6.3 Principles of Bond Pricing (Summary)
Exercise
Can you explain each of the following principles? (Many of these are related to the time value of money.)
- Ceteris paribus, bond prices will change with the mere passage of time (unless they are priced at par). That’s Maturity Pull!
- Dollar price and Yield-to-Maturity are inversely related. That’s TVM! (Discount rate goes up, price goes down – and vice versa.)
- Longer-term bonds are more sensitive to changes in yield. That’s TVM!
- We tentatively showed that for a Zero-coupon bond, but that will also be true for positive coupon bonds.
- The price sensitivity to changes in yield increases with maturity, but at a decreasing rate. That’s TVM! Remember: PV = Price.
Concepts Review
- “Sensitivity” or “Volatility” refers to the extent to which a bond’s price will change given a change in market yield. The more the price changes, the more sensitive to yield changes the bond is said to be.
- Think of a bond as a portfolio, or collection, of coupon payments. The more distant the payments are, the more sensitive each payment will be. Thus, the longer the term of the bond, the longer many of its payments will be, and the more sensitive the bond overall.
Think of a Zero-coupon bond as our base case in comparison to other bonds.
- The higher a bond’s coupon, the less sensitive its dollar price will be to yield changes (and vice versa). A Zero-coupon has only one, very distant, and hence “volatile,” payment occurring at the horizon. A positive coupon bond has some cash flows coming in sooner and those earlier inflows will be less price-sensitive to yield changes.
- Coupon and price are positively related (all else equal). A Zero-coupon bond will have the lowest possible price, the greatest discount. As the coupon increases, so will the dollar price.
On a related note…
There are two elements – or concepts – that must be considered in calculating a bond’s actual return to the investor:
- Price risk: when rates go up (down) bond prices go down (up). This is simply the effect of the Time Value of Money (present values).
- Reinvestment Rate risk: since the YTM is the same Mathematically as a bond’s IRR, it is assumed in calculating the YTM that interest payments are reinvested at the bond’s YTM (IRR). However, if reinvestment rates differ from the YTM along the duration of the bond’s life, actual, or “realized” returns will differ also. If interim rates decrease, so too will “realized returns.”
