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## Topic 2 Price Yield Conventions and Repo Markets

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**Topic 2**Price Yield Conventions and Repo Markets**Nature of cash flows in Debt Markets**• Coupons – paid periodically (annual, semi-annual, quarterly, etc.) • Balloon payment – paid at maturity. • Other cash flows – payments when the debt is called, converted into equity, or when the issuer defaults and settles through a bankruptcy procedure. • We will take a look at cash flows when there is no credit risk, and assume that fixed coupons and a terminal balloon payments are promised by the issuer. Treasury debt securities fall in this category.**Bond Basics**• Two basic yield measures for a bond are its coupon rate and its current yield.**Straight Bond Prices and Yield to Maturity**• The price of a bond is found by adding together the present value of the bond’s coupon payments and the present value of the bond’s face value. • The Yield to maturity (YTM) of a bond is the discount rate that equates the today’s bond price with the present value of the future cash flows of the bond. Is also the IRR of a bond’s cash flow….**Price as present value of future cash flows**With annual compounding, the price P of a bond that pays annual dollar coupons of C for N years, per $100 of face value, is PV of balloon payment PV of an annuity**Price as present value of future cash flows**With semi-annual compounding, the price P of a bond that pays semi annual dollar coupons of C/2 for N periods, per $100 of face value, is PV of balloon payment PV of an annuity**Price as present value of future cash flows**In reality, bonds are bought and sold on dates that are not necessarily their coupon dates. This leads to partial first coupons – the buyer will have to compensate the seller for the partial coupon earned. We need to modify the formulas in previous slides to reflect this practice. Let z = number of days from settlement date to next coupon date. x = number of days between the last coupon date and the next coupon date. N = number of remaining coupons.**Market conventions and quotes**Treasury debt with coupons are called T-notes (with 2 to 10 yrs at-issue maturity) and T-bonds (> 10yrs at-issue maturity). Treasury debt with no coupons with an at-issue maturity of 1 year or less are known as Treasury bills. A plus sign (+) means 1/64th. ++ means 1/128th Prices are quoted in 1/32nd**Market conventions and quotes**Treasury bills are quoted on a discount yield basis. The procedure for obtaining the invoice price from discount quotes is illustrated in the next example, in which quotations for settlement on June 26, 2008, for three- and six-month U.S. Treasury bills are shown in Table 2.4 .**Market conventions and quotes**The invoice price, P , using the discount yield is then calculated as follows: where the T-bill has n days remaining from the settlement date to maturity and has a discount yield d per $100 face amount. For the three-month T-bill, the price is computed as follows:**T-bills with a maturity of less than 182 days**Discount yield of a T-bill: • where the T-bill has n days remaining from the settlement date to maturity date and has a discount yield d per $100 face amount. • Gain is divided by 100 rather than the price, which is • the initial investment. • b. Annualization is done by using 360 days per year.**BEY - T-bills with a maturity of less than 182 days**BEY of a T-bill: where the T-bill has n days remaining from the settlement date to maturity and has a discount yield d per $100 face amount. T-bills are quoted in discount yields. BEY is a better measure of returns.**BEY - T-bills with a maturity of more than 182 days**EXCEL automatically takes the maturity into account in computing BEY of T-bills.**Coupon paying Treasury Securities – Notes and Bonds**Accrued interest: Number of days of coupon that has accrued but not paid. Clean price: Price excluding accrued interest. Dirty price: Clean price plus accrued interest.**Coupon paying Treasury Securities – Notes and Bonds**Last Coupon Date (LCD or PCD) Settlement Date (SD) Next Coupon Date (NCD)**Price-Yield relationship is generally convex**Price Yield**Price-Yield relationship is for callable debt**can exhibit negative convexity Par Price Call option is unlikely To be exercised as yields are high. The bond behaves like a non-callable security. Bond can be called at par: this “compresses” the price to par as yields fall. Yield**Examples of Debt Securities with Negative Convexity**• Many debt securities issued by Fannie and Freddie are callable (Why?). They exhibit negative convexity. • Mortgage-Backed Securities exhibit negative convexity. (Why?) • Spreads between MBS and “otherwise identical” non-callable debt securities will widen as yields decrease – explain why this is the case.**Duration**• Bondholders know that the price of their bonds change when interest rates change. But, • How big is this change? Point of tangency…. • How is this change in price estimated? 1st derivative of the pricing function wrt to yield (modified) • Macaulay Duration, or Duration, is the name of concept that helps bondholders measure the sensitivity of a bond price to changes in bond yields. That is: • Two bonds with the same duration, but not necessarily the same maturity, will have approximately the same price sensitivity to a (small) change in bond yields.**Example: Using Duration**• Example: Suppose a bond has a Macaulay Duration of 11 years, and a current yield to maturity of 8%. • If the yield to maturity increases to 8.50%, what is the resulting percentage change in the price of the bond?**Calculating Macaulay’s Duration**• Macaulay’s duration values are stated in years, and are often described as a bond’s effective maturity. • For a zero-coupon bond, duration = maturity. • For a coupon bond, duration = a weighted average of individual maturities of all the bond’s separate cash flows, where the weights are proportionate to the present values of each cash flow.**Duration Properties**• All else the same, the longer a bond’s maturity, the longer is its duration. • All else the same, a bond’s duration increases at a decreasing rate as maturity lengthens. • All else the same, the higher a bond’s coupon, the shorter is its duration. • All else the same, a higher yield to maturity implies a shorter duration, and a lower yield to maturity implies a longer duration.**Topic 2 - Conclusions/Main insights**• Debt securities are often quoted in terms of yields. • There is a direct relationship between prices and yields. • Market conventions differ from one segment (Treasury, for example) to another (Corporate, for example) within the same country. • EXCEL has useful functions to take out the tedious calculations – you should familiarize yourself with these functions. • Quoted prices exclude accrued interest, which must be added to the quoted price to get the actual price that must be paid to complete the transaction.