Spot and Forward Rate Essay Example

year T- bond is yielding YTM =8%,what is the expected return on a 10 – year bond starting at the end of Year 5 ? Bond’s Duration The formula use to calculate the bonds basic duration is the Macaulay duration, which was created by Fredrick Macaulay in 1938. it, has been commonly used since 1960s. It is also known as Macaulay’s duration.

Bond duration is the average amount of time required by the security to receive the interest and the principle. Therefore duration is a weighted average of time that interest payments and the final returns of principle received. The weights are present value of payments, using the bonds yields to maturity as the discount t rate. The duration, therefore, calculated the weighted average of the cash flows (interest and principal payments) of the bond, discounted to the present time. Duration is stated in terms of years. The duration measure will predict by how much a bonds price should change given a 1% change in interest rate.

Thus, a bond with duration of 4 years will decrease by 4 % in price if the yields rise by 1%. Duration helps an investor to identify the percentage change in the price of a bond. For example, if a bond has duration of 8 years and interest rate falls 6% to 4% ( a drop of a 2% point), the bonds price expected to rise by 16% (8 ? 2). The duration of bonds can be computed by the following formula:

Or, D = (W x T) PV (Ct)= PRESENT VALUE

OF the cash flows to be received at time t P0=current market price of bond T= bond remaining life

D = Macaulay s duration Alternatively,

1+ y _ (1+y ) + T (c –y)

D = y c [(1+ y)n – 1] + y

Where, C= the annual coupon rate (as a percentage) T = the number of years to maturity Y= the yield to maturity Illustration 1 Consider a Rs. 1000 bond with three years to maturity and a 9% coupon rate. Currently, the rate of interest on comparable bonds is 12%.

Duration of 2. 75 years mean that the bondholder collects, on the average, all the payment in 2. 75 years. Clearly, all the payments are not made exactly in 2. 75 years into the future. Rs. 90 is received at the end of year one, Rs. 0 received at the end of year two: and R. 1090 is received at the end of year three. The weighted average of all these payments is 2. 75 years. Duration may be computed when payments arte semiannual: in which case the annual payment and interest rate on comparable debt are divided by 2 and the number of payment is multiplied by 2.

By making this calculation for bonds with different coupon and different maturities, the investor standardized for price fluctuation. Bonds with the same duration will experience similar price fluctuations, while the prices of bonds with a longer duration will fluctuate more. Since bonds with larger durations are more volatile, investor reduces the risks associated with changes in the interest rates by acquiring bonds with shorter durations. If two bonds have same term to maturity, the bond with the smaller coupon will have the longer duration, since the larger proportion of the bonds total payment is repayment of principle.

If

two bonds have the same coupon, the one with the longer maturity have the longer duration, as the payment s is spread over a longer period of time. Duration is used by professional portfolio managers such as managers of pension plans, who know where and what amount of funds will be needed. This professional investor seeks to match the duration of their portfolios with the timing of the need for funds. Such match reducing the interest rate risk associated with the portfolios. Modified duration Modified duration is version of the Macaulay duration that accounts for changing interest rate.

Because they affect yield, fluctuating interest rates will effect duration. Therefore, modified duration shows how much the duration changes for each percentage in yield. There is an inverse relationship between the modified duration. Formula shows how a bonds duration changes in a relation to interest rate movements, the formula is an appropriate for investor wishing to measure the volatility of a particular bond. The formula for modified duration is:

Modified duration = D/[1+y/m]

Duration is key concepts in fixed income portfolio management for three reasons. First it is the average maturity period of the portfolio. Second, it is essential tools in immunizing interest rate sensitivity of a portfolio. Duration also is used to determine the amount by which a bond price will fluctuate for small changes in interest rate.