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BOND YIELDS AND PRICESFixed Income SecuritiesA debt security is a claim on a specified periodic stream of income.

Debt securities are often called fixed income securities

These securities are easy to understand and are relatively less risky.A bond is a security that is issued in connection with a borrowing arrangement. BondsThree basic characteristics of a bond are: Face Value, Coupon Rate and Maturity.

The bond prices that are quoted in the financial pages are not actually the prices that the investors pay for the bond. The quoted price (called the clean price) does not include the interest that accrues between coupon payment dates. The price including the accrued interest is called the dirty price.

Types Of BondsGovt. Bonds Corporate Bond Convertible Bonds Non-convertible Bonds Callable Bonds Puttable Bonds Zero-coupon Bonds

Fixed-rate BondsFloating-rate Bonds Inverse Floaters Asset-backed Bonds Catastrophe BondsIndexed Bonds International Bonds Bond Prices and Interest Rates

There is an inverse relationship between bond prices and yields.

Bond Price

The relationship between bond prices and yields is convex.

Interest RateBond Yields

Current Yield is the ratio of the coupon interest to current market price.

Yield to Maturity (YTM) is defined as the compound rate of return an investor will receive from a bond purchased at the current market price and held to maturity.

YTM makes the present value of a bonds payments equal to its price.

Yield to Maturity Where P = the current price of the bond T = the number of semi-annual periods to maturity ytm = the semi-annual yield to maturity to be solved for c = the semiannual coupon in amount FV = the face value (or maturity value or par value)

The annual YTM (bond equivalent yield) is equal to 2 x ytm

Example-YTMCoupon Rate : 10% Time to Maturity: 3 yearsCoupon Payment : Half-yearly FV: Rs.1,000 MV: Rs.1052.42

Since the bond is selling at a premium , ytm is lower than thecoupon rate.

With a 4% discount rate the PV is Rs.1052.10. The semi-annualyield is 4% and annual yield is 8%

YTM-An ApproximationYTM can be approximated using the following equation:

Where C is the coupon payment per period, M is the maturity value of the bond , P is the present price of the bond and n the number of coupon payments,

YTM of Zero-Coupon BondThe yield to maturity of a zero-coupon bond is given by:

For a premium bond, Coupon Rate > Current Yield > YTM

Example YTM of ZeroA zero-coupon bond has 12 years to maturity and is selling for Rs.300. The ytm is given by:

= YTM = 10.3%

Yield to CallThe yield to call is the expected yield to the end of the deferred call period when a bond can first be called.

wherefc = the number of semiannual periods until the first call dateyc = the yield to first call on a semiannual basisCP = the call price to be paid by the issuer if the bond is called

Example Yield to CallAn 8% coupon , 30 year maturity bond sells for Rs.1,150 and is callable in 10 years at a call price of Rs.1,100.Its Yield to Call will be:

= 6.64%

PV at discount rate of 3.5% = Rs.1121.32PV at a discount rate of 3% = Rs. 1204.4By interpolation, discount rate =3.32%

Realized Compound YieldRealized compound yield measures the compound yield on the bond investment actually earned over the investment period, taking into account all intermediate cash flows and reinvestment rates. It cannot be determined until the investment is concluded and all of the cash flows are known.The semi-annual realized compound yield can be calculated using the following formula:

Example-RCYAn investor invested Rs.1,000 two years ago in a 10% bond with a two year maturity. The promised YTM is 10%.

If the reinvestment rate is 10%, the ending wealth will be Rs.1,210 and the RCY will be:

If the interest is reinvested at 8%, the ending wealth will be Rs.1,208 and the RCY will be:

Bond Prices, Coupon Rates and Interest RatesA bond will sell at par value when the coupon rate equals market interest rate. When the coupon rate is lower than the market interest rate, the bond has to be sold below par value to provide a capital gain on the investment. When the coupon rate exceeds the market interest rate, the bond would sell at a premium. The extra cash flows from coupons are offset by capital losses at maturity.Although the capital gain and income components differ, each bond is priced to offer the same rate of return to investors.Bond Prices over Time

Prices of zero-coupon bonds rise exponentially over time, providing a rate of appreciation equal to the rate of interest.

Though, at maturity, all bond prices converge to their face value, but before maturity date, bond prices are continually changing with changes in interest rates and yields.

The two bond variables of major importance in assessing the change in the price of a bond, given a change in interest rates, are its coupon and its maturity.

A decline (rise) in interest rates will cause a rise (decline) in bond prices, with most volatility in bond prices occurring in longer maturity bonds and bonds with low coupons.Bond Prices over Time

In order to receive the maximum price impact of an expected change in interest rates, a bond buyer should purchase low-coupon, long maturity bonds.

If an increase in interest rates is expected (or feared), an investor contemplating a bond purchase should consider those bonds with large coupons or short maturities or both.

Treasury Strips

Longer term zero-coupon bonds are commonly created from coupon bearing notes and bonds with the help of treasury. The treasury breaks down the cash flows to be paid by be the bond into a series of independent securities where each security is a claim to one of the payments of the original bond.The treasury program under which coupon stripping is permitted is called STRIPS (Separate trading of registered interest and principal of securities).

Default Risk and Bond Pricing

When bonds are subject to default, the promised yield will not be realized. To compensate bond investors for default risk, bonds must offer default premiums, that is promised yield in excess of those offered by default-free government securities. The default premiums depend on rating by credit-rating agencies. Higher rated bonds are considered investment grade and lower-rated bonds are classified as speculative-grade or junk bonds.

Determinants of Bond Safety Bond safety is often measured using financial ratios such as liquidity ratios, coverage ratios, leverage ratios, profitability ratios and cash flow ratios.

Discriminant analysis can be used to predict bankruptcy.

Bond Indentures

Bond Indentures are a safeguard to protect the claims of debenture holders.

Common , indentures specify :

Sinking fund requirements,

Collateralization of the loan,

Dividend restrictions and

Subordination of future debt.