Central Bank of Egypt Bond Basics Characteristics Prepared

Central Bank of Egypt Bond Basics & Characteristics Prepared & Presented By: Heba Hamdy Sep-2018 Heba Hamdy

Index Central Bank of Egypt I. Bond Basics 1. Term to maturity, Coupon, Principal 2. YTM, Price-Yield Relationship II. Types of Bonds 1. Government, Corporate 2. Municipals, Zero Coupon 3. Fixed Vs Floating bonds III. Risk of Bonds 1. Interest Rate & Reinvestment Risk 2. Credit & Exchange Risk 3. Liquidity & Prepayment Risk IV. Auctions 1. Dutch Vs American Style Auctions V. Bond Characteristics I. Cash flows II. Coupons III. Prices IV. Value Determination V. Accruals VI. Duration Sep-2018 Heba Hamdy

Central Bank of Egypt I. Bond Basics 1. Definition of a Bond : A Bond is a debt instrument requiring the issuer (borrower of cash) to repay the lender for the amount borrowed plus interest over a specified period of time. 2. Type of Issuer: • • • Federal Government & its agencies Municipals Corporations Sep-2018 Heba Hamdy

Central Bank of Egypt I. Bond Basics 3. Term to Maturity: • The term to maturity is the number of years over which the issuer has promised to meet the conditions of the obligations. • Bonds with a maturity between one and five years are considered short term, bonds with maturity between 5 and 12 years are viewed as intermediate term, long term bonds are those with a maturity of more than 12 years. Sep-2018 Heba Hamdy

Central Bank of Egypt I. Bond Basics 4. Principal and Coupon Rate: • The principal value (face value, par value) is the amount the issuer agrees to repay the bondholder at the maturity date. • The coupon rate is the interest rate the issuer agrees to pay each year. The annual or semi annual amount of interest payment is called the coupon Sep-2018 Heba Hamdy

Central Bank of Egypt I. Bond Basics 5. • Yield to Maturity: The rate of return anticipated on a bond if it is held until the maturity date and based on the assumption that all coupons are reinvested at the same yield to maturity. Sep-2018 Heba Hamdy

Central Bank of Egypt I. Bond Yield 6. Shortcomings of YTM: • YTM considers not only coupon but also capital gain that the investor will gain if the bond is held to maturity • It also considers reinvestment of coupons but 2 assumptions are made that could be unrealistic: Ø It assumes that the bond will be held to maturity Ø It assumes that all future coupons are reinvested at the same rate (YTM) • The investor will realize the initially assumed yield only if the reinvestment rate actually equals the YTM used to discount the future cash flows Ø If the reinvestment rate is higher than YTM, the realized return will be higher and vice versa • The true return of a bond cannot be known with certainty because the interest rate at which future coupons will be reinvested is unknown Rania Elsawy

Central Bank of Egypt I. Bond Basics 7. Price-Yield Relationship • A fundamental property of a bond is that its price ( present value of the cash flows) changes in the opposite direction from the change in the required yield. As the required yield increases, the present value of the cash flow decreases; hence the price decreases & vice versa • Sep-2018 Heba Hamdy

Central Bank of Egypt II. Types of Bonds 1. • Government Bond: Ex: U. S. Government Bonds which are regarded as the safest issues in the world giving its deep liquidity. 2. • Corporate Bond: Corporate bonds are characterized by higher yields because there is a higher risk of a company defaulting than a government. The higher the quality of the company, the lower the interest rate the investor receives. Ex: Microsoft Bond, Toyota Bond Sep-2018 Heba Hamdy

Central Bank of Egypt II. Types of Bonds 3. Municipal Bonds: • Sate and Local governments issue municipal bonds to raise funds. The returns of Municipals are non taxable , therefore, the yield on municipals are usually lower than that of a regular taxable bond. • Sep-2018 Heba Hamdy

Central Bank of Egypt II. Types of Bonds 4. Zero Coupon Bonds: • This is a bond that makes no coupon payments during the life of the bond and instead, pays the interest at the maturity. It is issued at a discount to par value. They are usually long term investments 10 years or more. Pension funds usually invest in zero coupon bonds Ex: Education Fund • • Sep-2018 Heba Hamdy

Central Bank of Egypt II. Types of Bonds 4. Treasury Inflation Protected Securities (TIPS) • A Treasury security that protects investors from inflation where its par value rises with an inflation index like the CPI. TIPS are issued by U. S Government and its interest rate is fixed. • Sep-2018 Heba Hamdy

Central Bank of Egypt II. Types of Bonds 5. • Fixed Rate Bonds: It a bond with a fixed coupon rate 6. • Floating Rate Bonds: It’s a bond that contains a variable coupon that is equal to a money market reference rate plus a specified spread. Libor is the most widely used MM reference rate for floaters. Example : Coupon= 6 Month Libor + 50 bps • Sep-2018 Heba Hamdy

Central Bank of Egypt II. Types of Bonds • The issuer and the investor of the bond can limit their exposure to extreme fluctuations in the reference rate by placing upper and lower limits on the coupon rate. • The upper limit is called a CAP, which puts a maximum on the interest rate paid by the issuer. • The lower limit, on the other hand, is called a FLOOR which puts a minimum on the periodic interest payment received by the bondholders. • When both limits are present simultaneously, the combination is called a COLLAR Sep-2018 Heba Hamdy

Central Bank of Egypt III. Risk of Bonds 1. Interest Rate Risk: • The price of a bond will change in the opposite direction of the change in interest rates; as rates rise, prices will fall and vice versa. If an investor has to sell a bond prior to the maturity date at a higher interest rate that means the investor will realize a capital loss. • Sep-2018 Heba Hamdy

Central Bank of Egypt III. Risk of Bonds 2. Reinvestment Risk: • The risk where the interest rate at which the interim cash flows can be reinvested will fall. Reinvestment risk is greater for longer holding periods or for bonds with large cash flows. • Interest rate risk and reinvestment risk have offsetting effects. Sep-2018 Heba Hamdy

Central Bank of Egypt III. Risk of Bonds 3. Credit Risk: • The risk that the issuer of a bond will fail to satisfy the timely payment of interest and the amount borrowed. This type of risk is called default risk. 4. • Exchange Rate Risk: Ex: from the perspective of a U. S investor, a non dollar denominated bond ( whose payments are in foreign currency) has unknown USD cash flows since they are dependant on the exchange rates. Sep-2018 Heba Hamdy

Central Bank of Egypt III. Risk of Bonds 5. Liquidity Risk: • Liquidity depends on the ease with which an issue can be traded near its value. • The wider the bid ask spread the more the liquidity risk • U. S. treasuries are the most liquid bonds in the world. Sep-2018 Heba Hamdy

Central Bank of Egypt III. Risk of Bonds 6. Prepayment Risk: • Arises from the fact that the issuer might call back the security at times of falling interest rates and therefore the investor will receive early payments. An investor must reinvest these prepayments at a lower new rate. Sep-2018 Heba Hamdy

Central Bank of Egypt IV. Auctions • Treasuries are sold in regularly scheduled auctions through competitive and non competitive bids ( Ex: five year bonds are auctioned monthly) • The majority of investors place non competitive bids, agreeing to accept the final auction price and yield of the bond. • On the other hand, competitive bidders ask for a specific price and yield, but may or may not be successful in purchasing the bonds. • Primary dealers can submit their bid up to specified time on the auction day. Sep-2018 Heba Hamdy

Central Bank of Egypt IV. Auctions • Treasuries most recently issued are referred to as on the run issues, and older issues are referred to as off the run issues. • Hence, on the run issues tend to be more liquid and more expensive than the off the run securities. • An important indication of the strength and success of the auction is the bid to cover ratio • The ratio compares the total amount of bids received relative to the total amount of bids accepted. The higher the ratio the higher the demand. Sep-2018 Heba Hamdy

Central Bank of Egypt IV. Auctions 1. • • • Dutch Style Auctions (Single Price): The U. S Government issues bonds using a Dutch style auction. Primary dealers submit their bids along with bids of their clients to the U. S. Treasury. EX: U. S Government needs to raise $5 Billion in 10 year bonds. Competitive bids from different primary dealers are submitted as follows: $1 Billion at 3% $1. 5 Billion at 3. 5% $2 Billion at 4% $1 Billion at 4. 5% $ 2 Billion at 5% Sep-2018 Heba Hamdy

Central Bank of Egypt IV. Auctions • Bids will be filled from the lowest yield (highest price) until the entire $5 billion is raised. • This means that the first 3 amounts (bids) will be filled in full and the fourth amount (bid) will be filled only by 50%. • Therefore, only $0. 5 Billion from the fourth Bid will be filled and the clearing rate (rate at which all bidders get accepted) will be 4. 5%. • The $ 0. 5 Billion will be distributed on a pro rate basis on all bidders. Sep-2018 Heba Hamdy

Central Bank of Egypt IV. Auctions 2. American Style Auction (Multiple Price Auction): • The U. K government issues bonds using an American style auction. • The American style differs from the Dutch Style as each bidder gets the rate they bid for as long as its below the clearing rate. • In the previous example suppose it was the U. K Treasury issuing 5 billion bonds for 10 years: • Therefore, 1 Billion would have been issued at 3% , 1. 5 Billion at 3. 5%, 2 Billion at 4 % , and finally 0. 5 Billion at 4. 5% Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics 1. Cash flows: • The cash flow of a bond consists of the price which is paid by the investor at T=0 The investor receives semi annual or annual coupon payments throughout the life of the bond. At maturity, the investor receives the maturing amount ( Par value or face value) of the bond along with the final coupon payment. • • Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics • Ex: U. S. treasury Note 5 years Maturity paying coupons semi annually. Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics 2. Coupons: • A coupon payment on a bond is a periodic interest payment that the bondholder receives during the time between when the bond is issued and when it matures. • Ex: If the bond has a Face (Par) value of $1000 and a coupon rate of 4%. Therefore, the annual coupon = Face Value X Coupon Rate Annual coupon = 1000 X 4% Annual Coupon = $40 Semi Annual Coupon = $20 • • Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics 3. • • • Prices: Bond prices are expressed as a percentage of par value (100), which means that the price is always given in relation to 100. At Maturity, the investor receives par value. A bond price above 100 means the bond is trading above par, below 100 means its below par If Coupon rate > YTM therefore the bond will be trading above par If Coupon rate < YTM therefore the bond will be trading below par. IF Coupon rate = YTM therefore price of the bond is 100. Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics • Ex: A European government bond with a $1000 par value quoted at 85. 70 would have a market value of $1000 X 85. 70/100= $857. • Face value X Price = Market Value • U. S government bonds are quoted in fractions • EX: 102 -21 3/8 , 105 -20+, 101 -20 ¼ • • 102 -21 3/8 = 102. 67 105 -20+ = 105. 64 101 -20 ¼ = 101. 63 103 -20 5/8 = ? Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics 4. Value determination: • The price of a bond is equal to the present value of its expected cash flows. • Price = C [ 1 - 1/(1+r)n ] + M r (1+ r )n Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics • Ex: Consider a 20 year 10% coupon bond with a par value of $1000, the required yield on the bond is 11% • Therefore, coupon = $50 , number of period= 40 • R= 0. 055 , M= $1000 • Present Value of the coupons = $802. 31 • Present Value of the maturity value (par)= $117. 46 • The present value of the bond is equal to the sum of the two present values. • $802. 31+$117. 46 = $919. 77 Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics • Suppose that instead of an 11% required yield , the required yield is 6. 8% • Therefore, the present value of the coupon payments= $1084. 51 • Present value of the par amount = $262. 53 • Price or present value of the bond = $1347. 04 Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics • Ex: What is the price of a zero coupon bond that matures in 15 years if the maturity value is $1000 and the required yield is 9. 4% • Therefore, M=1000 , R= 0. 094, N= 15 • Present value = M / (1+r)n • Present Value= $259. 86 Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics 5. Accruals: • When an investor purchases a bond between coupon payments , the investor (buyer) must compensate the seller of the bond for the coupon interest earned from the time of the last coupon payment to the settlement date of the bond • This amount is called accrued interest • The amount that the buyer pays the seller is the agreed upon price plus accrued interest , this is referred to as the dirty price • Dirty Price= Clean Price + Accrued Interest Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics Accrual period Last coupon date Trade Settlement date Coupon period Sep-2018 Heba Hamdy Next coupon date

Central Bank of Egypt V. Bond Characteristics • • • Coupon rate : 3. 625% (semiannual pay) Clean Price : 99. 5 Par value : 100 Maturity date : 04/30/07 Settlement date : 05/12/05 Last coupon date: : 04/30/05 Next coupon date: : 10/31/05 Accrual period : 04/30/05 - 05/12/05 (12 days) Coupon period : 04/30/05 - 10/31/05 (184 days) Accrued Interest : (. 03625/2) * 100 * (12/184) = 0. 1182 Dirty Price : 99. 5+0. 1182= 99. 6182 Sep-2018 Heba Hamdy

Central Bank of Egypt V. Bond Characteristics • Coupon rate : • Clean Price : • Par value : • • 4% (semiannual pay) 98 100 Settlement date : 01/Aug/06 Last coupon date: : 31/Mar/06 Next coupon date: : 30/Sept/06 Accrual period : Coupon period : Accrued Interest : Dirty Price : Sep-2018 Heba Hamdy

Central Bank of Egypt VI. Duration 1. Duration Definition: • Duration is a measure of the approximate price sensitivity of a bond to interest rate changes • Price-yield relationship is negative, meaning that the price and yield move in opposite directions • Duration gives an approximate percentage change for a 100 bp change in rates. Sep-18 Heba Hamdy

Central Bank of Egypt VI. Duration • It allows a manager a way to compare bonds regarding the interest rate risk under certain circumstances • A portfolio’s duration is equal to the weighted average of the durations of the bonds in the portfolio. The weight is proportional to how much of the portfolio consists of a certain bond. • As interest rates decrease, the duration of the bond will increase Sep-18 Heba Hamdy

Central Bank of Egypt VI. Duration 2. Calculating Duration: • Duration is a measure of the approximate price sensitivity of a bond to interest rate changes • More specifically it is the approximate percentage change in price for 100 basis points change in rates Duration = Price if yields decline – Price if yields rise 2 (initial price) (change in yield in decimal) Sep-18 D = P- - P+ 2 P 0 Δy Heba Hamdy

Central Bank of Egypt VI. Duration 3. Yield Shocks and Duration Calculation: • In calculating duration, it is necessary to shock interest rates (yields), up and down by the same number of basis points • The below example shows how the size of the rate shock will affect duration • For option-free bonds, duration estimates are not materially affected by the size of the rate shocks Sep-18 Heba Hamdy

Central Bank of Egypt VI. Duration 4. Duration Calculation Example: Assume a 5 year 5% par bond and • Δy = 0. 3% • P- = 101. 31 • P+ = 98. 71 D= P- +P+ = 101. 31 – 98. 71 = 4. 33 2 P 0Δy 200 x 0. 003 A duration of 4. 33 years means that the price of the bond will change approximately by 4. 33% for 100 basis point change in the yield. Sep-18 Heba Hamdy

Central Bank of Egypt VI. Duration can now be used to project how the price of a bond will change for a given change in interest rates. Approximate percentage price change = -Duration x Δy x 100 Continuing the previous example to calculate the expected new price from duration we will find that there is a minor discrepancy: Sep-18 Heba Hamdy

Central Bank of Egypt VI. Duration For the same 5 year 5% par bond: D = 4. 33 P = 100 Δy = 0. 3% ΔP = - D x Δy x 100 = - 4. 33 x - 0. 003 x 100= 1. 299 P = 100 + 1. 299 = 101. 299 If we compare this to the previous example, we see that the price actually changed to 101. 31 Sep-18 Heba Hamdy

Central Bank of Egypt VI. Duration Dollar Duration (DV 01) and PVBP: • Dollar duration is another measure of a bond’s price volatility or interest rate risk • It’s the dollar change in a bond’s price for a given change in its yield • Price Value of a Basis Point (PVBP) is the dollar duration of a bond for a 1 basis point change in its yield Sep-18 Heba Hamdy