Ch. 14 - Bond Prices and Yields

Callable Vs. Non-Callable Bonds

- As interest rates decline, the PV of the scheduled cash flows from a bond increases. - However, the call feature in the callable bond allows the issuer to repurchase the bond at the call price. - If the call price is less than the PV of the scheduled cash flows, the bond will most likely be called. - Therefore, the values of the callable bond and non-callable bond will begin to diverge when interest rates fall. - In contrast, when interest rates are high, the likelihood of call is very low and the values of the callable and non-callable bond will begin to converge.

Callable Bonds

- Call provision = Allows the issuer of a bond to repurchase it from the investor at a specified call price before its maturity date. - The firm's benefit of having a call option represents a burden/loss to the investor. - Callable bonds usually come with a period of call protection (i.e. they become callable after a period): these bonds are referred to as deferred callable bonds.

Promised (Stated) YTM Vs. Expected YTM

- Corporate bonds are subject to default risk, which implies that we must differentiate between the promised YTM and the expected YTM. - Promised YTM is the YTM of the bond assuming that the investor will receive all the promised or stated cash flows. - Expected YTM is calculated based on expected cash flows, accounting for the likelihood of default

Bond Characteristics

- Debt securities represent a claim on a specified periodic stream of income: A bond is the basic debt security - A bond underlies a simple borrowing arrangement in which the bond is sold to the investor in exchange for cash - The bond contract (indenture) fixes the coupon rate, par value, and maturity. - The bond price is determined in the marketplace.

Coupon Bond

- In a coupon bond, the borrower/issuer is obligated to make specified payments (coupons) on specified dates (usually every 6 months). - When the bond matures, the borrower/issuer repays the debt by paying the investor (bondholder) the par value (face value/principal) of the bond. - The coupon rate determines the interest payment: Annual coupon = coupon rate * face value of the bond

Zero-Coupon Bonds

- Original Issue Discount (OID) bonds are bonds that are sold with low coupon rates (relative to market rates) that cause them to sell at a discount from par value. - An extreme example of an OID is a zero-coupon bond that pays no interest and provides all of its returns from price appreciation. - Investors in a zero-coupon bond (or zero) receive only one cash flow at maturity. - Treasury bills are an example of a short-term zero and the Treasury Strips represent a long-term zero. - Coupon-paying bond = Series (or portfolio) of zero-coupon bonds - The formula to value a zero-coupon bond: V = Face Value / (1+r)^T

Yield To Maturity Vs. Holding Period Return

- The YTM depends only on the coupon rate, current bond value (price), maturity date, and par value. All of these are observable today, so the YTM can be calculated today. - In contrast, the HPR represents the return over a particular period and depends on the market price of the bond at the end of the period, which is unknown today. Therefore, we can (at best) forecast the HPR today.

Bond Value

- The value of a bond equals the present value of the future cash flows from the bond. - Bond Value = PV of coupon payments + PV of face value V = C/r[1 - 1/(1+r)^T] + Face Value/(1+r)^T - C = coupon payment per period - r = rate per period - T = # of periods

Zero-coupon Bonds

- These bonds pay no coupons - An investor in a zero-coupon bond does not receive any (coupon) interest and receives only the face value at maturity.

Bond Prices Over Time

- When the coupon rate = YTM, bond value = par value. In this case, investors receive fair compensation on their investment in the bond. - When the coupon rate < YTM, bond value < par value. In other words, the bond sells at a discount to par. In a discount bond, the return from the coupon is less than what investors can earn in the market. To provide a fair return to investors, discount bonds would have to sell below par value so as to offer a built-in price appreciation (capital gain) over time. - When the coupon rate > YTM, bond value > par value. In other words, the bond sells at a premium. In a premium bond, the return from the coupon is greater than what investors can earn in the market and its price is bid above par. As the bond approaches maturity, fewer of the higher coupons remain causing the bond value to decline. Therefore, the bond has built-in price depreciation (capital loss) over time. - Premium Bond: As time approaches maturity date, price of bond decreases as it moves towards par value - Discount Bond: As time approaches maturity date, price of bond increases as it moves towards par value

Relationships Between Bond Price and YTM

1. As rates (YTM) increase, bond values decrease. Therefore, interest rates and bond values are inversely related. 2. The price decline for a given increase in yield is less than the price increase for a decrease in yield of same magnitude. Therefore, the relationship between rates (yields) and bond prices is convex. - The change in bond value is not symmetric for a given change in yield in either direction. 3. Longer-term bonds are more sensitive to interest rate changes than short-term bonds.

Coupon Rate

Coupon rate = Annual coupon / Par value

Current Yield

Current Yield = Annual coupon / Bond price

Yield to Call (YTC)

For a given level of nominal interest rates: 1) Yield on a callable bond > Yield on an otherwise identical non-callable bond - Investors take on the call risk so they demand a higher interest rate 2) Value of a callable bond < Value of an otherwise identical non-callable bond To compensate investors for the call risk, callable bonds are issued with a higher coupon rate (and higher YTM) than comparable non-callable bonds.

Horizon Analysis

Forecasting the realized compound yield over various holding periods (or investment horizons) is referred to as horizon analysis.

Holding Period Return

Holding Period Return (HPR) = Total Return = (Income + Change in Bond Value) / Initial Bond Value = [Coupon + (V1 - V0)] / V0 - Income component: Coupon/V0 - Price change component: (V1-V0)/V0 The price change component is negative for premium bonds, positive for discount bonds, and zero for par value bonds.

Nominal Risk-Free Rate Equation

Nominal Risk-Free Rate = Real Risk-Free Rate (RF) + Premium for Inflation

Bond Trading Types

Premium bond = Bond price is greater than the face value - Coupon rate > Current yield > YTM Discount bond = Bond price is less than the face value - Coupon rate < Current yield < YTM Par value bond = Bond price equals its face value - Coupon rate = Current yield = YTM

Required Return Equation

Required Return = Nominal RF Rate + Risk Premia for Various Risks

Realized Compound Return

The YTM assumes that all interim payments can be invested at a rate that equals the YTM on the bond. Therefore, the YTM will equal the rate of return realized over the bond's life only if the reinvestment rate equals the YTM on the bond. - If the reinvestment rate = YTM, then the realized compound return = YTM

Yield to Maturity (YTM)

The YTM is the interest rate ('r') at which: Bond value = PV of the cash flows from the bond - The YTM assumes that the investor purchases the bond today and holds it until maturity. - YTM is equivalent to the bond's IRR - Annualized YTM is referred to as Bond Equivalent Yield or Annual Percentage Rate (APR) - YTM can be interpreted as the compound rate of return over the bond's life assuming that all the interim coupons can be invested at a rate = YTM - The reported value of YTM ignores compounding.

YTM Equation

YTM = Nominal RF Rate + Risk Premium for Default Risk + Risk Premium for Call Risk + Risk Premia for Other Risks