Central Bank of Egypt Derivatives Prepared Presented By

Central Bank of Egypt Derivatives Prepared & Presented By: Rania Elsawy 1

Central Bank of Egypt Index I. Introduction to Derivatives II. Forward Rate Agreements III. SWAPS IV. Credit Derivatives Rania Elsawy 2

Central Bank of Egypt I-Derivatives • A derivative instrument is a contract between two parties that specifies conditions (especially the dates, resulting values of the underlying variables, and notional amounts) under which payments are to be made between the parties • Derivatives can be used for speculation ("bets") or to hedge ("insurance"). Rania Elsawy 3

Central Bank of Egypt I-Derivatives • Futures contracts, forward contracts, options and swaps are the most common types of derivatives. Derivatives are contracts and can be used as an underlying asset. • There are even derivatives based on weather data, such as the amount of rain or the number of sunny days in a particular region. • One of the oldest derivatives is rice futures, which have been traded on the Dojima Rice Exchangesince the eighteenth century Rania Elsawy 4

Central Bank of Egypt I-Derivatives • Under US law and the laws of most other developed countries, derivatives have special legal exemptions that make them a particularly attractive legal form to extend credit • However, the strong creditor protections afforded to derivatives counterparties, in combination with their complexity and lack of transparency, can cause capital markets to underprice credit risk Rania Elsawy 5

Central Bank of Egypt I-Derivatives • This can contribute to credit booms, and increase systemic risks • Indeed, the use of derivatives to mask credit risk from third parties while protecting derivative counterparties contributed to the financial crisis of 2008 in the United States Rania Elsawy 6

Central Bank of Egypt FRAs Rania Elsawy 7

Central Bank of Egypt II-Forward Rate Agreements Definition: • A common type of forward contract, which is a Interest rate …………forward contract. • What type of risk(s) are FRAs used to manage? Hedge Interest Rate Risks Speculate on future directions of interest rates Rania Elsawy 8

Central Bank of Egypt II-Forward Rate Agreements Main Characteristics: • Underlying Rate: ? – Bonds – Eurodollar Deposits – FX Rates • Underlying Notion: – Fixing the interest rate for a predetermined period (tenor) at a future non-spot date Rania Elsawy 9

Central Bank of Egypt II-Forward Rate Agreements Main Characteristics continued: • Available in Major Currencies • Large OTC market but smaller than SWAP • 2 Parties involved- Long(BUY)/Short(SELL) Market Maker’s Grid* 6. 3% 6. 25% Sell the FRA Buy the FRA Like “Lending” Like “Borrowing” *Source: Resource City TM 1999 -2001 Rania Elsawy 10

II-Forward Rate Agreements Central Bank of Egypt • Formula: Notional principal (LIBOR at expiration - FRA rate) x x Days in FRA period (360) 1 + LIBOR at expiration x Days in FRA period (360) Example: The treasurer of Company A expects to receive a cash inflow of $15 mio in 90 days. The treasurer expects short term rates to fall during the next 90 days. In order to hedge against this risk, the treasurer decides to use an FRA that expires in 90 days and is based on 90 -day LIBOR. The FRA is quoted at 5 percent. At expiration, LIBOR is 4. 5%. Assume that the notional principal on the contract is $15 mio. Short 3 x 6 A) Indicate whether the treasurer should take a long or short position to hedge interest rate risk. $18, 541. 41 B) Using the appropriate terminology, identify the type of FRA used here. C) Calculate the gain or loss to Company A as a consequence of entering the FRA. Rania Elsawy 11

Central Bank of Egypt II-Forward Rate Agreements • • 1 x 3 1 x 4 1 x 7 3 x 6 3 x 9 6 x 12 12 x 18 1 month 3 months ………… 60 day LIBOR 90 day LIBOR 180 day LIBOR ………………. . The Forward/Forward Formula to Derive the Implied FRA rate 1 + C = 1 + (360) b% x b days (c? ) (b) a% x a days - 1 x (360) c days (360) Rania Elsawy b days c days a days (a) 12

II-Forward Rate Agreements Central Bank of Egypt • Example: A dealer borrowed cash for 6 months and only lent cash for 3 months. Calculate the implied c period FRA rate from the cash forward/forward price equivalent, given: (c) (b) – 6 month (181 days): 3 5/8 -1/2 – 3 month (91 days): 3 5/8 -1/2 1 + C = 1 + • 3. 5% b days 91 0. 03625 181 days x (360) 0. 035 91 days x (360) - 1 x days 90 (c? ) 90 c days 181 a days 3. 625% C=3. 72% (360) A party wants to engage in a contract expiring in 44 days on 119 -day Libor. – Is the above a standard FRA, under what arrangement can this FRA be conducted? – No, off the run FRA • Risks associated with FRAs – Market Risk – Credit Risk Rania Elsawy 13

Central Bank of Egypt SWAPS Rania Elsawy 14

Central Bank of Egypt III-SWAPS Definition: • A common type of derivative agreement between two parties to exchange a series of future cash flows • Judging by size of market, they are probably most important Rania Elsawy 15

Central Bank of Egypt III-SWAPS Main Characteristics: • Types of SWAPS: – Interest rate – Currency – Equity return – Commodity – Credit • 2 Parties involved • OTC Rania Elsawy 16

Central Bank of Egypt III-SWAPS Main Characteristics cont’d • In some swaps, both sides are floating. • Technically SWAPS may have a single payment, but most involve multiple legs • A SWAP with one payment only is a forward • Hence, a swap is a series of forward contracts • No Payment at initiation except currency swaps Rania Elsawy 17

III-SWAPS Central Bank of Egypt Interest Rate Swaps Definition: • An OTC (private agreement) between two counterparties to exchange series of future cash flows (most commonly fixed for floating) based on a notional amount without exchange of principal IRSs are used for: • Asset/Liability management • Currency risk management x • Speculate on changes in short-term interest rates • Manage Interest Rate risk Rania Elsawy 18

Central Bank of Egypt III-SWAPS Main Characteristics Buyer Pays Fixed (SWAP rate) Receives Floating Short the Bond market Seller Pays Floating *(Libor) Receive Fixed Long the Bond market Long SWAP Shortens Duration Short SWAP Adds Duration *Reference rate, typically Libor Rania Elsawy 19

Central Bank of Egypt III-SWAPS Interest Rate Swaps IBM Fixed Payments at 6. 2% Interest Payments at LIBOR + 25 bps JP Morgan Floating Payments LIBOR Citibank Net Effect on IBM? What is IBM trying to achieve? Rania Elsawy 20

Central Bank of Egypt III-SWAPS Interest Rate Swaps • Cash Flow to IBM on SWAP with Citibank To IBM Dec 11 To Citibank $368, 750 Mar 12 $382, 192 $TBD Jun 12 $382, 192 Rania Elsawy $TBD Sep 12 $382, 192 $TBD Dec 12 $382, 192 21

Reuters Function Central Bank of Egypt III-SWAPS Rania Elsawy 22

Central Bank of Egypt III-SWAPS • The fixed rate is set to equate the PV of fixed rate payments and floating rate payments • The SWAP at inception has to have a …. . zero value to both counterparties Rania Elsawy 23

Central Bank of Egypt III-SWAPS Rania Elsawy 24

Central Bank of Egypt III-SWAPS Rania Elsawy 25

Bloomberg Function Central Bank of Egypt III-SWAPS Rania Elsawy 26

Central Bank of Egypt III-SWAPS Valuing an ongoing SWAP PV of fixed payments – PV of floating payments Floating rate payments are based on Eurodollar futures prices Rania Elsawy 27

III-SWAPS Central Bank of Egypt Valuation of a SWAP at start (short hand approach) Assuming a fixed for floating bond approach: Given, PV of Floating Cash flows = Par= 1 Given, PV of Fixed= PV Cash flows (coupon payments) +PV of Principal that is ∑PV of coupons + PV of Principal Hence, to equate the present value of fixed payments with the present value of the floating payments ∑PV of coupons + PV of Principal= 1 Rania Elsawy 28

Central Bank of Egypt III-SWAPS Consider a one-year interest rate swap with quarterly payments. Assume a notional principal of $15 mio. Calculate the annualized fixed-rate on the swap. The current term structure of LIBOR interest rates is as follows: L 0 (90) =0. 0656 L 0 (180)=0. 0640 L 0 (270)=0. 0621 L 0 (360)=0. 0599 PV (90)= 1/{1+0. 0656(90/360)}=0. 9839 PV(180= 1/{1+0. 0640(180/360)}=0. 9690 PV (270)= 1/{1+0. 0621(270/360)}=0. 9555 PV (360)= 1/{1+0. 0599(360/360)}=0. 9435 Fixed rate= 1 - 0. 9435 = 0. 0147 0. 9839+ 0. 9690+ 0. 9555+ 0. 9435 The annualized fixed rate (or payment per $1 of notional principal) is 0. 0147(360/90)=0. 0588 Rania Elsawy 29

Central Bank of Egypt III-SWAPS Calculate the market value of the swap 30 days later from the point of view of the party paying the floating rate and receiving the fixed rate and the opposite counterparty. L 30 (60) =0. 0384 L 30 (150)=0. 0379 L 30 (240)=0. 0382 L 30 (330)=0. 0406 PV (60)= 1/{1+0. 0384(60/360)}=0. 9936 PV(150)= 1/{1+0. 0379(150/360)}=0. 9845 PV (240)= 1/{1+0. 0382(240/360)}=0. 9752 PV (330)= 1/{1+0. 0406(330/360)}=0. 9641 PV of Fixed rate= PV of coupons under new Spot rates + PV of Principal PV of Fixed rate= 0. 0147(0. 9936+ 0. 9845+ 0. 9752+ 0. 9641) +1(0. 9641)=1. 0217 PV of Floating rate= PV (First floating payment + Par Value) PV of Floating rate= PV(0. 0656*90/360+1)=0. 9936(1. 0164)=1. 0099 Based on a notional principal of $15 mio, to the floating payer, receive fix party is $177, 000 Rania Elsawy 30

Central Bank of Egypt III-SWAPS To calculate the duration (modified duration) of a swap, we compute the modified duration of the long leg minus the modified duration of the short leg. Duration for the fixed leg is the presentvalue-weighted average maturity of the cash flows, whereas duration of the floating leg is the time to the next reset for the floating leg. The duration calculations (for both sides) divided by 1/(1 + YTM) is the modified duration for each side. MD = Leg DV 01 *10, 000 Leg PV Swap MD = MD of Receive Leg − MD of Pay Leg Rania Elsawy 31

Central Bank of Egypt III-SWAPS Rania Elsawy 32

Central Bank of Egypt III-SWAPS Budget Balance expectations “In a cyclical slowdown, market participants might expect tax revenues to fall, leading to increased government borrowing, Government bonds prices could fall in response to the extra supply-government bond yields would increase and swap spreads would tighten” Source: Understanding and modeling swap spreads, Fabio Cortes of the Bank’s of Foreign Exchange Division Rania Elsawy 33

III-SWAPS Central Bank of Egypt The slope of the yield curve “In a steep yield curve environment the cost of funding long-dated fixed-rate liabilities increases, and these institutions (issuers of corporate debt) prefer to swap their long-maturity fixed-rate bond issuance for shorter-maturity liabilities by paying floating in the short end and receiving fixed payments in the long end…and swap spreads tighten” Source: Understanding and modeling swap spreads, Fabio Cortes of the Bank’s of Foreign Exchange Division Rania Elsawy 34

Central Bank of Egypt III-SWAPS Rania Elsawy 35

III-SWAPS Central Bank of Egypt Risk and Liquidity Premia “A general increase in the perceived level of uncertainty is also often associated with ‘flight to quality’…spikes in uncertainty, as measured by the implied volatility of equity markets, have at times been associated with increases in swap spreads. ” Source: Understanding and modeling swap spreads, Fabio Cortes of the Bank’s of Foreign Exchange Division Rania Elsawy 36

III-SWAPS Central Bank of Egypt Risk and Liquidity Premia “During economic downturns the liquidity premium between swap rates and yields on the on-the-run benchmark government bond usually rises, widening swap spreads” Source: Understanding and modeling swap spreads, Fabio Cortes of the Bank’s of Foreign Exchange Division Rania Elsawy 37

III-SWAPS Central Bank of Egypt Mortgage prepayment hedging in the United States “When interest rates fall sufficiently, US homeowners may exercise an option to refinance their fixed-rate mortgages at the lower rates. GSEs…which own portfolios of MBS, may find themselves with a fall in the duration of their assets…to extend duration, receive fixed and pay floating, causing swap spreads to tighten” Source: Understanding and modeling swap spreads, Fabio Cortes of the Bank’s of Foreign Exchange Division Rania Elsawy 38

Central Bank of Egypt III-SWAPS Source: Understanding and modeling swap spreads, Fabio Cortes of the Bank’s of Foreign Exchange Division Rania Elsawy 39

Central Bank of Egypt III-SWAPS Source: Understanding and modeling swap spreads, Fabio Cortes of the Bank’s of Foreign Exchange Division Rania Elsawy 40

Central Bank of Egypt III-SWAPS Rania Elsawy 41

Central Bank of Egypt III-SWAPS Rania Elsawy 42

Central Bank of Egypt III-SWAPS Pre-Financial Crisis Swap spreads were high as investors were hedging their long position in MBS by buying swaps During the Financial Crisis Spreads narrowed as investors were selling their MBS positions and hedge through selling swaps From October 2008 till March 2010 As investors were expecting the Fed to end its program (of buying MBS) in March, they started selling their MBS positions and hence hedged their short positions through selling swaps so spreads narrowed further reaching negative 7. 63 basis From March 2010 till current period IRS spreads are experiencing an upward trend due to risk aversion driven by budget deficit issues Rania Elsawy 43

Central Bank of Egypt III-SWAPS • During the height of the financial crisis which is marked by the fall of Lehman Brothers, the three-month Libor-OIS spread reached a high of 364 basis points by October of 2008 • On March 23, 2010: the rate to exchange floating- for fixed-interest payments for 10 years fell below the comparable-maturity Treasury yield for the first time with swap spreads reaching negative 7. 63 basis points • During June-July 2010: Corporate bond sales are back to levels not seen since April as interest-rate swap spreads show investors are gaining confidence that Europe’s debt crisis is contained. Rania Elsawy 44

Central Bank of Egypt III-SWAPS Rania Elsawy 45

Central Bank of Egypt III-SWAPS Risks associated with a SWAP • Interest Rate Risk • Credit /Counterparty Risk – the possibility that the other party will fail to meet its obligations Existing a SWAP • Enter an offsetting swap with another party • Sell the swap to someone else • Use a Swaption Rania Elsawy 46

Central Bank of Egypt III-SWAPS SWAPTIONS • It is an option granting its owner the right but not the obligation to enter into an underlying swap. “Swaptions" typically refer to options on interest rate swaps. • There are two types of swaption contracts: – A payer swaption gives the owner of the swaption the right to enter into a swap where they pay the fixed leg and receive the floating leg. – A receiver swaption gives the owner of the swaption the right to enter into a swap where they will receive the fixed leg, and pay the floating leg. Rania Elsawy 47

III-SWAPS Central Bank of Egypt Equity Swaps Definition: • An OTC (private agreement between two counterparties) to exchange series of future cash flows, namely, the return on a stock or stock index against a fixed rate payment, floating rate or the return on another equity • The Equity Swap return is distinguished from other swaps because: • The party making the fixed payment may also have to make a variable payment if the equity return drops • The payment is is not known until the end of the settlement • In some cases the rate of return is structured to include both dividends &capital gains Rania Elsawy 48

Central Bank of Egypt III-SWAPS Equity SWAP Example: • Suppose that Vanguard Asset Allocation Fund (NASDAQ: VAAPX) would like to sell $100 mio in US large-cap equities and invest proceeds in a fixed stream • It engages with Morgan Stanley (NASDAQ: MWD) in a swap allowing it to pay the return on S&P 500 Total Return Index • In return MWD will pay VAAPX a fixed rate in the last day of March, June, September and December for one year at 6. 5% using an actual/365 convention. • The swap initiates on 31 December with an index value of 3, 517. 76 Rania Elsawy 49

Central Bank of Egypt IV-CREDIT DERIVATIVES Definition: • A derivative whose payoff depends on the creditworthiness of one or more entities Single Name Company/ Country Multiname Payoff to protection buyer depends on what happens to one company or country Rania Elsawy Company/ Country Payoff to protection buyer depends on what happens to a portfolio of debt instruments 50

Central Bank of Egypt IV-CREDIT DERIVATIVES Credit Default Swaps • The most common credit derivative • A contract that provides protection against the risk of default (credit event) by a company or country • The buyer of the insurance is entitled to the right to sell bonds issued by the company/country for their face value when a credit event occurs • CDS spreads can be calculated from default probability estimates Default protection buyer Periodic payments Default protection seller Payment in credit event Rania Elsawy 51