READING 60: RETURNS, SPREADS, AND YIELDS

Gross and Net Realized Returns

        The gross realized return for a bond is the difference between end-of-period total value (including end-of-period price and coupons) and starting period value divided by starting period value:

         The net realized return for a bond is its gross realized return minus per period financing costs.

Spread of A Bond

        The difference between bond market price and bond model price (according to the term structure) is known as the spread. A bond’s spread helps investors identify whether fixed-income investments are trading cheap or rich.

Yield-To-Maturity

        Yield is an internal rate of return found by equating the present value of the cash flows to the current price of the security. An iterative process is used for the actual computation of yield. On a financial calculator, it can be found by inputting all other variables and solving for YTM.

Compute A Bond’s YTM

        For a security that pays a series of known annual cash flows, the computation of yield uses the following relationship:

Annuity and Perpetuity

        The present value, or price, of a perpetuity can be found by dividing the coupon payment by the YTM.

Spot Rates and YTM

        When pricing a bond, YTM or spot rates can be used. The YTM will be a blend of the spot rates for the bond.

The Relationship Between YTM, Coupon Rate, and Price

        If two bonds are identical in all respects except their coupon, the bond with the smaller coupon will be more sensitive to interest rate changes.
         When the bond is trading at par, the coupon rate is equal to the YTM. When the bond is trading below par, the coupon rate is less than the YTM, and is said to trade at a discount. When a bond is trading above par, the coupon rate is greater than the YTM, and the bond then trades at a premium.

Bond Return decomposition

        A bond’s P&L is generated through price appreciation and explicit cash flows. Total price appreciation can be broken down into three component parts for price effect analysis: carry-roll- down, rate changes, and spread change.

Carry-Roll-Down Scenarios

        For an expected term structure, no change scenarios include: realized forwards, unchanged term structure, and unchanged yields. Realized forwards assume that forward rates are equal to expected future spot rates. Unchanged term structure assumes that the term structure will remain unchanged. Unchanged yields assume that bond yields remain unchanged.