ANALYSIS OF FIXED INCOME SECURITIES


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1 ANALYSIS OF FIXED INCOME SECURITIES Valuation of Fixed Income Securities Page 1
2 VALUATION Valuation is the process of determining the fair value of a financial asset. The fair value of an asset is its price. Often times the market also used yield and yield spread as a relative measure of value. DEFINITIONS OF FIXED INCOME SECURITY TERMINOLOGIES Fixed Income Security is a financial obligation of an entity that promises to pay a specified sum of money at a specified future dates. The entity that promises to pay is called the issuer. Fixed Income Securities fall into two broad categories: 1. Debt obligations here the issuer is the borrower and the lender is the investor or creditor. The issuer promises to pay interest and principal at maturity at agreed future dates e.g. bonds, mortgage backed securities, asset backed securities and bank loans 2. Preferred Stock  represents an ownership interest in a corporation with fixed dividend payments. Dividend is however paid from after tax profit and is payable only when there is profit but in preference to the ordinary stock holders Indenture & Covenants are the terms in terms of rights of the holders and the promises of the issuer. These terms are usually managed by a Trustee on behalf of all bondholders. As part of the indenture there are affirmative and negative covenants. Term to Maturity is the number of years over which the issuer promises to meet the obligation. The term to maturity is the same as the tenor only on the date the security is issued, thereafter the term to maturity is lower than the tenor as time elapses. Par Value is the amount the security promises to repay at maturity i.e. the principal, face value, redemption value and maturity value. The practice is to quote the price of a security as a percentage of its Par Value i.e. the Par Value is deemed to be 100. Valuation of Fixed Income Securities Page 2
3 When a security is trading at below its Par Value, it is said to be trading at a Discount. When it is the converse i.e. it is trading above its Par Value, then it is said to be trading at a Premium. Coupon rate is the interest rate that the issuer agrees to pay each year. Also, called the nominal rate. The actual monetary amount paid annually is called the Coupon. Not all fixed income securities promises to pay a coupon. When a security promises to pay only one fixed amount, it is called a ZeroCoupon instrument. BASIC PRINCIPLES OF VALUATION The Price of any financial instrument is equal to the present value of the expected cash flows from the instrument. There are 3 (three) basic steps to valuation  Step 1: Estimate of the expected cash flows periodic coupon payments to maturity date par (or maturity) value at maturity Step 2: Estimate of the appropriate discount rate on comparable bonds in the market i.e. noncallable bonds of the same credit quality and same maturity. Step 3: Calculation of the Present Value (PV) of the expected cash flows in Step 1 using the discount rate(s) in Step 2. STEP 1: ESTIMATE THE EXPECTED CASH FLOWS Cash flow is simply the cash that is expected to be received in the future from an investment whether it is interest or principal. The expected cash flows for some instruments are easy to compute, for others, the task is more difficult e.g.: Valuation of Fixed Income Securities Page 3
4 1. When the issuer or investor has the option to change the contractual date of the repayment of the principal e.g. callable/putable bonds, mortgage backed securities, asset backed securities, etc. 2. The coupon payment is reset periodically based on a formula that depends on some value or values for reference rates, prices or exchange rates e.g. floating rate securities 3. The investor has a choice to convert or exchange the security into common shares e.g. convertible bonds and exchangeable bonds STEP 2: DETERMINING THE APPROPRIATE RATE(S) The minimum rate an investor should use is that on a defaultfree cash flow (i.e. Treasuries) with the same maturity. The premium over this rate should reflect the additional risks of the specific instrument which the investor takes. Consequently, the required rate is the rate for financial instruments with comparable risk or alternative (or substitute) investments for each of the tenors of the expected cash flows. STEP 3: DISCOUNTING THE CASH FLOWS In general, the price of a bond is given by P = C + C + C + + C + M 1+ r (1+ r) 2 (1+ r) 3 (1+ r) n (1+ r) n or: P = C + M (1+ r) t (1+ r) n where: C = coupon payments usually semiannual P = price of the investment n = number of periods r = periodic interest rate M = maturity value t = time period when the payment is received Valuation of Fixed Income Securities Page 4
5 This valuation model supports the use of a different discount rate for each cash flow otherwise we may use the Annuity Concept. A shortcut formula for computing the value of a security when a single discount rate is used is to compute the present value of the Annuity (the interest payments) and then adding the Present Value of the maturity value. The present value of an annuity is equal to 11 Annuity payment X (1 + r) n r PRESENT VALUE PROPERTIES A bond that matures in 4 years time has a coupon rate of 10% with an annual interest payment frequency. a. Assuming applicable discount rate for similar security is 8%, what is the price of the bond today? b. If the discount rate is changed to 12%, what will the price be? Year Cash Flow Present 8% Present 12% 1 N Price Valuation of Fixed Income Securities Page 5
6 NOTE: TIMING: The longer the term to maturity, the lower the value of the cash flow today DISCOUNT RATE: The higher the discount rate, the lower the security value RELATIONSHIP OF COUPON RATE, DISCOUNT RATE & PRICE RELATIVE TO PAR: Coupon rate = yield required; price = par value Coupon rate < yield required; price < par value Coupon rate > yield required; price > par value CHANGE IN VALUE AS TIME MOVES CLOSE TO MATURITY: A bond s valueo Decreases over time if the bond is selling at a premium o Increases over time when the bond is selling at a discount o Is unchanged if the bond is selling at par value o At maturity is equal to its Par Value VALUATION USING MULTIPLE DISCOUNT RATES The proper way to value the cash flows of any security is to use a different discount rate that is unique to the time period in which the cash flow will be received. Suppose we have a 4year 10% coupon bond with annual interest payment and the appropriate discount rates are as follows: Year 1 6.8% Year 2 7.2% Year 3 7.6% Year 4 8.0% The present value or price for this instrument today is: Valuation of Fixed Income Securities Page 6
7 Cash flow Discount rate Discounted value Year % Year % Year % Year % Price Practice: What is the value of a 5year 7% coupon bond assuming the payments are received annually and the discount rates for each year are as follow: Year 1 3.5% Year 2 3.9% Year 3 4.2% Year 4 4.5% Year 5 5.0% VALUING SEMIANNUAL CASH FLOWS For semiannual cash flows, the computation remains the same except that both the cash flow and discount rate are adjusted to half of the annual. A period is a sixmonth period i.e. the number of periods will double. VALUING ZEROCOUPON BOND A zero coupon bond has only one cash flow the maturity value. The value of a zerocoupon bond that matures n years from now is Maturity value (1 + i) n x 2 Where i is the semiannual discount rate n is the number of years to maturity Valuation of Fixed Income Securities Page 7
8 Note: The number of periods is n X 2 for consistency with the pricing of coupon bearing bonds in the market. Exercise: Complete the following table for a 10 year zero coupon bond with a maturity value of $1,000 for each of the following annual discount rates. Annual rate 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% Semiannual rate Price Valuation of Fixed Income Securities Page 8
9 COMPLICATIONS IN VALUING FIXED INCOME SECURITIES 1. Next Coupon Payment in less than six months For coupon paying securities, a complication arises when we try to price the instrument between coupon payments. This is because one of the cash flows (the immediate) encompasses two components as shown below: Interest earned by seller Interest earned by buyer Last coupon Settlement Next coupon payment date date payment date Interest earned by the seller is the interest accrued between the last coupon payment and the settlement date. This is called Accrued interest. The buyer must compensate the seller for this and recovers it from the next interest payment. The Price determined using the present value concept is called the Full or Dirty Price is that is the amount paid by the investor. From the Full Price, the accrued interest is deducted to get the Clean Price which is true price of the bond. In computing the Full price of a bond, the formula is  Present value t = expected cash flow (1 + I ) t 1+w Where: w period = days btw settlement and next coupon date no of days in coupon period Valuation of Fixed Income Securities Page 9
10 Illustration: A 5year semiannual 10% coupon security is being sold on a day that is 78 days between the settlement date and the next coupon date. There are 182 days in the coupon period. w = 78/182 = periods Period 1: Present Value 1 = 5 = (1.04) Period 2: Present Value 2 = 5 = (1.04) Period 3: Present Value 3 = 5 = (1.04) Period 4: Present Value 4 = 5 = (1.04) Period 5: Present Value 5 = 105 = (1.04) Full Price is the sum of the PV of the cash flows, which is The Accrued Interest (AI) is computed as Semiannual coupon payment X (1 w) AI = N5 X ( ) = N Clean Price = N = N Practice: Suppose a bond is purchased between coupon periods. The days between settlement date and the next coupon period is 58. There are 183 days in the coupon period. Valuation of Fixed Income Securities Page 10
11 Suppose that the bond purchased has a coupon rate of 7% and there are 10 semiannual coupon payments remaining. a. What is the full price for this bond if a 5% annual discount rate is used? b. What is the Clean Price? DAY COUNT CONVENTIONS Different dayyear (interest basis) conventions apply to instruments in different markets. Those of us who engage in international capital markets, should be familiar with the conventions: Eurodollar (LIBOR) market Actual/360 Eurobond market (AIBD) 360/360 US Treasury/ Ghanaian Money Market Actual/365 Nigeria Money Market (NMM) Actual/Actual The numerator depicts the number of days interest is to be earned while the denominator depicts the number of days in a year in the relevant market. Example: A coupon bearing US Treasury security whose previous coupon payment was March 1 and the next is September 1. Suppose this Treasury security is purchased with a settlement date of July 17 th. Days between Settlement and Next Coupon Dates is actual days from July 17 th to September 1 st Valuation of Fixed Income Securities Page 11
12 US Treasury Eurobond July 17 to July days 13 days August 31 days 30 days September 1 1 day 1 46 days 44 days The number of days in the coupon period is computed as follows March 30 days 29 days April May June July August September 1 1 Total 184 days 180 days 2. Cash flows are unknown This problem occurs largely with callable or putable bonds. With these bonds, the cash flows will depend on the current level of interest rate relative to the coupon rate. The valuation of these securities is done using valuation models such as the Binomial model (which seeks to price the embedded interest rate options) and the Monte Carlo Simulation Model (which is used for mortgaged backed securities and certain types of asset backed securities. This prices both embedded interest rate options and prepayment options) Valuation of Fixed Income Securities Page 12
13 VALUATION OF FIXED INCOME SECURITIES Exercises 1. What is the price of a 5year security that pays 7% annually assuming a discount rate of 5%. 2. A 5year amortizing security with a par value of N10,000 and a coupon rate of 5% has an expected cash flow of N2, per year assuming there are no prepayments. The annual cash flow includes interest and principal repayment. What is the present value of this amortizing security assuming a discount rate of 6%. 3. What will be the initial offering price for the following bonds: a. A 15year zero coupon bond, assuming a discount rate of 12% b. A 20year zero coupon bond, assuming a discount rate of 10% 4. An 8.4% coupon bond issued by the State of Indiana sells for $1,000. The income on this bond is tax exempt. What coupon rate on a corporate bond selling at its par $1,000 value would produce the same aftertax return to the investor as the municipal bond if the investor is in the: a. 15% marginal tax bracket b. 25% marginal tax bracket c. 35% marginal tax bracket 5. At what price would you expect a bond with the following characteristics to trade in the market assuming the expected yield for this quality of bond is 10% Par Value $1,000 Coupon rate 8% Valuation of Fixed Income Securities Page 13
14 Payment frequency annually Term to maturity 10 years 6. What is the value of a 5year 5.85% coupon bond if the appropriate discount rate for each cash flow is as follows: Year Discount rate % % % % % 7. Suppose a bond is selling between coupon periods. The days between the settlement date and the next coupon period is 115. There are 183 days in the coupon period. Suppose the bond has a coupon rate of 7.4% and there are 10 semiannual coupon payments remaining. a. What is the dirty price of the bond? b. What is the Accrued Interest? c. What is the clean price? 8. What is the value of a zero coupon bond that matures in 20 years, has a maturity of $1 million and is selling to yield 7.6% 9. What factors will you take into consideration in valuing bonds? 10. What are the factors that complicate bond pricing and why? Valuation of Fixed Income Securities Page 14
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