[PDF] Interest Rate Swaps and Duration Gap Management in Bloomberg

View - Download Interest Rate Swaps and Duration Gap Management in Bloomberg

Previous PDF

Next PDF

Copyright © 2015 by Akin Sayrak Page 1 of 10 Interest Rate Swaps and Duration Gap Management in Bloomberg Terminal by Akin Sayrak Katz Graduate School and College of Business Administration University of Pittsburgh Pittsburgh, PA 15260 Please do not quote without consent from the author. akins@pitt.edu, 412-512-5720 Abstract: Interest rate swap and its application in the context of managing duration gap of depository banks are fairly challenging topics for advanced finance students in the college or graduate levels. The purpose of this pape r is to de monstrate how to utilize t he Bloomber g system i n order to build the necessary links with the markets framework so that the technical elements of the study do not overshadow the intuitive ones. I provide step-by-step instructions as well as detailed Bloomberg screenshots in order to demonstrate the entire process of determining the swap contract specifications that fulfill regulatory requirements.

Copyright © 2015 by Akin Sayrak Page 2 of 10 1. Introduction Financial institutions, more specifically, depository banks pose unique ch allenges in managing balance sheet risk. Of course, there are profit-driven considerations, which are multiplied by regulatory requirements that change over time and across borders. These issues add to the risks born by banks due to their raison d'être, term intermediation. As financial regulation is varied, we will set the stage with a hypothetical, simplified case that is general enough to capture the main problem, but also easy to update with specific concerns, if necessary. Assume the following balance sheet represents the current holdings of a depository bank: Table 1. Balance Sheet Information Note that the balance sheet in Table 1 provides the assets and liabilities based on par values and not market prices. The computations for the fair market values require the usage of discount factors from the term structure of LIBOR rates. Once the d isco unt factors are available, and the fair market values are stated, we can begin to assess the risk exposure of the bank's balance sheet. To assess the risk exposure, we use the measure of "Bloomberg Risk" or dollar risk. This metric is simply based on the notion of modified duration, converting the p ercentage change implied therein to a chan ge valu e that is measured in actual dollars. The objective is to satisfy the regulatory mandate of reducing the dollar duration gap to no more than 50bps of the asset size by using a plain-vanilla interest rate swap (IRS.) Stated as such, this o bjective c an be achieved in more than one unique way. Essentially, we have the freedom to choose the maturity of the swap contract, given that the range for maturity goes out to 30 years for USD swaps. Assets Liabilities 250 million 5-year note, c=5%, semi 350 million 0.5-year note, c=25bps, semi 150 million 3-year note, c=3%, semi Book Value of Equity = 50 million

Copyright © 2015 by Akin Sayrak Page 3 of 10 2. The IRS Market IRS data is accessible via {USSW} in Bloomberg. A screenshot with the Bid/Ask midpoint rates highlighted is provided in Exhibit 1 as of March 31, 2017. Exhibit 1: Swap Rates Given typical arrangements in the swap markets, the swap rates are par yields based on the term -structure of LIBOR rates. Revisiting a v alue-neutral swap contract a s the exchange of a long- term bond with a short-term bond (pay-fixed-receive-floating), it is evident that the swap rate is the par yield on a fixed-rate bullet bond. Since the short-term bond will always be priced at par, this exchange is cost-free. However, note that, once the contract is established, the value of the swap may shift to positive or negative territory depending on the way the LIBOR rates change over time. An increase (decrease) in LIBOR rates implies a negative (positive) valuation for a pay-fixed-receive-floating, as the long-term bond depreciates (appreciates) more than its short-term counterpart. Of course, the way LIBOR rates change, specifically the slope of the term-structure, may moderate this general rule, which is only valid for parallel shifts across the entire term-structure.

Copyright © 2015 by Akin Sayrak Page 4 of 10 To oper ationalize the swap rates for our purp ose, we need t o access th e LIBOR discount factors via {SWPM} in Bloomberg. Exhibit 2 provides a screenshot of the available data: Exhibit 2: LIBOR Discount Factors Note that on the {SWPM} screen, the {Cash Flow} tab has been activated as seen above. Also, we have selected "semi-annual" for the "Reset Freq" and "Pay Freq" options from the pull-down menus available on the first screen in {SWPM}. This ensures that Bloomberg provides the disc ount factors that are based on a se mi-annual frequency a s consistent with the swap contract we are required to construct. In Table 2, we present the LIBOR discount factors tabulated using a 30-year time frame and 30-year contract. Of course, we may not need all discount factors displayed on this screen, if we choose to use a swap with a maturity of lower than 30 years. However, we will definitely use all 10 discount factors out to 5 years. Recall that we need to compute the fair market value of the bank's balance sheet, which has instruments with a maximum maturity of 5-years.

Copyright © 2015 by Akin Sayrak Page 5 of 10 Table 2. Discount Factors Pay Date Discount Pay Date Discount Pay Date Discount 10/04/2017 0.993751 10/04/2027 0.775336 10/05/2037 0.580377 04/04/2018 0.986243 04/04/2028 0.764096 04/05/2038 0.572415 10/04/2018 0.977629 10/04/2028 0.752940 10/04/2038 0.564571 04/04/2019 0.968226 04/04/2029 0.741910 04/04/2039 0.556845 10/04/2019 0.958154 10/04/2029 0.731295 10/04/2039 0.549194 04/06/2020 0.947220 04/04/2030 0.720828 04/04/2040 0.541661 10/05/2020 0.936395 10/04/2030 0.710397 10/04/2040 0.534244 04/06/2021 0.925030 04/04/2031 0.700122 04/04/2041 0.526982 10/04/2021 0.913858 10/06/2031 0.689783 10/04/2041 0.519794 04/04/2022 0.902317 04/05/2032 0.679719 04/08/2042 0.512603 10/04/2022 0.890784 10/04/2032 0.670093 10/06/2042 0.505768 04/04/2023 0.879114 04/04/2033 0.660582 04/06/2043 0.499003 10/04/2023 0.867503 10/04/2033 0.651136 10/05/2043 0.492346 04/04/2024 0.855772 04/04/2034 0.641860 04/04/2044 0.485793 10/04/2024 0.844159 10/04/2034 0.632654 10/04/2044 0.479310 04/04/2025 0.832549 04/04/2035 0.623619 04/04/2045 0.472965 10/06/2025 0.820886 10/04/2035 0.614656 10/04/2045 0.466688 04/07/2026 0.809333 04/04/2036 0.605817 04/04/2046 0.460545 10/05/2026 0.797970 10/06/2036 0.597006 10/04/2046 0.454468 04/05/2027 0.786560 04/07/2037 0.588415 04/04/2047 0.448521 Recall that for a semi-annual coupon-paying bond,

P 0,T 100y
2

×DF

t t=1 2T +FV×DF T

We have that, AN

T =DF t t=1 2T , and FV=100.

For a par bond,P

0,T =100,and therefore: 100=
100y
par 2

×AN

T +100×DF
T ⇒y par =2× 1-DF T AN T

Copyright © 2015 by Akin Sayrak Page 6 of 10 We calculate the swap rates using the discount factors obtained above and compare them to those observed in Bloomberg's {USSW} . Using the formulation above and the discount factors Table 2, we compute the par yields out to 30 years as follows: Table 3: Par Yields Note that the computed par-yields that correspond to 2, 3, 4, 5, 7, 10, and 30 years that are highlighted are directly comparable to t he swap rate s indicated in Exhibit 1. Tautologically, a quick comparison will sho w th at the par-yields are virtually indistinguishable (within the Bid/Ask spread) from the swap rates offered in the markets on the same day. 3. Balance Sheet Revisited As we are equipped with the LIBOR discount rates, we are now able to restate the balance sheet. Assuming that the bank's and their clients' credit rating is AA, we compute the fair market values as follows:

Copyright © 2015 by Akin Sayrak Page 7 of 10

P 5 =6,250,000×DF t +250,000,000×DF
10 t=1 10 =$285,009,393.75 y 5 =2.040% P 3 =2,250,000×DF t +150,000,000×DF
6 t=1 6 =$155,203,251.75 y 3 =1.807% P 0.5 =437,500×DF t +350,000,000×DF
1 t=1 1 =$348,247,616.06 y 0.5 =1.26% Observe that, the market value of equity is given by:

Assets

M -Liabilities M =$91,965,029.44

As expected, book value of equity may be substantially different from the market value of equity or market capitalization of the bank. 4. Measuring Risk The next step is to represent the risk exposure of the bank. For this, we first start with computing the modified duration of all parts (except for the equity) of the balance sheet.

P= C t (1+ym) m×t t=1m T =C t t=1m T (1+ym) -m×t where C t is the cash flow at time t, m is the frequency of compounding, and y is the bond-equivalent yield. Taking the first derivative w.r.t. y: dP dy =-mtC t t=1m T (1+ym) -mt-1 (1m)=- 1 1+ym t C t (1+ym) -mt t=1m T

Dividing through by P,

Copyright © 2015 by Akin Sayrak Page 8 of 10

Modified Duration≡

1 P dP dy 1 1+ym t C t (1+ym) -mt t=1m T /P=- D 1+ym Using m=2 for semi-annual cash-flows we obtain he following values for duration: MD 5 =4.4788 MD 3 =2.8676 MD 0.5 =0.4968 Using the relationship between modified duration and Bloomberg Risk,

BloombergRisk=

MD 100

×Price

, we compute the following values for the dollar risk: Risk 5 =$12,765,051.94 Risk 3 =$4,450,632.69 Risk 0.5quotesdbs_dbs2.pdfusesText_3

[PDF] courbe zero coupon

[PDF] calcul propositionnel cours

[PDF] logique propositionnelle exercice corrigé

[PDF] calcul propositionnel exercices corrigés

[PDF] logique propositionnelle table de vérité

[PDF] calcul propositionnel formel

[PDF] calcul des propositions exercices corrigés

[PDF] le resultat dune multiplication est

[PDF] comment calculer le taux de possession du stock

[PDF] cout de stockage annuel

[PDF] calcul du stock moyen

[PDF] exercice cout de passation et possession

[PDF] calcul tangente formule

[PDF] calcul tangente fonction

[PDF] calcul tangente en ligne