,8.451745379876797,8.947296372347708,9.451060917180014,9.946611909650924]
["Cash Flow:",{"$f":"$R$9","v":0.3125},{"$f":"$R$9","v":0.3125},0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,{"$f":"100*(1+'Repo Fin'!D3/2)","v":100.3125}]
["df (@ytm):",{"$f":"EXP(-B16*$B$14)","v":0.9967182359345},{"$f":"EXP(-C16*$B$14)","v":0.9931521994398321},0.9895597297880496,0.9860193048385959,0.9824331820716565,0.9789182543272518,0.9753579578689688,0.9718490987900965,0.9682569901509797,0.9648500983587182,0.9613028948355259,0.9578635665661887,0.954398744361316,0.9509841176090857,0.9475441800207033,0.9441353812593106,0.9407015890716807,0.9373359676991806,0.9339269047756231,0.9305855217189967]
["PV:",{"$f":"B17*B18","v":0.3114744487295313},{"$f":"C17*C18","v":0.31036006232494756},0.3092374155587655,0.3081310327620612,0.3070103693973927,0.30591195447726616,0.30479936183405276,0.3037028433719052,0.30258030942218117,0.30151565573709943,0.30040715463610185,0.29933236455193396,0.29824960761291125,0.2971825367528393,0.2961075562564698,0.2950423066435346,0.2939692465849002,0.2929174899059939,0.2918521577423822,93.34936014743685]
[{"$f":"SUM(B19:U19)","v":{"v":99.07914402173913,"d":"99.079144"}}]
["Convergence Criterion:",null,{"$f":"(C12-A20)^2","v":{"v":0,"d":"0.0000000000000000"}}]
["The ytm on this note (to a buyer) is 72.16 bps."]
[]
["The first off-the-run note:",null,0.00625,"May 15 2030",null,null,"Bid:","97-30+",null,"AI:",{"$f":"(F8-O24)/(O25-O24)*R24","v":0.18851902173913043},null,null,"Dated Date:","2020-05-15","Semi-annual coupon:",null,{"$f":"50*C24","v":0.3125}]
[{"$nulls":6},"Ask:","97-31+","Cash buy:",null,{"$f":"97+31.5/32+K24","v":98.17289402173913},null,null,"Next Int:","2020-11-15"]
["ytm:",0.008403901191451188,"(cc)"]
["Date:","2020-11-16","2021-05-17","2021-11-15","2022-05-16","2022-11-15","2023-05-15","2023-11-15","2024-05-15","2024-11-15","2025-05-15","2025-11-17","2026-05-15","2026-11-16","2027-05-17","2027-11-15","2028-05-15","2028-11-15","2029-05-15","2029-11-15","2030-05-15"]
["T (Yrs):",{"$f":"(B27-$F$8)/365.25","v":0.2026009582477755},0.7008898015058179,1.1991786447638604,1.6974674880219027,2.198494182067077,2.6940451745379876,3.1978097193702943,3.696098562628337,4.199863107460644,4.695414099931554,5.204654346338125,5.69472963723477,6.201232032854209,6.699520876112252,7.197809719370294,7.696098562628337,8.199863107460644,8.695414099931554,9.19917864476386,9.69472963723477]
["Cash Flow:",{"$f":"$R$9","v":0.3125},{"$f":"$R$9","v":0.3125},0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,{"$f":"100*(1+C24/2)","v":100.3125}]
["df (@ytm):",{"$f":"EXP(-B28*$B$26)","v":0.9982988102321098},{"$f":"EXP(-C28*$B$26)","v":0.9941271046313469},0.9899728318146773,0.9858359189337292,0.9816937057599086,0.9776138831063365,0.9734838178963586,0.9694158095468084,0.9653203782336912,0.9613086015217035,0.9572033713463081,0.9532691939402421,0.9492201357366513,0.9452535208153244,0.9413034816421743,0.9373699489502227,0.933409899812278,0.9295307399154803,0.9256038086015228,0.9217570900533563]
["PV:",{"$f":"B29*B30","v":0.3119683781975343},{"$f":"C29*C30","v":0.3106647201972959},0.30936650994208664,0.3080737246667904,0.30677928304997143,0.30550433847073016,0.3042136930926121,0.3029424404833776,0.30166261819802853,0.30040893797553236,0.29912605354572125,0.29789662310632564,0.29663129241770353,0.2953917252547889,0.29415733801317945,0.2929281090469446,0.2916905936913369,0.2904783562235876,0.28925119018797585,92.4637580959773]
[{"$f":"SUM(B31:U31)","v":{"v":98.17289402173883,"d":"98.172894"}}]
["Convergence Criterion:",null,{"$f":"(K25-A32)^2","v":{"v":8.905924075583135e-26,"d":"0.0000000000000000"}}]
[]
[]
["So we see the on-the-run premium."]
[null,null,"The yield to maturity on the on-the-run note is almost 12 basis points lower than the ytm on the first off the run note, despite their seimilarities."]
[]
["Let's consider a convergence trade where we short the on-the-run and go long the off-the-run.  Hold until the November note auction."]
["We'll assume that the ytm on the 2 notes will be the same on 11/16/2020."]
["First, we have to buy the May 2030 note.  Let's do his trade to a $50 million par value.",{"$nulls":4},"We'll naively use the same par for both positions.  In a few weeks we'll have a better strategy to hedge interest rate risk."]
["Par note:",{"v":50000000,"d":"50,000,000"}]
["Purchase May note:",null,{"$f":"B42*K25/100","v":{"v":49086447.01086956,"d":"49,086,447.01"}}]
["Conditions in repo:",null,"general collateral rate (ask):",null,1.5E-3,"Haircut:",0.01,null,"Firm cost of capital (cc): ",null,0.085]
[null,"Repo:",{"$f":"(1-G44)*C43","v":{"v":48595582.54076087,"d":"48,595,582.54"}}]
[null,"Firm Capital:",{"$f":"C43-C45","v":{"v":490864.4701086953,"d":"490,864.47"}}]
[]
["Close the position on 11/13/20 for settlement on:",null,null,"2020-11-16","  Number of days:",null,{"$f":"D48-F8","v":74}]
["Financing:"]
[null,"Repo interest:",{"$f":"G48/360*E44*C45","v":{"v":14983.637950067932,"d":"14,983.64"}}]
[null,"Cost of firm Cap:",{"$f":"C46*(EXP(G48/365.25*K44)-1)","v":{"v":8526.42341794255,"d":"8,526.42"}}]
[]
[null,"Receive coupon:",{"$f":"B42*C24","v":{"v":312500,"d":"312,500"}}]
[{"$nulls":3},"Tick to accommodate bid-ask spread:",null,null,0.000317," (and partial convergence)"]
["Sell the May note:",{"$nulls":6},"Last cpn:","2020-11-15","Next Coupon:","2021-05-15",null,"2021-05-17","2021-11-15","2022-05-16","2022-11-15","2023-05-15","2023-11-15","2024-05-15","2024-11-15","2025-05-15","2025-11-17","2026-05-15","2026-11-16","2027-05-17","2027-11-15","2028-05-15","2028-11-15","2029-05-15","2029-11-15","2030-05-15"]
["AI:",{"$f":"R24*(D48-I55)/(K55-I55)","v":1.7265193370165745E-3},"If the ccytm is:",{"$f":"0.0065+G54","v":0.006817},{"$f":"0.0075+G54","v":0.007817},{"$f":"0.0085+G54","v":0.008817},{"$f":"G54+0.0095","v":0.009817},{"$f":"0.0105+G54","v":0.010817},{"$nulls":3},"T:",{"$f":"(M55-$D$48)/365.25","v":0.49828884325804246},{"$f":"(N55-$D$48)/365.25","v":0.9965776865160849},1.4948665297741273,1.995893223819302,2.4914442162902124,2.9952087611225187,3.4934976043805612,3.997262149212868,4.492813141683778,5.002053388090349,5.492128678986996,5.9986310746064335,6.496919917864476,6.995208761122519,7.493497604380561,7.997262149212868,8.492813141683778,8.996577686516085,9.492128678986996]
[{"$nulls":3},99.47383693319716,98.56002246805743,97.65475578467102,96.75795653061681,95.8695451103235,{"$nulls":3},"df (@ytm):",{"$f":"EXP(-$G$56*M56)","v":0.9951202433130033},{"$f":"EXP(-$G$56*N56)","v":0.9902642986513309},0.9854320498180931,0.9805970248511401,0.9758381776816573,0.971024126040389,0.9662857645681083,0.9615188373487772,0.9568525768140623,0.952081005394221,0.947511478827315,0.9428118290659623,0.9382111367384981,0.9336328946701836,0.9290769933092167,0.9244936261825784,0.9200070493679774,0.9154684265232447,0.91102564909286]
[{"$nulls":11},"CF:",{"$f":"C29","v":0.3125},{"$f":"D29","v":0.3125},0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,0.3125,100.3125]
[{"$nulls":11},"PV:",{"$f":"M57*M58","v":0.31097507603531355},{"$f":"N57*N58","v":0.3094575933285409},0.3079475155681541,0.30643657026598126,0.3049494305255179,0.3034450393876216,0.30196430142753383,0.3004746366714929,0.2990164302543945,0.29752531418569406,0.2960973371335359,0.2946286965831132,0.29319098023078066,0.2917602795844324,0.2903365604091302,0.28890425818205573,0.28750220292749296,0.286083883288514,91.38726042462751]
[{"$nulls":11},{"$f":"SUM(M59:AE59)","v":96.75795653061681}]
[null,null,"Profit on Note:",{"$f":"$B$42*(D57-$K$25)/100","v":{"v":650471.4557290185,"d":"650,471.46"}},{"$f":"$B$42*(E57-$K$25)/100","v":{"v":193564.2231591501,"d":"193,564.22"}},{"v":-259069.11853405036,"d":"(259,069.12)"},{"v":-707468.745561158,"d":"(707,468.75)"},{"v":-1151674.4557078127,"d":"(1,151,674.46)"},{"$nulls":3},"Remember that when we compute a note's value using the ytm, this is the cash value."]
[null,null,"Coupon:",{"$f":"$C$53","v":{"v":312500,"d":"312,500"}},{"$f":"$C$53","v":{"v":312500,"d":"312,500"}},{"v":312500,"d":"312,500"},{"v":312500,"d":"312,500"},{"v":312500,"d":"312,500"}]
[null,null,"-Financing Cost:",{"$f":"$C$50+$C$51","v":{"v":23510.06136801048,"d":"23,510.06"}},{"$f":"$C$50+$C$51","v":{"v":23510.06136801048,"d":"23,510.06"}},{"v":23510.06136801048,"d":"23,510.06"},{"v":23510.06136801048,"d":"23,510.06"},{"v":23510.06136801048,"d":"23,510.06"}]
[null,null,"Profit on Long side:",{"$f":"D61+D62-D63","v":{"v":939461.3943610081,"d":"939,461.39"}},{"$f":"E61+E62-E63","v":{"v":482554.16179113963,"d":"482,554.16"}},{"v":29920.820097939162,"d":"29,920.82"},{"v":-418478.8069291685,"d":"(418,478.81)"},{"v":-862684.5170758232,"d":"(862,684.52)"}]
[]
[null,null,"YTM for buyer:",{"$f":"D56-2*$G$54","v":0.006183},{"$f":"E56-2*$G$54","v":0.007182999999999999},0.008183,0.009183,0.010183000000000001]
[]
["Sell the O-the-run note short."]
["Proceeds from short sale:",null,{"$f":"B42*C12/100","v":{"v":49539572.01086956,"d":"49,539,572.01"}}]
["Place cash proceeds with repo dealer as loan collateral (You are lending this cash -- the securities lender uses the note as collateral for this loan)."]
["Specialness:","180 bps",0.018]
["Earn on cash collateral:",null,{"$f":"E44-C71","v":-0.016499999999999997}]
["Repo:",null,{"$f":"(1+G44)*C69","v":{"v":50034967.73097826,"d":"50,034,967.73"}},"  The security lender requires that we post the full cash received from selling the security plus the haircut in our repo account."]
["Tie-up Firm Capital:",null,{"$f":"C73-C69","v":{"v":495395.7201086953,"d":"495,395.72"}},"    This ``margin account'' would be makrked to market on a dally basis.",{"$nulls":7},"ytm:",{"$f":"H66","v":0.010183000000000001}]
["Purchase the August 2030 note:",{"$nulls":10},{"$f":"A15","v":"Date:"},{"$f":"B15","v":"2021-02-16"},{"$f":"C15","v":"2021-08-16"},"2022-02-15","2022-08-15","2023-02-15","2023-08-15","2024-02-15","2024-08-15","2025-02-18","2025-08-15","2026-02-17","2026-08-17","2027-02-16","2027-08-16","2028-02-15","2028-08-15","2029-02-15","2029-08-15","2030-02-15",{"$f":"U15","v":"2030-08-15"}]
[{"$nulls":3},100.21395599653495,99.2711014981491,98.337296998445,97.41245518810484,96.49648960184156,{"$nulls":3},{"$f":"A16","v":"T (Yrs):"},{"$f":"(M75-$D$48)/365.25","v":0.2518822724161533},{"$f":"(N75-$D$48)/365.25","v":0.7474332648870636},1.2484599589322383,1.7440109514031485,2.2477754962354553,2.7433264887063653,3.247091033538672,3.7453798767967146,4.257357973990418,4.744695414099931,5.253935660506502,5.749486652977413,6.250513347022587,6.746064339493498,7.2470910335386725,7.745379876796714,8.24914442162902,8.744695414099931,{"$f":"(AE75-$D$48)/365.25","v":9.248459958932239},{"$f":"(AF75-$D$48)/365.25","v":9.744010951403148}]
[{"$nulls":11},{"$f":"A17","v":"Cash Flow:"},{"$f":"B17","v":{"v":0.3125,"d":"0.312500"}},{"$f":"C17","v":{"v":0.3125,"d":"0.312500"}},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":0.3125,"d":"0.312500"},{"v":100.3125,"d":"100.312500"}]
[null,null,"Profit on Note:",{"$f":"$B$42*($C$12-D76)/100","v":{"v":-567405.9873979118,"d":"(567,405.99)"}},{"$f":"$B$42*($C$12-E76)/100","v":{"v":-95978.73820498392,"d":"(95,978.74)"}},{"v":370923.5116470637,"d":"370,923.51"},{"v":833344.4168171412,"d":"833,344.42"},{"v":1291327.2099487826,"d":"1,291,327.21"},{"$nulls":3},{"$f":"A18","v":"df (@ytm):"},{"$f":"EXP(-$M$74*M76)","v":0.9974383694095127},{"$f":"EXP(-$M$74*N76)","v":0.9924177782392535},0.9873674019176928,0.9823975028122429,0.9773708702663516,0.9724512885540171,0.9674755477949593,0.9625789374139887,0.9575736170367328,0.9528333748239293,0.9479051572461691,0.9431338907612727,0.9383343182683122,0.9336112264588022,0.9288601144422316,0.9241589454160857,0.9194303020519617,0.9148023633264006,0.9101215947786475,0.9055405112924437]
[null,null,"Repo Interest:",{"$f":"C73*C72/360*G48","v":{"v":-169701.93222090122,"d":"(169,701.93)"}},{"$f":"D79","v":{"v":-169701.93222090122,"d":"(169,701.93)"}},{"$f":"E79","v":{"v":-169701.93222090122,"d":"(169,701.93)"}},{"v":-169701.93222090122,"d":"(169,701.93)"},{"v":-169701.93222090122,"d":"(169,701.93)"},{"$nulls":3},"PV:",{"$f":"M77*M78","v":0.31169949044047274},{"$f":"N77*N78","v":0.3101305556997667},0.308552313099279,0.3069992196288259,0.30542839695823487,0.30389102767313037,0.30233610868592475,0.30080591794187145,0.299241755323979,0.2977604296324779,0.29622036163942783,0.2947293408628977,0.29322947445884756,0.2917535082683757,0.29026878576319737,0.28879967044252675,0.28732196939123805,0.2858757385395002,0.28441299836832734,90.83703253902326]
[null,null,"Cost of Firm Capital:",{"$f":"C74*(EXP(G48/365.25*K44)-1)","v":{"v":8605.132223458657,"d":"8,605.13"}},{"$f":"D80","v":{"v":8605.132223458657,"d":"8,605.13"}},{"v":8605.132223458657,"d":"8,605.13"},{"v":8605.132223458657,"d":"8,605.13"},{"v":8605.132223458657,"d":"8,605.13"},{"$nulls":3},{"$f":"SUM(M79:AF79)","v":96.49648960184156}]
[null,null,"Profit on Short Side:",{"$f":"D78+D79-D80","v":{"v":-745713.0518422717,"d":"(745,713.05)"}},{"$f":"E78+E79-E80","v":{"v":-274285.8026493438,"d":"(274,285.80)"}},{"v":192616.44720270383,"d":"192,616.45"},{"v":655037.3523727814,"d":"655,037.35"},{"v":1113020.1455044227,"d":"1,113,020.15"}]
[]
[]
[null,null,"Net Profit:",{"$f":"D64+D81","v":{"v":193748.34251873638,"d":"193,748.34"}},{"$f":"E64+E81","v":{"v":208268.35914179584,"d":"208,268.36"}},{"v":222537.267300643,"d":"222,537.27"},{"v":236558.54544361285,"d":"236,558.55"},{"v":250335.62842859956,"d":"250,335.63"}]
[]
[]
[]
[null,"Sensitivity Checks:"]
[null,null,"1) Transactions costs: A 1-tick spread does not destroy profitability."]
[null,null,"2) Partial Covergence","12 bps to 6 bps","  We are sill profitable in all cases, but reduced."]