assignment3_solutions

Mark Rempel mark.rempel@utoronto.ca November 7 , 2022 ECO 349 – Assignment 3 Problem set 3 : Fixed income markets Due Date: Tuesday, 11 am, Oct. 18 th. In groups of 2 - 3 , complete the following problems. Provide a single excel and pdf writeup. P roblem 1 : getting our hands dirty with the canadian bond market Grading: 50 points for problem 1 ( 4 bonus points), 80 points for problem 2 . 1 . Go to https://bondtradedata.iiroc.ca/#/search and browse the data. Within your group, pick three different issuers, one government, one corporate (bank) and one corporate (non-bank) each with at least 8 different bonds outstanding • I) For each of these issuers, download (copy) all the data on the current bonds out- standing (pay attention to small name changes (e.g. "Air Canada and "AIR CDA") into the excel template provided (i.e. copy into column A row 2 of RawSheetIssuer 1 , RawSheetIssuer 2 , etc.). 1 • II) Google the company around the time of the latest bond issuance, is there any new investment which predicated the bond issuance, or news coverage which discusses it? Provide a link to any article referenced, and briefly describe what drove the bond issuance to be timed when it was. • III) In a separate excel sheet (SummaryStats): (a) Compute the average / standard deviation by issuer of: coupon rate, current yield, maturity length issued, time since issued, number of trades and yield to maturity (compute the corresponding variable first from the data if it doesn’t exist). (b) In your pdf writeup, compare / comment on these summary statistics across issuers. Which bonds look most attractive / least attractive. Make an argument for what drives the differences across issuers. (c) Compute the correlation of number of trades to each of the other variables you summarized above. In your pdf writeup indicate which variable has the strongest correlation with number of trades? Does it vary across issuer / issuer type? (d) Sort bonds across issuers based on yield to maturity, which bond characteristics seem most important for determining the yield? • IV) Choose one of the bonds, use the last bond price and bond characteristics to compute the yield for yourself using the formula from class. How does the yield you computed compare with what they gave? Try to explain the discrepancy (if any) 1 Use your cursor to select the relevant data, copy it into the raw data column of the excel. If it copies as a single column, the formula’s to the right in the excel provided sheet 1 should transpose the data into an analyzable format. IMPORTANT catch any inconsistent data types from the copying and add an empty row in the raw data column where the empty cell should be. e.g. for issuer 407 INTERNATIONAL INC the bond with Security ID "BBG 0019 K 2 JP 2 " has an empty cell for coupon rate, so in the reformatted data (row 7 ), this bond has Last Traded Price value of " 407 INTERNATIONAL INC" (cell R 7 ). To fix, add a row in column 1 (raw data) where the missing cell should be (the newly inserted cell is highlighted in red in the excel template. 1

Mark Rempel mark.rempel@utoronto.ca November 7 , 2022 ECO 349 – Assignment 3 • V) In your writeup plot the yield across maturity for each issuer. Is this an appropriate graph of the yield curve for this issuer? Comment on the pattern observed and how it compares across issuers. • VI) Give one interesting tidbit you discovered while getting your hands dirty with the bond data P roblem 2 : ( theory exercise ) what is the impact of otc markets for bond pricing Suppose you are issuing a zero coupon bond to fund your investment I 0 = $1. Your (the entrepreneur’s) investment is risky with expected payoff E [ V ] = 5 4 × I 0 and Var [ V ] = 1 8 I 2 0 and is normally distributed. Your expected utility over final payoff is E [ V − I 0 ( 1 + r )] − Var [ V − I 0 ( 1 + r )] There are 3 banks willing to finance with discount rates ρ given by 1 % for Bank 1 , 2 % for Bank 2 and 3 % for Bank 3 . Each bank gets payoff 1 + r 1 + ρ I 0 − I 0 . 1 . Assume the entrepreneur has no other way to repay but from V . Should the banks be concerned about you (the entrepreneur) defaulting on the loan? Why or why not? Answer: project expected payoff is E [ V ] = 1.25 . As the payoff V is normally distributed the probability that V is within 2 standard deviations of V is about 95 %, since the lower bound of this confidence interval is E [ V ] − 1.962 ∗ p Var [ V ] = 5 4 − 1 4 = 1 which is far above zero suggesting default risk is quite low for this project. 2 . Plot the financial payoff of the investment and repayment of the bond paid to the banks over realizations of V (on the x-axis). Answer: Same qualitative graph as in class notes. V on x-axis with x-intercept of 0 , V = I 0 = 1 labelled on x-axis, two lines: 1 increasing linearly crossing the x-axis at I 0 = 1 , the other breaking off from the first with a kink where full repayment at 1 ∗ ( 1 + r ) (flat from that point) 3 . Ignore any credit risk concerns from here-on. Suppose the bond will be initially issued via an auction 2

Mark Rempel mark.rempel@utoronto.ca November 7 , 2022 ECO 349 – Assignment 3 Answer: Yes there is a unique equilibrium obtained from backward induction here (this is almost always the case for full information sequential games). The unique sequentially rational equilibrium is that bank 1 , 2 and 3 will offer you 25 % and you will accept bank 1 ’s bid. This is established by solving for the equilibria found by backward induction and showing that it is unique. First note that your payoff depends on r only through the expected value and so to maximize your payoff all that is relevant is your expected financial payoff = E [ V − 1 ( 1 + r )] = 1.25 − ( 1 + r ) = 25% − r % return To solve, work backwards: i. Start with you and bank 3 negotiating..bank 3 gets to make you an offer knowing that • if you reject, you won’t get financed, so your expected financial return is zero • if you accept, you get 1.25 − ( 1 + r bank 3 ) • therefore your best response is to accept any offer up to and including r bank 3 = .25 • the only credible optimal strategy of bank 3 is then to offer r bank 3 = .25 if they have the opportunity to give the last offer ii. Now move to bank 2 who gets to make the offer before bank 3 • if you reject, you can get to bank 3 , where you and bank 2 know in equilibrium bank 3 will give you r bank 3 = .25 • if you accept, you get 1.25 − ( 1 + r bank 2 ) • therefore you will accept any offer up to and including r bank 2 = .25 • thus r bank 2 = r bank 3 = .25 iii. Finally move to bank 1 who gets to make the first offer • if you reject, you can get an offer from bank 2 / 3 of r bank 2 = r bank 3 = .25 • if you accept, you get 1.25 − ( 1 + r bank 1 ) • thus bank 1 can give you any offer below .25 which will guarantee you accept • if you accept at r bank 1 = .25% no bank or you have any incentive to de- viate...you get no return regardless, bank 1 gets the highest surplus they possibly could (any higher and you will reject and go to the next bank; any lower gives worse payoff); bank 2 and bank 3 get nothing, but cannot credibly (in a sequentially rational equilibrium) lower the rate. 2 (c) Which bank will finance you in equilibrium and at what yield? Answer: A unique sequentially rational equilibrium is that bank 1 , 2 and 3 will offer you 25 % and you will accept bank 1 ’s bid, so Bank 1 at 25 % is the equilibrium 4

Mark Rempel mark.rempel@utoronto.ca November 7 , 2022 ECO 349 – Assignment 3 bank/yield. (d) Would your answer change if you visited banks in reverse order? Answer: The equilibrium rate would not change, but bank 3 would be the one to make the loan. Here the market structure results in the first bank to make an offer having all the market power. (e) Who is better or worse off with this OTC market rather than the auction? Answer: The first-moving bank (here Bank 1 ) is made the best of from the OTC market. You are worse off here rather than in the simultaneous bid auction. The other banks if they know their discount rates and the sequence in which they move in the OTC market as given are indifferent (get zero either way), but if they randomly draw their order in OTC would strictly prefer OTC since they always lose in the auction, but would win if first in the OTC market leading to market distortions from the efficient outcome. (f) Which of the two market structures more closely resembles the market for Government of Canada bonds? Answer: ( 6 points) - full points given for any of the following answers • Government of Canada bonds are issued in a primary market with a simulta- neous (closed-bid) auction structure which more closely resembles the original setup. • The secondary bond market for recent issues also is fairly liquid / traded on exchanges so may in outcomes more closely resemble the original auction setup. • For old, off-the-run, long-maturity bonds, demand and supply of these assets is very thin (few potential buyers / sellers, e.g. not traded on a daily basis). Thus, in this case the OTC market model here may be closer. (g) Do you think a switch from one structure to the other (e.g. OTC market to an exchange or vice-versa depending on above) for trading of government bonds would improve the yield offered to the government? Answer: 5