Question

b) Consider a risk-free bond. “Macaulay duration is a weighted average of the times to payment of a bond's cashflows and therefore is a natural measure of a bond's interest rate risk.” Assess this statement, paying particular attention to why times to cashflow are important for the determination of interest rate risk and why the particular mathematical form of the duration measure is the right way to measure such risk.

Answer 1

A risk-free bond refers to a bond issued by an entity that's considered absolutely bound to pay back both its principal and interest, with no risk of default. Generally, bonds issued by governments of sovereign developed nations, such us U.S. Treasury bonds, are considered to be risk-free.

In practice, government bonds of financially stable countries are treated as risk-free bonds, as governments can raise taxes or indeed print money to repay their domestic currency debt. as an example , us Treasury notes and us Treasury bonds are often assumed to be risk-free bonds.

Duration is usually utilized in portfolio and risk management of fixed-income instruments. Using rate of interest forecasts, a portfolio manager can change a portfolio’s composition to align its duration with the expected level of interest rates.

The Macaulay duration is that the weighted average term to maturity of the cash flows from a bond. Macaulay’s duration may be a measure of a bond price sensitivity to changes in market interest rates.The weight of every income is decided by dividing this value of the income by the worth . Macaulay duration is usually employed by portfolio managers who use an immunization strategy.

In general, the upper the duration, the more a bond's price will drop as rate of interest s rise (and the greater the interest rate risk). Likewise, if interest rates fall by 1%, an equivalent bond's price will increase by about 5% (1% X 5 years). Certain factors can affect a bond's duration, including: Time to maturity.

The metric is known as after its creator, Frederick Macaulay. The Macaulay duration are often viewed because the economic balance point of a gaggle of money flows. differently to interpret the statistic is that it's the weighted average number of years an investor must maintain an edge within the bond until this value of the bond's cash flows equals the quantity purchased the bond.

The rate of interest risk may be a function of how farther the cash flows of a bond are from zero. A zero-coupon bond has higher rate of interest risk that a coupon-paying bond of an equivalent maturity. The Macaulay’s duration assesses the rate of interest risk with regard to the duration of a zero-coupon bond. The duration of a zero-coupon bond equals its time duration, i.e. its maturity (in years). The duration of a coupon-paying bond are often calculated by considering each income as a separate zero-coupon bond.

How to Calculate Macaulay Duration

The Macaulay Duration formula reflects the very fact that Duration = Present value of a bond’s cash flows, weighted by the length of your time to receipt, and divided by the bond’s current market price .

Factors Affecting Duration

A bond's price, maturity, coupon and yield to maturity all factor into the calculation of duration. All else equal, as maturity increases, duration increases. As a bond's coupon increases, its duration decreases. As interest rates increase, duration decreases and therefore the bond's sensitivity to further rate of interest increases go down. Also, a fund in situ , a scheduled prepayment before maturity and call provisions lower a bond's duration.

Macaulay duration is beneficial in immunization, where a portfolio of bonds is made to fund a known liability. Modified duration may be a n extension of Macaulay duration and is a useful measure of the sensitivity of a bond’s price (the present value of its cash flows) to rate of interest movements.

It is a measure of the time required for an investor to be repaid the bond’s price by the bond’s total cash flows. The Macaulay duration is measured in units of your time (e.g., years).

The Macaulay duration for coupon-paying bonds is usually less than the bond’s time to maturity. For zero-coupon bonds, the duration equals the time to maturity.