THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE

DEPARTMENT OF FINANCE

IMPLICATIONS OF GCF-BASED DERIVATIVES HEDGING FOR BANK RISK MANAGEMENT

NICHOLAS ROBERT FAKELMANN FALL 2013

A thesis submitted in partial fulfillment of the requirements for baccalaureate degrees in Accounting and Finance with honors in Finance

Reviewed and approved* by the following:

Louis Gattis Clinical Professor of Finance Thesis Supervisor

James Miles Professor of Finance Honors Adviser

Heber Farnsworth Associate Professor of Finance Faculty Reader

* Signatures are on file in the Schreyer Honors College. i

ABSTRACT

In the wake of the Barclays- -rigging scandal, Federal Reserve Chairman Ben Bernanke suggested the practical use of repo rates in valuing derivatives, specifically the General Collateral Finance Repo Index. For large financial institutions, which actively exposure via the money market, opportunities may exist in which GCF-based instruments can provide better strategies for hedging interest rate risk (IRR). In this thesis, I will conduct a comparative study of the GCF Repo rates with other interest rates that are suitable for hedging interest rate risk in banks. This study will examine the period of 2005 - 2013, the period for which GCF rate data is available.

ii

TABLE OF CONTENTS

List of Figures ...... iii

List of Tables ...... iv

Acknowledgements ...... v

Chapter 1 Introduction: The Role of Repos in Financial Markets ...... 1

Chapter 2 Interest Rate Risk and Hedging ...... 3

Chapter 3 Pricing Financial Instruments Used to Hedge IRR ...... 7

Chapter 4 Qualitative Comparison of Interest Rates ...... 14

Chapter 5 Empirical Comparison of Interest Rates ...... 19

Chapter 6 Practical Application of Empirical Results: Hedging a GCF-based Asset ...... 23

Chapter 7 Conclusions and Further Research ...... 29

Appendix A Simple Investment Decision: 3M FRAs Net Cash Flows, 2005 - 2007 ..... 30 Appendix B Simple Investment Decision: 2-Year Net Cash Flows, 2005 - 2007 ...... 32 Appendix C Modified Duration Calculation: Asset Hedging Scenario ...... 34 Appendix D Basic Concepts & Definitions ...... 36 Appendix E Formulas ...... 37 BIBLIOGRAPHY ...... 41

iii

LIST OF FIGURES

Figure 1: The Relationship Between Yield and Bond Price ...... 3

Figure 2: Net Exchange of Cash Flows on a Swap Transaction ...... 5

Figure 3: Net Cash Flows in a Simple Swap Transaction ...... 10

Figure 4: Bootstrapped LIBOR , March 2005 - March 2010 ...... 12

Figure 5: Structure of a LIBOR-Based Swap Transaction ...... 13

Figure 6: Daily Changes in Overnight GCF TSY Rates and 3M LIBOR Rates (in bps), 2005 - 2013 ...... 19

Figure 7: Daily Changes in Overnight GCF ACY rates and 3M LIBOR Rates (in bps), 2005 - 2013 ...... 20

Figure 8: Daily Changes in Overnight GCF MBS rates and 3M LIBOR Rates (in bps), 2005 - 2013 ...... 20

Figure 9: Net Cash Flows for a GCF Asset Hedged with a LIBOR-Based Swap, 2005 - 2013 ...... 26

Figure 10: Net Cash Flows for a GCF Asset Hedged with a TBL-Based Swap, 2005 - 2013 ...... 27

iv

LIST OF TABLES

Table 1: Number of Futures Needed to Hedge $100 Million for Three Months ... 8

Table 2: Selected Spot LIBOR Rates: December 20, 2006 ...... 9

Table 3: Selected Rate Averages & Standard Deviations, 2005 - 2013 ...... 16

Table 4: Correlation Between Levels of Selected Rates, 2005 - 2013 ...... 17

Table 5: Summary of Key Interest Rate Benchmarks ...... 18

v

ACKNOWLEDGEMENTS

Dr. Gattis, thank you for helping me find success with this idea. Even after I had made errors in the face of multiple deadlines, you were still committed to helping me succeed. You are a wonderful researcher and teacher. Thank you for being such a positive influence in my work.

Dr. Farnsworth, thank you for lending your technical expertise. Through several quantitative challenges in performing this research, you helped me with the important steps of the research process. I can't thank you enough for being responsive and flexible when I needed you most.

Dr. Miles, thank you for your initial encouragement. When this idea seemed so far out of reach, you encouraged me to begin writing.

Mom, Dad, and Greg, thank you for all your love. I would not be an honors student without your undying care and support.

1

Chapter 1

Introduction: The Role of Repos in Financial Markets

The Significance of Repos in Modern Interest Rate History

Repos have received popular attention by market participants between 2008 and 2012.

First, during the financial crisis, commonly used interest rate benchmarks used for discounting collateralized lending and borrowing, such as the highly tracked Federal Funds rate, diverged from published repo rates. Analysts noticed that the spread between Fed Funds and repo rates was large, prompting managers to change the underlying rates used to value collateralized investments in their portfolios. Second, by mid-2007, money market rates published in London began moving against the expectations of market participants. In 2012, fears of outright manipulation were confirmed, as Barclays Plc admitted to rigging the widely accepted, universally used interest rate benchmark, the London Interbank Offered Rate (LIBOR). While members of the British Bankers'

Association (BBA) sought to restore confidence in LIBOR, market participants began to look to alternative investment options that were unbiased and accurate.

In July 2012, Federal Reserve Chairman Ben Bernanke suggested the practical use of the repo as short-term interest rate benchmark (Hannon and Hilsenrath). As reported in a Wall Street

Journal article, he implied that there might be advantages to pricing transactions using repo rates.

Those advantages are most available to the largest users of the repo market - financial institutions.

To examine the extent to which these advantages benefit large banks, I will compare

GCF rates with other key interest rates over the period of 2005 - 2013 in the context of hedging interest rate risk.

2

What is a Repo?

A repurchase agreement (repo) is an overnight loan to be repaid the next day. In a repo transaction, a debtor posts collateral on borrowed money and repays principal plus interest. There are two types of repos: special collateral and general collateral repos. A special collateral repo is one where the underlying collateral is specified by the lender. For instance, a bank may sell a repo (borrow money), and the lender could require that Treasury notes be posted for the repo transaction. For general collateral repos, any type can be posted as collateral for the loan (Bodie,

Kane, and Marcus 2009).

The Depository Trust and Clearing Corporation is a clearinghouse that publishes repo rates in the General Collateral Finance (GCF) Repo Index. GCF rates are collateralized rates tracking three specific types of debt. The index tracks interest charged on 30-year U.S. Treasuries

(TSY), agency securities (ACY), and mortgage-backed securities (MBS). Each is calculated as the weighted average of daily market transactions for Treasuries, agencies, and MBSs (Trontz).

3 Chapter 2

Interest Rate Risk and Hedging

Interest Rate Risk

Bonds and loans are an important source of income for banks. The value of a bond is inversely related to its yield; it exhibits a convex relationship.

Figure 1: The Relationship Between Bond Yield and Bond Price

Put another way, as the market rate increases, the value of the bond decreases.

Banks earn money by lending at long-term rates and borrowing at short-term rates. The liquidity preference in interest rate yield curves allows banks to profit on the difference between larger fixed payments and smaller floating rates. A floating rate, also referred to as a variable rate, is an interest rate that changes periodically (e.g. - the Federal Reserve Bank of New York publishes term deposit rates in the U.S. money markets daily). A bank that lends money at a fixed rate is locked into receiving identical cash flows during the lending period. While the fixed rate earned remains constant, floating market rates increase and decrease daily during the same lending period. If the floating rate increases, the bank loan value will decrease, thereby shrinking 4 the value of the asset. The exposure of a bond or a instrument to interest rate changes is called interest rate risk (IRR).

Interest rates of different maturities typically change together, however, this may not always be the case. The term structure of interest rates, also referred to as the yield curve, shows interest rates at certain maturities in the future. Rates can shift by the same amount for all maturities simultaneously (a parallel shift in the yield curve) or individual rates in the yield curve can shift at variable amounts (a flattening or steepening yield curve). Managers must be prepared to hedge these changes to maintain a desired value of assets and liabilities (Fabozzi 2001).

What Does It Mean to Hedge?

A hedge is an investment decision to take opposite positions in similar assets to safeguard a financial position against industry risks. The appropriate hedge for any asset should be an asset of similar or equal risk. Formulaically, the appropriate hedge is equal to the risk of the asset to be hedged divided by the risk of a similar asset multiplied by the correlation between each risk profile. There are a variety of tools available to a financial manager who hedges interest rate risk.

Forwards and Futures

A is a customized, over-the-counter (OTC) agreement where one party agrees to exchange an underlying asset at a specified future date using unique rates and terms.

Forward contracts are transacted directly between two parties. Each transacting party bears a risk that the other party may default on its payments. At the simplest level, a zero-coupon bond can be thought of as a forward contract. A zero-coupon bond is an investment that delivers one payment to the buyer at time t in the future. The present value of a zero is equal to the present value of the principal amount to be delivered in the future.

A is a standardized agreement purchased through market intermediaries

(i.e. - exchanges like the CME or CBOT), where one party agrees to deliver an asset at a future 5

date. Exchanges set the standard number of contracts to be traded as well as the rates investors

can buy (long) or sell (short) futures contracts. Market intermediaries bear the counterparty risk

and must collect payments from each transacting party (Fabozzi 2007).

Swaps

A swap is an OTC agreement wherein two parties agree to exchange interest payments.

Transacting parties agree on a notional principal amount (NPA), a theoretical amount of money

on which payments are made (however, notional principal is never exchanged). Parties trade

interest payments because they are interested in adjusting their exposure to rate changes. The

most common type of swap is a fixed for floating swap. For example, bank A currently receives

floating interest on an investment, but the bank believes interest rates will fall. It wants to lock in

fixed payments today. Bank B is receiving fixed payments on a note receivable but wants to

convert the cash flow into a variable rate. Both A and B agree to exchange interest payments on a

swap with notional principal of $100 million; bank A will pay a floating rate plus several basis

points to Bank B, who will pay a fixed rate to bank A (one basis point, or bp, is equal to 0.01%).

Floating Fixed Bank A A pays Floating Bank B @ y% @ z% B pays Fixed

Figure 2: Net Exchange of Cash Flows on a Swap Transaction

The is the quintessential hedging tool. This is due largely to the

comparative cost advantage of swaps over traditional forms of financing. Banks with different

credit ratings will raise money at different interest rates. However, when two parties agree to

exchange fixed for floating payments, each party agrees to more favorable terms than could be

obtained without the swap. The costs of using financial intermediaries in a swap transaction are

divided between the transacting parties (Nawalkha, Soto, and Beliaeva). 6

A Note on Bond Duration

Duration measures the average waiting period an investor will wait to receive all future payments. Also called the risk of a bond, duration measures the sensitivity of a bond price to changes in interest rates. In the context of risk management, it can be thought of as a measurement of the approximate change in the price of a bond for a 100 bp change in yield. As the maturity of a bond increases, duration, as well as the bond's sensitivity to interest rate changes, increases. In this study, we examine the modified duration of a bond portfolio. Modified duration measures the approximate percentage change in a bond's price for a 100 bp change in yield, assuming the bond's cash flows do not change with changes in yield. Modified duration incorporates the frequency of coupon payments into the duration equation.

It is important for risk managers to understand the relationship between duration and portfolio value. He can hedge exposure to IRR by keeping net portfolio duration close to zero.

Managers use these relationships to find investments that protect against both parallel and non- parallel shifts in the yield curve (Fabozzi 2007).

Complications in Hedging

This paper will conduct analyses that assume simple investment and hedging scenarios.

While futures, forwards, swaps, and other investments provide flexibility in developing a hedging strategy, a manager's estimate of IRR exposure is further complicated in the real world.

Prepayment risk, the risk that a counterparty may pay early, forces banks to adjust their exposed portfolios by buying or selling assets to rebalance a hedge. Reinvestment risk, the risk that a replacement investment cannot be found, places a burden on financial managers to find an investment of similar risk with which to hedge. Both of these risks prompt concerns of liquidity, particularly for managers who develop hedging strategies using non-standardized OTC contracts

(Fabozzi 2001). Prepayment risk and reinvestment risk are real issues faced by managers, but incorporating these additional hedging considerations is outside the primary scope of this paper. 7

Chapter 3

Pricing Financial Instruments Used to Hedge IRR

Hedging is implemented in practice using liquid financial instruments. Three of the most common instruments used by banks to hedge IRR are futures, FRAs, and swaps.

Interest Rate Futures

An interest rate future is a futures contract for the delivery of an interest-bearing deposit on a future date. Common types of interest rate futures include , Fed

Funds, and Treasury bills. The final value of a futures contract is given by the difference between

100 and the spot rate at settlement, multiplied by the contract's notional principal.

When looking to buy or sell a futures contract, market participants make bets on the movement of rates; if they believe interest rates will rise, then the future value of the deposit will fall, and they will sell the contract today. Conversely, if they believe interest rates will fall, then the futures price will rise, and they will buy the contract today. At the end of each trading day, positions in futures contracts are settled (also described as marked-to-market) meaning that investors receive money when futures prices fall or pay money when futures prices rise. The transaction costs on futures are small. Managers at large banks can make small adjustments to their positions frequently without incurring substantial costs ("Interest Rate Products").

Managers hedge their risk by buying or selling a certain number of futures to change their exposure. Let's assume that today is March 14, 2005, and we would like to borrow $100 million starting on June 13, 2005 for three months. In this scenario, we will pay fixed interest on a bond.

To hedge our exposure to changes in bond value, we will invest in Eurodollar futures. We 8

calculate the theoretical zero coupon bond prices from market data on ED futures to compute the

required Eurodollar hedge.

Forward Nominal Present Date Rate Days TW Zero Price Value of 1bp Value of 1bp ED Hedge 3/14/05 3.020% 91 1.0076 0.9924 6/13/05 3.495% 98 1.0172 0.9831 2,696.57 2,650.92 106.0 9/19/05 3.905% 91 1.0273 0.9735 2,503.07 2,436.64 97.5 12/19/05 4.155% 84 1.0372 0.9641 2,310.93 2,228.00 89.1 3/13/06 4.315% 98 1.0494 0.9529 2,690.62 2,563.95 102.6 6/19/06 4.440% 91 1.0612 0.9423 2,499.72 2,355.60 94.2 9/18/06 4.535% 91 1.0733 0.9317 2,499.13 2,328.35 93.1 12/18/06 4.620% 91 1.0859 0.9209 2,498.60 2,300.98 92.0 3/19/07 4.670% 91 1.0987 0.9102 2,498.29 2,273.86 91.0

Table 1: Number of Eurodollar Futures Needed to Hedge $100 Million for Three Months

We then compute the nominal and present value of a 1bp change in the value of the

Eurodollar futures contract. The value of the hedge required is equal to the present value of a 1bp

change in interest rates (i.e. - ± 0.01%) divided by $25 (Burghardt 2003).

If we decide we will borrow $100 million in three months, we should plan to purchase

106 Eurodollar futures contracts to hedge our exposure.

FRAs

Forward rate agreements (FRAs) are over-the-counter contracts between parties who

agree on a fixed rate to be paid starting at some future date. The buyer of the contract will receive

payments on the fixed rate; the buyer seeks to hedge against increases in rates. The counterparty

agrees to receive interest on a floating rate determined on the FRA termination date. The FRA

value is equal to the difference between the fixed rate and floating rate multiplied by the principal

and number of periods in which interest accrues (Smith 2011).

9

Years Settlement Date Spot Rate 0.25 3M 5.36500 0.50 6M 5.37063 0.75 9M 5.34000 1.00 12M 5.29000

Table 2: Selected Spot LIBOR Rates: December 20, 2006

FRAs play an important role in hedging IRR primarily because financial managers can set the terms of a contract today before interest begins to accrue. For example, consider the following set of LIBOR rates at the beginning of the new contract period:

When a manager knows the 3M and 6M spot rates, he can compute the interest earned starting at the end of three months from now (this rate is referred to as 3x6). The manager computes:

! 0.0537063$0.5*4 #1+ & " 4 % F3,6 = ! 0.05365$0.25*4 #1+ & " 4 %

F 5.37626% 3,6 =

He knows today that in three months he must borrow at a floating rate of 5.3763%. If, at the end of the borrowing period, the 3M LIBOR rate exceeds the floating forward rate, the manager pays the difference to the counterparty.

Swaps

The value of an interest rate swap is equal to the difference between the fixed rate and floating rate multiplied by the days in the period and the notional principal amount. To initially price a swap, one sets the value of the fixed component equal to the value of the floating 10

component. Because the value of the swap is priced by setting each leg of the swap equal at the

initiation of the swap agreement, each party will be locked into a profit or loss on the first

payment date. All future cash flows are unknown and payments are settled using the prevailing

floating rate on subsequent payment dates.

A swap can be priced as a series of FRAs in a single contract. Consider two parties A and

B who agree to exchange cash flows quarterly over a 1-year period starting December 20, 2006.

Principal of $100 million will be bought and sold by each; A agrees to receive 5.074% fixed and

B agrees to receive the prevailing floating rate. On December 20, 3M LIBOR is 5.365%. Using

Eurodollar futures prices, we can estimate the LIBOR rates on March 21st, June 20th, and

September 19th. A graphic representation of the swap payments shows the swap value over time:

12/20/06 3/21/07 6/20/07 9/19/07 fixed = 5.074% fixed = 5.074% fixed = 5.074% fixed = 5.074% float = 5.365% float = 5.150% float = 4.960% float = 4.810%

3/21/07 6/20/07 9/19/07 12/19/07 Net cash flow = Net cash flow = Net cash flow = Net cash flow = $72,537 to B $18,673 to B $27,755 to A $63,455 to A

Figure 3: Net Cash Flows in a Simple Swap Transaction

Notice that the sum of the estimated net cash flows is equal to zero (i.e. - both parties will receive

the same amount). At the initiation of a swap contract, this will always be true.

At contract initiation, both parties will know what payments come due on the first

payment date (in this example, March 21, 2007). However, neither A nor B will know the future 11 floating rates with certainty; thus, the future fair value of the swap will remain uncertain

(Burdghart 2003).

Swap Pricing: Bootstrapping Forward Curves

The value of the forward spot rate can be imputed using the traditional approach to value a swap. Market participants hold that Eurodollar futures provide the most competitive market information about the forward rate, and ED futures prices can be used to impute the forward spot rates. The Eurodollar futures prices quoted by the Chicago Mercantile Exchange (CME) provides today's estimate of the future value of LIBOR. The fixed rate will be equal to the floating rate when the same notional principal amount and same day counting convention are used. This method, also called bootstrapping, will estimate the forward yield curve of spot rates (Smith

2012).

For instance, the 3M spot LIBOR on March 16, 2005 is 3.04%. The corresponding fixed rate is the three-month Eurodollar rate subtracted from 100, or 3.505%. We can solve the following formula to find the spot rate three months from now:

3.505 / 4 3.505 / 4 +100 100 = + ! 3.04$ ! S $2 #1+ & 1+ June15 " 4 % # & " 4 %

Rearranging the equation, we solve for SJune15:

(3.505 / 4 +100) S = 4* June15 " 3.505 / 4 % $100 − ' # (1+.0304 / 4)&

The estimated 3M spot rate for June 15, 2005 is 3.507%. Using this simple bootstrapping process, we can find the estimated forward rates over a given time period. The resulting forward rates resemble a LIBOR yield curve. 12

0.06

0.05 Dates Payment Spot 0.04 (t) ($) (%) 3/16/05 3.505 3.52% 0.03 3/15/06 4.435 4.45% 3/21/07 4.715 4.74% 0.02 3/19/08 4.920 4.95% 3/18/09 5.110 5.15% 0.01 3/17/10 5.280 5.34%

0

Figure 4: Bootstrapped LIBOR Yield Curve, March 2005 - March 2010

Using these bootstrapped spot rates, the manager can estimate the total future value of the swap.

The value of the swap on the first payment date, however, is equal to the known net cash flows. Let's assume the value of notional principal on the swap is $100 million and interest payments will be made every quarter settling on term contract dates (i.e. - March, June,

September, and December settlements). On March 14, 2005, party A enters into a swap with party B and agrees to receive 3.5168% LIBOR and pay 3.91% fixed on the first settlement date.

The first payment to B will be $98,300 on June 15, 2005.

# dn & Π = NPA*(X − Fn )*% ( $360 '

Π =100, 000, 000 *(0.0391− 0.035168)*.25

Π = 98,300

13

3/14/05 6/15/05 9/21/05 12/21/05 fixed = 3.91% fixed = 3.91% fixed = 3.91% fixed = 3.91% float = 3.5168% float = ? float = ? float = ?

6/15/05 9/21/05 12/21/05 3/15/06 Net cash flow = Net cash flow Net cash flow Net cash flow

$98,300 to fixed

Figure 5: Structure of a LIBOR-Based Swap Transaction

14

Chapter 4

Qualitative Comparison of Interest Rates

An interest rate represents the intertemporal cost of borrowing and lending; a tradeoff exists for market participants to consume resources at different levels and different time periods.

Both time and the type of resource are relevant factors when deciding to use an appropriate rate.

Financial institutions borrow and lend using commodities, stocks, bonds, and a myriad of other investments. All of these investments are affected by changes in interest rates, and for banks interested in hedging IRR exposure, several key rates tied to hedging instruments offer alternatives.

The London Interbank Offered Rate (LIBOR) is the rate at which banks in London believe they may borrow money in the interbank money market. BBA member banks submit their perceived borrowing costs and Thomson Reuters computes an arithmetic average of the middle quartiles of rate submissions. This rate is published at 11:45am London time each trading day.

LIBOR-based derivatives are pervasively used for hedging interest rate risk (Burghardt 2003).

The Federal Funds (FF) rate is the rate earned by U.S. Federal Reserve member banks who are required to hold a certain portion of their deposits at the U.S. Federal Reserve Bank.

These deposits are called demand deposits. The Federal Reserve does not set FF, rather the

FOMC will buy and sell assets in the marketplace to increase or decrease the money supply to influence rate changes. The interaction between the supply and demand for deposits sets the rate.

In 1988 the Chicago Board of Trade issued the first exchange-traded Federal Funds Futures contract, which at settlement is equal to 100 minus the simple weighted average of daily transactions of fed funds brokers (Robinson and Thornton). There is a clear distinction between 15 the purpose of LIBOR and FF: LIBOR reflects a bank's credit rating or borrowing costs, while FF represents the demand for and supply of deposits in the U.S. money market.

The rate on U.S. Treasuries is the yield on U.S. at different maturities.

Treasury bills have a maturity of 1 month, 3 months, 6 months or 1 year and pay no coupon.

Treasury notes have a maturity of 2 years, 5 years, 7 years, or 10 years, and Treasury bonds have a maturity of 20 years or 30 years (both pay coupons). Most market participants view the

Treasury security as the most risk-free investment available under the assumption that fiduciary government obligations will always be repaid. LIBOR is similarly risk-free, but there is an important difference between the credit quality of the U.S. government and the credit quality of international banks. LIBOR is also an offer rate, not an observed market rate. Treasury rates are observed in the market based on supply and demand (Fabozzi 2007).

Nonfinancial commercial paper (NCP) is short-term, uncollateralized corporate debt issued for periods of no longer than 270 days. The level of rates is directly correlated with the company's credit rating. Although no collateral underlies each promissory note issued, the market for commercial paper is liquid and in most cases opens access to cheaper financing for corporations, when compared with borrowing from a bank. Rates charged on nonfinancial commercial paper are subject to fluctuations in the business cycle, whereas changes in LIBOR result from a bank's continuing ability to meet its debt obligations (Bodie, Kane, and Marcus

2009).

The General Collateral Finance (GCF) repo is an index tracking interest charged on 1)

30-year U.S. Treasuries (TSY), 2) agency securities (ACY), and 3) mortgage-backed securities

(MBS). Each is calculated as the weighted average of daily market transactions for Treasuries, agencies, and MBSs. Repo rates, unlike LIBOR, are calculated using daily trading volume and borrowing costs. Between TSYs, ACYs, and MBSs, repo rates are affected by the quality and 16 availability of the underlying collateral. The Fed Funds rate is also one of the greatest forces influencing GCF rates.

One of the hallmarks of corporate finance and capital budgeting is the notion that an interest rate represents an opportunity cost, the value of an alternative forgone. By making one investment decision, the financial manager sacrifices the opportunity to invest the same capital in an alternative investment. The risk profile of an asset must be considered when choosing the rate to be used for discounting (Hull). Suppose $100 million was to be received by a bank from a customer. Discounting the cash flows using LIBOR may provide the bank the greatest net cash flows, but LIBOR might not truly represent the risk of the underlying cash flow. For instance, if the bank's customer were a corporation borrowing money in the short-term, discounting the cash flows using non-financial commercial paper rates would better reflect the company's ability to pay short-term (Kuo, Skeie, and Vickery 2012).

Data comparing historical levels of selected interest rates have been provided below.

AVERAGE STD DEV FF 1.1822 1.7850 LBR 1.5547 1.8335 TBL 0.9892 1.5743 NCP 1.2533 1.7560 TSY 1.1461 1.7256 ACY 1.2110 1.7847 MBS 1.2323 1.7906

* Table 3: Selected Rate Averages & Standard Deviations, 2005 - 2013

* Assumes historical levels of interest rates are normally distributed 17

FF LBR TBL NCP TSY ACY MBS FF 1. 0.9688 0.9854 0.9918 0.9917 0.9983 0.9978 LBR 0.9688 1. 0.951 0.9854 0.9552 0.9664 0.9673 TBL 0.9854 0.951 1. 0.9842 0.9903 0.9848 0.9833 NCP 0.9918 0.9854 0.9842 1. 0.9852 0.9904 0.9903 TSY 0.9917 0.9552 0.9903 0.9852 1. 0.9938 0.9925 ACY 0.9983 0.9664 0.9848 0.9904 0.9938 1. 0.9996 MBS 0.9978 0.9673 0.9833 0.9903 0.9925 0.9996 1.

Table 4: Correlation Between Levels of Selected Rates, 2005 - 2013

18

Table 5: Summary of Key Interest Rate Benchmarks

Based on Actual Provides Method of Used to Rate Definition Maturities Market Indication of Calculation Price Transactions Trimmed Daily Perceived arithmetic 1 Week borrowing cost average of Eurodollars 1 Month of international Bank credit LBR No bank Swaps 2 Month banks in the risk perceived Futures 3 Month interbank borrowing 6 Month market costs 12 Month Rate charged The Demand of and on deposits intersection supply for Futures FF Yes held with the of demand Daily deposits with Swaps Federal and supply the Fed Reserve curves 1 Month - Borrowing 1 Year, Bills cost of the Government 2 Years - TBL Yes - Notes Bonds U.S. credit risk 10 Years, Futures government 20 Years - 30 Years Short-term borrowing rate Corporate Commercial Less than NCP No - for credit quality Paper 270 days corporations Weighted Rate charged Collateralized average of on overnight overnight total volume Repos GCF Yes Daily repurchase borrowing and of Futures agreements lending transactions conducted

19

Chapter 5

Empirical Comparison of Interest Rates

To introduce our comparison of the effects of hedging using instruments pegged to various interest rates, we conduct an analysis of historical changes in rates over time.

First, we will examine the historical spread between changes in GCF rates with LIBOR.

A time series of changes in 3M LIBOR rates and overnight GCF TSY rates shows the daily change in basis points.

Figure 6: Daily Changes in Overnight GCF TSY Rates and 3M LIBOR Rates (in bps), 2005 - 2013

Between 2005 and 2013, daily 3M LIBOR changes are much steadier; the average change in the daily 3M LIBOR rate was approximately -0.1 bps while the GCF TSY change was about -0.12 bps. Surprisingly, when regressing the changes in rates, an R2 of daily changes for GCF TSY and

LIBOR rates is equal to 0.00015. This low R2 infers that we can reject any explanation of variance in LIBOR with changes in TSY rates. 20

Figure 7: Daily Changes in Overnight GCF ACY rates and 3M LIBOR Rates (in bps), 2005 - 2013

GCF Agency rates averaged a daily change of about -0.177 basis points. However, the standard deviation of changes was 5.93%, compared with the GCF TSY standard deviation of 9.11%.

Volatility of changes in LIBOR between 2005 and 2013 was approximately 2.83%.

Figure 8: Daily Changes in Overnight GCF MBS rates and 3M LIBOR Rates (in bps), 2005 - 2013

21

Finally, Mortgage-Backed Security GCF rates changed on average by about -0.095 each day. The standard deviation of daily changes was the highest of all GCF rates, 14.3%. Between 2007 and

2009, there were six occurrences when daily MBS GCF rates changed by over 100 basis points.

Analyzing Actual FRA Cash Flows Between Selected Rates

Financial institutions primarily use LIBOR-based derivatives to hedge changes in net interest income. But, many quoted rates exhibit high correlation with each other. Comparing

LIBOR (LBR), Fed Funds (FF), T-bills (TBL), non-financial commercial paper (NCP), GCF

Treasuries (TSY), GCF Agencies (ACY), and GCF mortgage-backed securities (MBS) rates in pairs, we see that each pair has correlation of at least .95, implying that rate changes occur similarly between each pair. For example, from January 2005 through September 2013, spot

LIBOR rates were most highly correlated with non-financial commercial paper rates. The historical correlation between these rates is included in Chapter 4.

Viewed in isolation, these interest rates appear interchangeable. Historically, when rates are highly correlated, pricing a using any floating interest rate appears appropriate over a two- or three-year time horizon. However, the asset allocation decision, market risk, the passage of time, and institutional structures all limit the choice of interest rate. Let's make some simplifying assumptions to analyze rates in simple investment scenarios.

Assume the financial manager may invest $100 million at time t in 3M FRAs starting

March 16, 2005, and he will receive fixed and pay floating. For purposes of comparability between each interest rate type, let's assume the manager has a two-year time horizon, but rather than keep his rate fixed for two-years, he will purchase a new 3M FRA instead on the date of the current FRA's settlement.

At settlement of the first FRA, floating rates have fallen below the fixed payments, resulting in net cash flows to the manager. Rolling the FRA agreement forward over a two-year period, the counterparty earns the greatest net cash flows on LBR ($655,777). GCF TSY 22

generates the smallest net cash flows (to the counterparty). Over this two-year horizon, the GCF

TSY manages changes in risk the best. For the complete quarterly net cash flows disbursed in this

simple investment scenario, see Appendix A.

Net Cash Flow for 3M FRA Over 2 Years FF $(119,972) TBL $519,944 TSY $(14,603) MBS $(185,889) LBR $(655,777) NCP $(299,639) ACY $(167,203)

Analyzing Actual Swap Cash Flows Between Selected Rates

Assume the financial manager may only invest $100 million at time t, pay fixed and

receive floating interest quarterly on an interest rate swap. Assume it is possible that he may

receive interest using any of the considered rates (LBR, FF, TBL, NCP, TSY, ACY or MBS). For

this comparison, let's assume today is March 16, 2005, and the manager has a two-year time

horizon.

The rate providing the smallest net cash flow in this example is the TBL. TSY, ACY, and

MBS GCF rates provide the second, fourth, and fifth smallest payments, and FF provides the

third smallest. LBR provides the largest cash flow to the manager - over $1 million greater net

cash flow. Detailed cash flows are provided in Appendix B.

Net Cash Flow for 2-Year Swap FF $(1,312,500) TBL $(957,500) TSY $(1,287,750) MBS $(1,398,500) LBR $(2,001,253) NCP $(1,615,000) ACY $(1,372,750)

23

Chapter 6

Practical Application of Empirical Results: Hedging a GCF-based Asset

Managers at multinational banks like J.P. Morgan, Barclays, and Citi, will hedge interest rate risk in fixed income portfolios by creating complex investment strategies and building models to predict future risk. For example, in 2012, the notional principal of Bank of America

Corporation’s swaps was $112 billion with the net fair value of swaps at $5.59 billion (Securities and Exchange Commission). Compared with the notional amount of interest rate futures and forward hedges, the notional principal of interest rate swap hedges makes up the largest percent of IRR hedges on the balance sheets of the largest U.S. banks.

In the previous chapter, we examined the effect on net cash flows of pricing two financial instruments using various interest rates. In this chapter, we illustrate the effects of hedging a

GCF-based asset using an interest rate swap tied to LIBOR and T-bill rates. We will assume that the manager is only concerned with hedging interest rate risk.

Duration Targeting

A simple way for a bank to hedge the IRR of its fixed income portfolio is through duration targeting. In other words, to assure that loans and receivables are hedged, managers buy and sell contracts to affect total portfolio duration. In a hedged portfolio, the duration of outstanding assets and liabilities will be equal to the duration of hedging instruments (Fabozzi

2001). Formulaically,

if target duration - current duration > 0, adjust duration upward

if target duration - current duration < 0, adjust duration downward

24

Real-World Hedging of an Asset

Because large U.S. banks invest in many different types of assets, banks are exposed to changes in different interest rates. They primarily use interest rate swap transactions. However, not all swaps are pegged to LIBOR, or stated differently, not all assets should be hedged with

LIBOR-based swaps. Consider a bank that deals in short-term collateralized borrowing. LIBOR is a non-collateralized borrowing benchmark; collateral repo rates capture the risk and the maturity of this type of short-term borrowing.

In this hedging example, we assume a bank has an investment in a five-year GCF rate asset, where it will receive floating payments quarterly:

Principal Settlement Maturity

GCF TSY Bond 10,000,000 3/16/05 9/15/10

Principal Settlement Maturity

Swap 9,000,000 3/16/05 9/15/10

The bank wants to convert the floating payments it receives to fixed payments using an interest rate swap. To examine the differences in hedging, we assume the bank has the choice of hedging with a LIBOR-based swap or a Treasury bill-based swap.

First, we calculate the duration of the asset and the duration of the hedging instrument.

Using a simple duration targeting strategy, the net duration of the portfolio will equal zero. If both durations are approximately equal, the bank can calculate its profit and loss on changes in interest rates.

The modified duration of the GCF Treasury asset is equal to the sum of the time- weighted present value of all payments divided by 4 (in this case, for quarterly payments).

Between 2005 and 2010, GCF TSY rates decreased, and thus the present value of payments decreased as well. The modified duration of the asset is equal to 4.165 years. 25

We compute duration of the swap by calculating the duration of both the fixed and floating legs. The fixed component is calculated using the 5-year swap rates published by the St.

Louis Federal Reserve. The floating component's duration is simple to calculate; because the floating component is settled on each payment day, the duration is equal to the time to maturity of the first payment. In essence, the duration of the floating leg is equivalent to the duration of a zero-coupon bond. See the appendix for the detailed calculation of the fixed and floating legs of the swap.

Duration Duration GCF TSY Bond 4.165 Swap Fixed 4.93953 Swap Floating (0.2500) Swap, Net 4.68953 To calculate the total duration of the portfolio, we multiply the notional principal by the duration of each instrument.

Duration Principal D x P GCF TSY 4.16 10,000,000 41,647,091 Swap 4.70 9,000,000 42,324,944

Number of Swaps Required 0.98

The number of swaps required to create a hedge that converts floating to fixed payments is approximately 1.

Therefore, using the value of a swap formula, we compute the profit and loss on the swap position and add the profit from receiving floating interest on the asset.

Swap Bond Total

PV NCFs 760,821 13,844,446 14,605,267

The manager was interested in hedging against decreases in rates. To see the effect of this hedge, we examine the following chart tracking the quarterly net cash flows to the bank. 26

Realized benefit of swap hedge

Figure 9: Net Cash Flows for a GCF Asset Hedged with a LIBOR-Based Swap, 2005 - 2013

The bank manager entered the contract to hedge against a decrease in rates. The more

GCF TSY rates fell, the smaller the floating payments became. When GCF TSY rates fell in

2007, the net cash flows realized on the bond decreased to approximately $20,000/quarter for six quarters. However, because the manager locked into the fixed for floating swap, he made smaller floating payments and, starting in 2007, realized greater cash flows of approximately

$100,000/quarter on the swap.

The standard deviation of the swap NCFs was $46,250. Assuming changes in cash flows fit a normal distribution, 65% of the NCFs fall either $46,250 (i.e. - 1 standard deviation) above or below the arithmetic mean. The standard deviation of bond cash flows was $205,276.

What are the consequences of hedging this portfolio using a swap tied to Treasury bill rates? With a T-bill swap, the standard deviation of the swap NCFs was $46,616, slightly higher than the LIBOR swap. Using a T-bill swap, the total present value of NCFs is greater than the total present value of NCFs of the LIBOR-based swap by $456,305. 27

Figure 10: Net Cash Flows for a GCF Asset Hedged with a TBL-Based Swap, 2005 - 2013

Swap Bond Total PVCFs 1,217,126 13,844,446 15,061,572

As discussed in Chapter 4, the profit and loss consequences to the bank will vary with the type of floating rate chosen to value the transaction.

Conclusions

A GCF-based investment can be hedged effectively with different types of swaps.

However, these results don't exist in isolation. For a hedge to be effective, a financial manager must consider basis risk and liquidity risk. Basis risk in the hedging example above is represented by the difference between changes in GCF rates with LIBOR or GCF rates with T-bill rates. The difference between changes in rates is not always equal, and a manager would need to assess carefully each risk profile to hedge the portfolio properly. The choice of hedge depends on the underlying risk of the investment and the time to maturity. 28

Liquidity risk presents a significant issue for bank managers. As mentioned at the beginning of this paper, the GCF Repo Index is a relatively new benchmark; GCF futures contracts were published on the NYSE Liffe in June 2012. The number of market participants in

OTC and exchange-traded GCF products is much smaller than those in the market for LIBOR, T- bill, or Fed Funds products. A bank hedging IRR must have buying and selling flexibility, which is available only to markets with high (Fabozzi 2007).

29 Chapter 7

Conclusions and Further Research

This empirical study has attempted to show the implications of hedging strategies that incorporate a relatively new interest rate benchmark: the GCF Repo Index.

Since 2005, the daily levels of GCF rates have exhibited the highest degree of correlation with the Federal Funds rate; levels of GCF rates are least correlated with LIBOR. Examining a time series of these interest rates shows us that daily changes in LIBOR are much smaller than daily changes in GCF rates; the historical standard deviation of LIBOR changes (2.93%) was well below the standard deviation of GCF Agencies (5.83%). However, it appears there is a benefit to using these historically more volatile rates. From 2005 - 2007, net cash flows provided by

LIBOR-based FRAs and swaps were greater than each of the cash flows provided by swaps using the GCF rates. If a manager is seeking to minimize cash flow fluctuations, using securities tied to

GCF rates might be optimal.

However, the use of different rates provides incremental benefits in different situations.

Greater net cash flows and greater could be benefit managers engaged in business activities that earn volatile cash flows. Depending on the hedging strategy, there exist advantages to using each rate.

This empirical study can be taken a step further. Although only an active contract for over one year, the DTCC GCF Repo Futures contract could gain acceptability as a liquid hedging instrument. An empirical comparison between Eurodollar futures, Treasury bill futures, Federal

Funds futures, and GCF Repo futures might illustrate potential benefits of hedging using this new exchange-traded contract. Applying the minimum variance hedge ratio criteria of Ederington

(1979), we can estimate the hedge effectiveness of GCF-based forwards, futures, FRAs, and swap contracts and compare these results with the hedge effectiveness of other instruments. 30

Appendix A

Simple Investment Decision: 3M FRAs Net Cash Flows, 2005 - 2007

9/21/05 12/21/05 3/16/05 X1 F1 (3x6) S2 CF2 6/15/05 X1 F1 (3x6) S2 CF2 FF 0.03505 4.3254% 0.037 -58,528 FF 0.03815 4.1195% 0.041 -66,986 LBR 0.03505 4.3244% 0.040 -123,861 LBR 0.03815 4.4357% 0.045 -174,101 TBL 0.03505 4.3250% 0.033 44,917 TBL 0.03815 4.4364% 0.039 -21,486 NCP 0.03505 4.3249% 0.038 -69,417 NCP 0.03815 4.4363% 0.042 -104,903 TSY 0.03505 4.3255% 0.036 -35,389 TSY 0.03815 4.4369% 0.042 -103,639 ACY 0.03505 4.3255% 0.037 -46,006 ACY 0.03815 4.4369% 0.043 -117,542 MBS 0.03505 4.3254% 0.037 -52,267 MBS 0.03815 4.4368% 0.043 -120,069

3/15/06 6/21/06 9/21/05 X1 F1 (3x6) S2 CF2 12/21/05 X1 F1 (3x6) S2 CF2 FF 0.04205 4.3677% 0.0447 -61,833 FF 0.048 4.9838% 0.0491 -29,944 LBR 0.04205 4.3672% 0.0492 -166,833 LBR 0.048 4.9829% 0.0545 -176,604 TBL 0.04205 4.3684% 0.0451 -71,167 TBL 0.048 4.9842% 0.0479 2,722 NCP 0.04205 4.3676% 0.0475 -127,167 NCP 0.048 4.9835% 0.0529 -133,389 TSY 0.04205 4.3678% 0.0450 -69,533 TSY 0.048 4.9835% 0.0484 -9,528 ACY 0.04205 4.3677% 0.0456 -82,600 ACY 0.048 4.9834% 0.0493 -34,300 MBS 0.04205 4.3677% 0.0456 -83,533 MBS 0.048 4.9833% 0.0493 -35,933

9/20/06 12/20/06 3/15/06 X1 F1 (3x6) S2 CF2 6/21/06 X1 F1 (3x6) S2 CF2 FF 0.05115 5.1873% 0.0523 -29,069 FF 0.05605 5.6371% 0.0526 87,208 LBR 0.05115 5.1863% 0.0539 -68,725 LBR 0.05605 5.6358% 0.0537 60,667 TBL 0.05115 5.1872% 0.0481 77,097 TBL 0.05605 5.6374% 0.0484 193,375 NCP 0.05115 5.1867% 0.0521 -24,014 NCP 0.05605 5.6362% 0.0517 109,958 TSY 0.05115 5.1873% 0.0522 -25,783 TSY 0.05605 5.6372% 0.0522 97,067 ACY 0.05115 5.1871% 0.0523 -29,828 ACY 0.05605 5.6370% 0.0525 88,725 MBS 0.05115 5.1871% 0.0525 -34,631 MBS 0.05605 5.6370% 0.0526 88,219

3/21/07 6/20/07 9/20/06 X1 F1 (3x6) S2 CF2 12/20/06 X1 F1 (3x6) S2 CF2 FF 0.0538 5.1979% 0.0526 30,333 FF 0.05305 4.9911% 0.0527 8,847 LBR 0.0538 5.1976% 0.0535 7,583 LBR 0.05305 4.9909% 0.0536 -13,903 TBL 0.0538 5.1988% 0.0491 118,806 TBL 0.05305 4.9920% 0.0461 175,681 NCP 0.0538 5.1980% 0.0522 40,444 NCP 0.05305 4.9913% 0.0527 8,847 TSY 0.0538 5.1980% 0.0522 40,697 TSY 0.05305 4.9912% 0.0494 91,506 ACY 0.0538 5.1979% 0.0524 34,631 ACY 0.05305 4.9912% 0.0523 19,717 MBS 0.0538 5.1979% 0.0525 33,367 MBS 0.05305 4.9911% 0.0523 18,958

31

Net Cash Flow for 3M FRA Over 2 Years FF $(119,972) TBL $519,944 TSY $(14,603) MBS $(185,889) LBR $(655,777) NCP $(299,639) ACY $(167,203)

32

Appendix B

Simple Investment Decision: 2-Year Swap Net Cash Flows, 2005 - 2007

6/15/05 X1 S1 CF1 9/21/05 X2 S2 CF2 FF 0.03505 0.0257 $233,750 FF 0.03505 0.03050 $113,750 LBR 0.03505 0.0304 $116,250 LBR 0.03505 0.03421 $21,092 TBL 0.03505 0.0274 $191,250 TBL 0.03505 0.02940 $141,250 NCP 0.03505 0.0281 $173,750 NCP 0.03505 0.03280 $56,250 TSY 0.03505 0.02515 $247,500 TSY 0.03505 0.03040 $116,250 ACY 0.03505 0.02532 $243,250 ACY 0.03505 0.03073 $108,000 MBS 0.03505 0.02554 $237,750 MBS 0.03505 0.03090 $103,750

12/21/05 X3 S3 CF3 3/15/06 X4 S4 CF4 FF 0.03505 0.03720 $(53,750) FF 0.03505 0.04080 $(143,750) LBR 0.03505 0.03960 $(113,750) LBR 0.03505 0.04504 $(249,688) TBL 0.03505 0.03340 $41,250 TBL 0.03505 0.03900 $(98,750) NCP 0.03505 0.03760 $(63,750) NCP 0.03505 0.04230 $(181,250) TSY 0.03505 0.03635 $(32,500) TSY 0.03505 0.04225 $(180,000) ACY 0.03505 0.03674 $(42,250) ACY 0.03505 0.04280 $(193,750) MBS 0.03505 0.03697 $(48,000) MBS 0.03505 0.04290 $(196,250)

6/21/06 X5 S5 CF5 9/20/06 X6 S6 CF6 FF 0.03505 0.04470 $(241,250) FF 0.03505 0.04910 $(351,250) LBR 0.03505 0.04920 $(353,750) LBR 0.03505 0.05449 $(485,938) TBL 0.03505 0.04510 $(251,250) TBL 0.03505 0.04790 $(321,250) NCP 0.03505 0.04750 $(311,250) NCP 0.03505 0.05290 $(446,250) TSY 0.03505 0.04503 $(249,500) TSY 0.03505 0.04835 $(332,500) ACY 0.03505 0.04559 $(263,500) ACY 0.03505 0.04926 $(355,250) MBS 0.03505 0.04563 $(264,500) MBS 0.03505 0.04932 $(356,750)

12/20/06 X7 S7 CF7 3/21/07 X8 S8 CF8 FF 0.03505 0.05230 $(431,250) FF 0.03505 0.05260 $(438,750) LBR 0.03505 0.05387 $(470,470) LBR 0.03505 0.05365 $(465,000) TBL 0.03505 0.04810 $(326,250) TBL 0.03505 0.04840 $(333,750) NCP 0.03505 0.05210 $(426,250) NCP 0.03505 0.05170 $(416,250) TSY 0.03505 0.05217 $(428,000) TSY 0.03505 0.05221 $(429,000) ACY 0.03505 0.05233 $(432,000) ACY 0.03505 0.05254 $(437,250) MBS 0.03505 0.05252 $(436,750) MBS 0.03505 0.05256 $(437,750)

33

Net Cash Flow for 2-Year Swap FF $(1,312,500) TBL $(957,500) TSY $(1,287,750) MBS $(1,398,500) LBR $(2,001,253) NCP $(1,615,000) ACY $(1,372,750)

34

Appendix C

Modified Duration Calculation: Asset Hedging Scenario

Swap, Receive Fixed Dates Period Principal Receive YTM PV Receive % of PV Total Weighted Maturity 3/16/05 9,000,000 4.54% 6/15/05 1 9,000,000 102,150 4.30% 100,991 0.01016 0.010 9/21/05 2 9,000,000 102,150 4.44% 99,882 0.01005 0.020 12/21/05 3 9,000,000 102,150 4.95% 98,701 0.00993 0.030 3/15/06 4 9,000,000 102,150 5.18% 97,193 0.00978 0.039 6/21/06 5 9,000,000 102,150 5.66% 95,621 0.00962 0.048 9/20/06 6 9,000,000 102,150 5.17% 93,701 0.00943 0.057 12/20/06 7 9,000,000 102,150 5.00% 93,182 0.00938 0.066 3/21/07 8 9,000,000 102,150 4.97% 92,295 0.00929 0.074 6/20/07 9 9,000,000 102,150 5.55% 91,205 0.00918 0.083 9/19/07 10 9,000,000 102,150 4.82% 88,770 0.00893 0.089 12/19/07 11 9,000,000 102,150 4.35% 89,326 0.00899 0.099 3/19/08 12 9,000,000 102,150 3.22% 89,511 0.00901 0.108 6/18/08 13 9,000,000 102,150 4.47% 91,875 0.00925 0.120 9/17/08 14 9,000,000 102,150 3.63% 87,205 0.00878 0.123 12/17/08 15 9,000,000 102,150 1.92% 89,008 0.00896 0.134 3/18/09 16 9,000,000 102,150 2.57% 94,500 0.00951 0.152 6/17/09 17 9,000,000 102,150 3.02% 91,456 0.00920 0.156 9/16/09 18 9,000,000 102,150 2.83% 89,029 0.00896 0.161 12/16/09 19 9,000,000 102,150 2.69% 89,162 0.00897 0.170 3/17/10 20 9,000,000 102,150 2.61% 89,155 0.00897 0.179 6/16/10 21 9,000,000 102,150 2.33% 88,929 0.00895 0.188 9/15/10 22 9,000,000 102,150 1.61% 7,995,357 0.80468 17.703 PV Total 9,936,054 1.00000 4.953 Swap, Pay Floating

Dates Period Principal LBR Payment PV Payment % of PV Total Weighted Maturity 3/16/05 9,000,000 0.0304 6/15/05 1 9,000,000 0.0342 76,964 75,736 0.00848 0.008 6/15/05 1 9,000,000 0.0342 9,000,000 8,856,652 0.99152 0.992 PV Total 8,932,388 1.00000 0.25

Fixed Leg Floating Leg Notional Start End Duration Duration Duration of Swap Swap 9,000,000 3/16/05 9/15/10 4.953 0.25 4.70277 35

Receive Floating

Dates Period Principal GCF TSY Receive YTM PV Receive % of PV Total Weighted Maturity 3/16/05 10,000,000 4.54% 6/15/05 1 10,000,000 2.52% 251,500 4.30% 248,646 0.01798 0.01798 9/21/05 2 10,000,000 3.04% 304,000 4.44% 297,250 0.02150 0.04300 12/21/05 3 10,000,000 3.64% 363,500 4.95% 351,228 0.02540 0.07620 3/15/06 4 10,000,000 4.23% 422,500 5.18% 401,998 0.02907 0.11629 6/21/06 5 10,000,000 4.50% 450,300 5.66% 421,519 0.03048 0.15242 9/20/06 6 10,000,000 4.84% 483,500 5.17% 443,508 0.03208 0.19245 12/20/06 7 10,000,000 5.22% 521,700 5.00% 475,896 0.03442 0.24092 3/21/07 8 10,000,000 5.22% 522,100 4.97% 471,731 0.03412 0.27293 6/20/07 9 10,000,000 5.22% 521,900 5.55% 465,981 0.03370 0.30330 9/19/07 10 10,000,000 4.94% 494,300 4.82% 429,552 0.03107 0.31066 12/19/07 11 10,000,000 4.66% 465,700 4.35% 407,234 0.02945 0.32397 3/19/08 12 10,000,000 3.35% 335,200 3.22% 293,726 0.02124 0.25491 6/18/08 13 10,000,000 0.38% 38,200 4.47% 34,358 0.00248 0.03230 9/17/08 14 10,000,000 1.94% 194,200 3.63% 165,789 0.01199 0.16786 12/17/08 15 10,000,000 0.45% 45,100 1.92% 39,298 0.00284 0.04263 3/18/09 16 10,000,000 0.07% 6,600 2.57% 6,106 0.00044 0.00707 6/17/09 17 10,000,000 0.23% 22,800 3.02% 20,413 0.00148 0.02510 9/16/09 18 10,000,000 0.28% 28,000 2.83% 24,403 0.00176 0.03177 12/16/09 19 10,000,000 0.17% 17,200 2.69% 15,013 0.00109 0.02063 3/17/10 20 10,000,000 0.16% 16,400 2.61% 14,314 0.00104 0.02070 6/16/10 21 10,000,000 0.17% 17,400 2.33% 15,148 0.00110 0.02301 9/15/10 22 10,000,000 0.20% 19,700 1.61% 8,784,031 0.63527 13.97604 13,827,142 1.00000 4.16304

DURATION PRINCIPAL D x P GCF TSY ASSET 4.1630 10,000,000 41630380 LBR SWAP 4.7028 9,000,000 42324943.66

Number of Swaps Required 0.98

36

Appendix D

Basic Concepts & Definitions

Time value of money - The theory of finance which states that a dollar earned today is worth more

than a dollar earned tomorrow. This theory leads to the rationale of discounting future

cash flows to their present values.

Present value - The value of an asset today, or the future value of an asset discounted to today's

dollar amount.

Future value - The value of expected cash flows to be earned in the future.

Discounting - Because a future value amount cannot be compared with a present value amount,

we divide the future value by an annuity factor, which represents all interest that could be

earned over the investment period. Once all amounts are in present value terms, we can

compare differences in the present value of cash flows.

Liquidity - The characteristic of an investment that can be readily bought or sold in the market

without losing substantial value.

Opportunity Cost - The value of an alternative forgone. In investing, if we choose one investment

over another of similar risk, this alternative not chosen must be considered as a cost to the

value of the investment.

37

Appendix E

Formulas

Number of Contracts Required to Hedge

σ y Hedge = ρx,y σ x

ρx,y = correlation between variables x and y

σ y = standard deviation of asset y

σ x = standard deviation of asset x

Discount Factor for a Zero Coupon Bond

'! d $ ! d $* 1 n DFn = (#(1+ r1)* &*…#(1+ rn )* &+ )" 360% " 360%,

r1 = spot rate for period 1

d1 = number of days in forward period

rn = spot rate for period n

dn = number of days in period n 38

Terminal Wealth of a Zero

TWn =1/ DFn

Z = TWn *Cn

Z = Value of zero

Cn = Coupon Payment

TWn = Terminal wealth of a $1 investment today

Coupon Bond Price

N B TW *C = ∑[ i i ] + t i=1 (1+ rt )

th TWi *Ci = Present value of the i coupon payment N = notional principal amount of bond

rt = discount rate covering t periods t = number of periods

Duration

'! $* Ci )# t &, "(1+ ri ) % D = t *) , ∑ i ) B , i=1 ) , ( +

where,

ti = time in years

Ci = coupon at time t B = present value of bond price

39

Duration Relationship

ΔB = −BD*Δy

B = PV of bond price D = Duration of bond y = Annual percentage yield of bond

Portfolio Duration

n

Dp = ∑wiDi i=1

wi = ith investment's % value of total portfolio value

Di = duration of the ith investment

Fixed Component of a Swap

# ' % % %[1−TWn ]% C =100n$ n ( % TW % % ∑ i % & i=1 )

C = fixed coupon of swap n = number of periods

TWn = terminal wealth of final floating payment

TWi = terminal wealth of each payment

40

Value of Swap Payments

# dn & Π = NPA*(X − Fn )*% ( $360 '

Π = Net payment on swap NPA = Notional principal amount X = Fixed rate on swap th Fn = Floating rate on swap at payment date after n period

th dn = days in the n period

41

BIBLIOGRAPHY

Bodie, Zvi, Alex Kane, and Alan Marcus. "Essentials of Investments." McGraw-Hill Companies. New

York, 2009. Print.

Burghardt, Galen. "The Eurodollar Futures and Options Handbook." McGraw-Hill Companies. New York,

2003. Print.

Ederington, Louis H. "The Hedging Performance of the New Futures Markets." The Journal of Finance.

March 1979. .

Fabozzi, Frank J. "Bond Markets, Analysis, and Strategies." Pearson Prentice Hall. Pearson Education,

Inc. Upper Saddle River, NJ. 2007. Print.

Fabozzi, Frank J. "Bond Portfolio Management." Frank J. Fabozzi Associates. New Hope, PA, 2001. Print.

Hannon, Paul and Jon Hilsenrath. "Fixes Are Sought in Rate Scandal." The Wall Street Journal. Dow Jones

& Company. 19 July 2012. Web. 20 Aug 2012.

.

Hull, John. "Risk Management and Financial Institutions." Pearson Prentice Hall. New Jersey, 2007. Print.

Kuo, Dennis, David Skeie, and James Vickery. "A comparison of Libor to other measures of bank

borrowing costs." Federal Reserve Bank of New York. June 2012.

.

London, Justin. "Modeling Derivatives Applications in Matlab, C++, and Excel." Pearson Education, Inc.

Upper Saddle River, NJ, 2007.

.

Nawalkha, Sanjay K., Gloria M. Soto, and Natalia A. Beliaeva. "Interest Rate Risk Modeling: The Fixed

Income Valuation Course." John Wiley & Sons, Inc. Hoboken, NJ, 2005. Print.

Robertson, John and Daniel Thornton. "Using Federal Funds Futures Rates to Predict Federal Reserve

Actions." St. Louis Fed. .

42

Smith, Donald. "A Teaching Note on Pricing and Valuing Interest Rate Swaps with LIBOR and OIS

Discounting." Boston University.

Pricing-and-Valuing-Interest-Rate-Swaps-with-LIBOR-and-OIS-Discounting.pdf>.

Trontz, Bari. "NYSE Liffe's Futures Based On the DTCC GCF Repo Index." The Depository Trust and

Clearing Corporation. 2012.

.

"Interest Rate Products." CME Group, Inc. Contract Specifications.

.

Bloomberg Terminal. Historical Futures Data.

Federal Reserve Bank of St. Louis. . Selected Interest

Rates for Swaps, LIBOR, Fed Funds, T-bills, and Commercial Paper Rates.

Securities and Exchange Commission. Annual 10-K. Regulatory Filings.

ACADEMIC VITA

Nicholas Robert Fakelmann 513 Horizon Way, Neshanic Station, NJ 08853 ______

Education

The Pennsylvania State University University Park, PA Schreyer Honors College, Smeal College of Business, Class of 2013 Master of Accounting, Bachelor of Science in Accounting Bachelor of Science in Finance

Honors and Awards

Robert W. “Bear” Koehler Award for Distinguished Service Robert W. Koehler Academic Excellence in Accounting Scholarship

Association Memberships/Activities

Presidential Leadership Academy University Park, PA Class of 2013, Member April ’10 - April ’13 Addressed global and local issues through honors classes, special projects, and field trips Published blog articles analyzing global issues in critical thinking ePortfolio

Schreyer Honors College University Park, PA Career Development Program, Lead Mentor Oct. ’11 - Dec. '13 Provide career resources for honor students to help guide their professional development Build a network of faculty, advisors, and alumni to assist students with their career goals

SHO Time Mentoring Program, Mentor Jan. ’10 - Sept. ’12 Introduced freshmen students to academic programs, residence life, and co-curricular opportunities

Professional Experience

Deloitte & Touche LLP, Life Sciences & Health Care Philadelphia, PA ERS Intern June ’13 - Aug. '13 Established rationale for estimating bad debt and contractual allowance amounts on client P&L Assisted engagement team with implementation of cash, bad debt, and revenue recognition controls

Johnson & Johnson, Global Finance Services Skillman, NJ Finance Co-Op Dec. ’10 - July ’11 Entered forward foreign currency contracts to mitigate transactional and balance sheet exposure Reconciled a multibillion dollar ledger discrepancy before quarter close Designed transition guide for new employees, standardizing on-boarding across all departments

Bank of New York Mellon, Corporate Trust New York, NY Sales Intern June ’12 - Aug. ’12 Identified most profitable trust clients to help forecast revenue for management Developed a client information database to assist sales team manage relationships with clients

Khayat and Son Distribution, Business Plan Development Team University Park, PA Project Leader Aug. ’10 - Dec. ’10 Created a five-year, strategic business plan for a local proprietorship Forecasted financial statements and developed a market strategy to guide future growth

Professional Presentations

"Streamlining The Owens & Minor European Supply Chain System Using the Movianto Entity" USC Marshall International Case Competition