# Index. 1. Financial Markets: Overview. 2. The Bond Market. 3. Risks Associated with Fixed Income Investments. 4. Bond Characteristics and Valuation

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1 Index 1. Financial Markets: Overview 2. The Bond Market 3. Risks Associated with Fixed Income Investments 4. Bond Characteristics and Valuation 5. Macro Environment

2 Chapter 24 Bond Characteristics and Valuation

3 Bond Characteristics The variations in the coupon, length of the loan period, interest rate and other features of the debt security change the price of the bond. Bonds are tradable long-term debt and therefore in this chapter we will illustrate the main characteristics in bond valuation and the risks associated with each.

4 Bond Valuation Bond Valuation is all about calculating the present value of the promised cash flows. There are three steps in the bond valuation process: 1. Estimate the cash flows over the life of the security. This includes, (1) coupon payments as well as the (2) return of the principle. 2. Determine the appropriate discount rate based on the risk of the receipt of the estimated cash flows. 3. Calculate the present value of the estimated cash flows by discounting it to a present value.

5 Bond Valuation present value of coupon payments Present Value of a Bond = + the present value of the par value of the bond In this calculation, you have 5 components: Present value of bond Principle amount (future/par value) Coupon (payments receivable) Discount Factor (interest rate/yield) Time to Maturity - PV - FV - PMT - r - n Given four of these components, one can calculate the fifth component. This is the basics of time value of money calculations, which are simply used to price bonds.

6 Bond Valuation For simplicity, consider a bond that will pay R 100 per year for 10 years and makes a single R1 000 payment at maturity. If the appropriate discount rate is 8% for all the cash flows, the value of the bond is: Coupon (PMT) Coupon Coupon Coupon Coupon Coupon Coupon Coupon Coupon Principal Payment + Coupon PP = PPP + PPP + PPP + (1+r) 1 (1+r) 2 (1+r) 3 PPP+PPPPPPPPP (1+r) n = (1+0.08) 1 (1+0.08) 2 (1+0.08) (1+0.08) 10 = R = present value of future cash flows

7 Sources of Return Debt securities that make explicit interest payments have three sources of return: 1. The periodic coupon payments made by the issuer. 2. The recovery of principle, along with any capital gain or loss that occurs when the bond matures, is called, or is sold. 3. Reinvestment income, or the income earned from reinvesting the periodic coupon payments (i.e. the compound interest on reinvested coupon payments) Reinvestment income is important because if the reinvestment rate is less than the yield to maturity (YTM), the realized yield on the bond will be less than the YTM. This is known as reinvestment risk.

8 Reinvestment Risk Other things being equal, a coupon bond s reinvestment risk will increase with: Higher coupons because there s more cash flow to reinvest. Longer maturities because more of the total value of the investment is in the coupon cash flows (and interest on coupon cash flows). In both cases, the amount of reinvested income will play a bigger role in determining the bond s total return and, therefore, introduce more reinvestment risk. A noncallable zero-coupon bond has no reinvestment risk over its life because there are no cash flows to reinvest prior to maturity.

9 Pricing Relationships As seen in the formula, the various inputs affect the price of the bond differently. Bond Values and Interest Rates: Bond Values and Bond Yields are INVERSELY related. An increase in the discount rate will decrease the present value of a bonds expected cash flows and visa versa.

10 Pricing Relationships Bond Values and the Passage of Time: Prior to maturity, a bond can be selling at a significant discount or premium to par value. However, regardless of its required yield, the price will converge to par value as maturity approaches (pull to par effect).

11 Pricing Relationships Coupon, Yield and Price: If the coupon percentage is equal to the yield then the bond will be priced at par If the coupon percentage less then yield, the bond will trade at a discount If the coupon percentage is greater than yield, bond will trade at premium

12 Pricing Relationships Duration: Duration or Modified Duration is the rate of change of price with respect to yield or a linear measure of how the price of a bond changes in response to interest rate changes. As interest rates change, the price does not change linearly, but rather is a convex function of interest rates. This convex function is due to the nature of the price yield relationship as illustrated below:

13 Duration of a Nominal Bond Coupon (PMT) Coupon Coupon Coupon Coupon Coupon Coupon Coupon Coupon Principal Payment + Coupon D

14 Bonds Included in ALBI Bond Code Maturity Coupon MTM All in price Modified Duration Running Yield R Dec % R Sep % R Sep % ES18 20-Apr % R Dec % R Jan % DV22 07-Feb % TN20 17-Sep % R Mar % ES23 25-Jan % DV23 27-Feb % R Feb % TN23 06-Nov % ES26 02-Apr % R Dec % R Feb % ES33 15-Sep % R Mar % R Feb % R Feb %

15 Income from a Government Bond Example : R157 bond has a coupon rate of 13.5% and matures in 3 equal tranches in 2014/2015/2016 So on a nominal amount of R100 : Pays income of 13.5%/2 = R6.75 every 6 months Pays R100 (made up of R33.3 x 3) at maturity Current Price at yield of 5.21% : R Thus Running Yield = 13.5 / = 11.41% Running yield is the ratio of the annual coupon payment and the bond's current all in price *MTM in the previous table is yield to maturity

16 Income from a Government Bond Pull to Par effect example of the R157 Current Price at yield of 5.207% : R As bond approaches maturity, price will approach R100. This means that for the R157, over the next 2.38 years, it will lose value (on average) at the rate of : ( ) / 2.38 = 7.67% per year. On initial price of R this represents : 7.67 / = 6.48 % CAPITAL LOSS per year.

17 Inflation Linked Bonds Bonds linked to the inflation rate Cut out inflation risk of an investment or as a hedge against inflation Pay a periodic coupon that is equal to the product of the inflation index and the nominal coupon rate (not a fixed coupon rate) A rise in coupon payments is a result of an increase in inflation expectations, real rates, or both.

18 Inflation Linked Bonds Coupon Coupon Coupo n Coupo n Coupon Coupon Coupon Coupon Coupon Principal Repayment The ILB s coupon payments AND the Principal amount grow with inflation.

19 Inflation Linked Bonds Bond Code Maturity Coupon MTM All in price Modified Duration R Jan R Jan R Jan R Dec I Jan R Mar R Dec I Jan I Dec

20 Duration Calculation of Nominal vs. ILB The R186 (Nominal Bond) and I2050 (Inflation Linked bond) has yields of 6.8% and 1.96% respectively. While their durations are 7.9 and As such we can calculate how sensitive they are to interest rate moves. Let us assume a 20 bp up move for the R186 and the I2050 to 7% and 2.16%. Price change = (-) x (Move) x Duration R186 = (-) * (0.2%) * 7.9 = -1.58% I2050 = (-) * (0.2%) * 25.1 = -5.02%

21 Duration of ILB s Coupon Coupon Coupon Coupon Coupon Coupon Coupon Coupon Coupon Principal Repayment D

22 Pricing Relationships Convexity: Convexity is a measure of the curvature of how the price of a bond changes as the interest rate/yield changes. Specifically, duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question, and the convexity as the second derivative. Convexity helps to approximate the change in price that is not explained by duration.

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