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Where: P m =the current market price of the bond n = the number of years to maturity C i = the annual coupon payment for bond i i = the prevailing yield to maturity for this bond issue P p =the par value of the bond
The value of the bond equals the present value of its expected cash flows
where: P m = the current market price of the bond n = the number of years to maturity C i = the annual coupon payment for Bond I i = the prevailing yield to maturity for this bond issue P p = the par value of the bond
Nominal Yield Measures the coupon rate Current yield Measures current income rate Promised yield to maturity Measures expected rate of return for bond held to maturity Promised yield to call Measures expected rate of return for bond held to first call date Realized (horizon) yield Measures expected rate of return for a bond likely to be sold prior to maturity. It considers specified reinvestment assumptions and an estimated sales price. It can also measure the actual rate of return on a bond during some past period of time.
Any long-term interest rate simply represents the geometric mean of current and future one-year interest rates expected to prevail over the maturity of the issue
Long-term securities should provide higher returns than short-term obligations because investors are willing to sacrifice some yields to invest in short-maturity obligations to avoid the higher price volatility of long-maturity bonds
Magnitudes and direction of yield spreads can change over time
29.
What Determines the Price Volatility for Bonds
Bond price change is measured as the percentage change in the price of the bond
Where: EPB = the ending price of the bond BPB = the beginning price of the bond
30.
What Determines the Price Volatility for Bonds
Four Factors
1. Par value
2. Coupon
3. Years to maturity
4. Prevailing market interest rate
31.
What Determines the Price Volatility for Bonds
Five observed behaviors
1. Bond prices move inversely to bond yields (interest rates)
2. For a given change in yields, longer maturity bonds post larger price changes, thus bond price volatility is directly related to maturity
3. Price volatility increases at a diminishing rate as term to maturity increases
4. Higher coupon issues show smaller percentage price fluctuation for a given change in yield, thus bond price volatility is inversely related to coupon
32.
What Determines the Price Volatility for Bonds
Since price volatility of a bond varies inversely with its coupon and directly with its term to maturity, it is necessary to determine the best combination of these two variables to achieve your objective
A composite measure considering both coupon and maturity would be beneficial
Duration is defined as a bond’s price sensitivity to interest rate changes
Higher the duration, greater is the sensitivity
Number of years to recover the trust cost of a bond
For instance, if the interest rate increases from 6% to 7%, the price of a bond with 5 years duration will move down by 5%, and that of 10 years duration by 10%....... so on.
Bond price movements will vary proportionally with modified duration for small changes in yields
An estimate of the percentage change in bond prices equals the change in yield time modified duration
Where: P = change in price for the bond P = beginning price for the bond D mod = the modified duration of the bond i = yield change in basis points divided by 100
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