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Concepts of Insurance and Risk Management

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Concepts of Insurance and Risk Management CHAPTER VALUATION OF FIXED INCOME SECURITIES MODULE - 2 - 2 VALUATION OF FIXED INCOME 2 SECURITIES Bond Valuation A bond is a security that obligates the issuer to make interest and principal payments to the holder on the specified dates. Bond’s price is equal to the present value of future cash flows received in the form of coupon and principal payment. Important points to note in Bonds Valuation: Bond price moves up with the decrease in the interest rate and vice versa. Longer-term bonds are more sensitive to interest rate changes than short term ones. Valuation of Coupon Bond n CM V tn T1 (1 r) (1 r) Where V = Price of the bond n = number of years C = annual coupon payments M= maturity value T = time period when the payment is received r = yield to maturity Bond Yields The general definition of yield is the return an investor will receive by holding a bond to maturity. So if you want to know what your bond investment will earn, you should know how to calculate yield. Required yield, on the other hand, is the yield or return a bond must offer in order for it to be worthwhile for the investor. The required yield of a bond is usually the yield offered by other plain vanilla bonds that are currently offered in the market and have similar credit quality and maturity. The returns to an investor in bond are made up of three components: coupon, interest from re- investment of coupons and capital gains/loss from selling or redeeming the bond. When we are able to compare the cash inflows from these sources with the investment (cash our flows) of the investor, we can compute yield to the investor. Depending on the manner in which we treat the time value of cash flows and re-investment of coupons, we are able to get various interpretations of the yield on an investment in bonds. The return of a bond is largely determined by its interest rate. The interest that a bond pays depends on a number of factors, including the prevailing interest rate and the creditworthiness of the issuer, which, of course, is what is assessed by the credit rating companies. The higher the credit rating of the issuer, the less interest the issuer has to offer to sell its bonds. The prevailing interest rate—the cost of money—is determined by the supply and demand of money. Like virtually anything else, the greater the supply and the lower the demand, the lesser the interest rate, and vice versa. An often used measure of the prevailing interest rate is the prime rate charged by banks to their best customers. Most bonds pay interest semi-annually until maturity, when the bondholder receives the par value of the bond back. Zero coupon bonds pay no interest, but are sold at a discount to par value, which is paid when the bond matures. Developed by AAFM India for SBI Exclusif 9 2 - VALUATION OF FIXED INCOME SECURITIES MODULE - 2 Once an investor has decided on the required yield, he or she must calculate the yield of a bond he CHAPTER or she wants to buy. Let’s proceed and examine these calculations. Nominal Yield, Coupon Rate Nominal yield, or the coupon rate, is the stated rate of interest of the bond. This yield percentage is the percentage of par value. Thus, a bond with a Rs. 1,000 par value that pays 5% coupon pays Rs.50/- per year in 2 semi-annual payments of Rs. 25/-. The return of a bond is the return/investment, or in the example just, Rs.50/Rs.1,000 = 5%. Current Yield Because bonds trade in the secondary market, they may sell for less or more than par value, which will yield an interest rate that is different from the nominal yield, called the current yield, or current return. The current yield calculates the percentage return that the annual coupon payment provides the investor. In other words this yield calculates what percentage the actual coupon payment is of the price the investor pays for the bond. Current yield relates the annual coupon interest to the market price. It is the ratio of the annual interest payment to the bond’s current price. The current yield therefore refers to the yield of the bond at the current moment. The price of bonds moves in the opposite direction of interest rates. If rates go up, the price of bonds decrease; if the rates go down, then the bonds increase in value. To see why, consider this simple example. You buy a bond when it is issued for Rs. 1000 that pays 8% interest. Suppose you want to sell the bond, but since you bought it, the interest rate has risen to 10%. You will have to sell your bond for less than what you paid, because why is somebody going to pay you Rs. 1000 for a bond that pays 8% when they can buy a similar bond of equal credit rating and get 10%. So to sell your bond, you would have to sell it so that the Rs. 80 that is received per year in interest will be 10% of the selling price—in this case, Rs. 800, Rs. 200 less than what you paid for it. (Actually, the price probably wouldn’t go this low, because the yield-to-maturity is greater in such a case, since if the bondholder keeps the bond until maturity, he will receive a price appreciation which is the difference between Rs. 1000, the bond’s par value and what he paid for it.) Bonds selling for less than par value are said to be selling at a discount. If the market interest rate of a new bond issue is lower than what you are getting, then you will be able to sell your bond for more than par value—you will be selling your bond at a premium. Current Yield = (Annual coupon payment / Market price of the Bond) 100 Example: You purchased a bond with a par value of Rs. 100/- for Rs. 95/- and it paid a coupon rate of 5%, then calculate the current yield. ((0.05 100)/95) 100 = 5.26% Note that if the market price for the bond is equal to its par value then: Current yield = Nominal Yield. Example: A 10% coupon bond is trading at the price of Rs.1050. Here the coupon amount is Rs. 100(1000 0.10) Current yield= 100/1050 = 0.0952 or 9.52%. Notice how this calculation does not include any capital gains or losses the investor would make if the bond were bought at a discount or premium. Because the comparison of the bond price to its par value is a factor that affects the actual current yield, the above formula would give a slightly inaccurate answer - unless of course the investor pays par value for the bond. To correct this, investors can modify the current yield formula by adding the result of the current yield to the gain or loss the price gives the investor: [(Par Value – Bond Price)/Years to Maturity]. 10 Developed by AAFM India for SBI Exclusif CHAPTER VALUATION OF FIXED INCOME SECURITIES MODULE - 2 The modified current yield formula then takes into account the discount or premium at which the - 2 investor bought the bond. This is the full calculation: AnnualCoupon (100 MarketPrice) AdjustedCurrent Yield 100 MarketPrice Years toMaturity Let’s re-calculate the yield of the bond in our first example, which matures in 30 months and has a coupon payment of Rs.5/-: = ((5/95) 100 ) + ((100-95)/2.5) = 5.26 + 2 = 7.26% The adjusted current yield of 7.26% is higher than the current yield of 5.26% because the bond’s discounted price (Rs.95/- instead of Rs.100/-) gives the investor more of a gain on the investment. Now we must also account for other factors such as the coupon payment for a zero-coupon bond, which has only one coupon payment. For such a bond, the yield calculation would be as follows: 1 Future Value n 1 PurchasePrice Yield = n = Years left until maturity If we were considering a zero-coupon bond that has a future value of Rs.1,000/- that matures in two years and can be currently purchased for Rs.925/-, we would calculate its current yield with the following formula: 1 Rs.1000 2 1 Rs.925 Yield = Relationships in Bond Pricing Theory Bond prices and yields move in opposite directions. Bond prices are more sensitive to yield changes the longer their maturities. The price sensitivity of bonds to yield changes increases at a decreasing rate with maturity. High coupon bond prices are less sensitive to yield changes than low coupon bond prices. With a change in yield of a given number of basis points, the associated percent gain is larger than the percent loss. Yield to Maturity (YTM) If an investor buys a bond in the secondary market and pays a price different from par value, then not only will the current yield differ from the nominal yield, but there will be a gain or loss when the bond matures and the bondholder receives the par value of the bond. If the investor holds the bond until maturity, he will lose money if he paid a premium for the bond, or he will earn money if he paid for it at a discount. The yield-to-maturity (YTM), or true yield, of a bond that is held to maturity will have to account for the gain or loss that occurs when the par value is repaid.
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