What is Income Fund duration and modified duration?

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	One may be well aware of the risks inherent in investing in equity markets. But do you fully understand the risks associated with the bond markets? While the risk of default is always innate, a more measurable and inflicting form of risk in bond markets is the interest rate risk. We are aware that interest rates and bond prices are inversely related. Let's consider an investor who has recently purchased a 5 year bond with a face value of Rs. 1000 with a coupon of 6%. Now, if the interest rates rise to 7%, the bond that the investor had bought becomes a less attractive proposition for other investors and consequently its price comes down. But how do we determine the volume of change in the bond price? A fund manager may be interested in knowing the volume of change in the bond price when there is a certain change in interest rate. Duration captures this interest rate sensitivity of a bond. Read on further to appreciate the dynamics between bond duration and prices and how interest rates, coupon rate and maturity affect the duration.
Duration and Average Maturity When there is a movement in the interest rates, different bonds will show a different price change. Some bonds may have greater while others may have lesser sensitivity with respect to interest rate changes. This sensitivity is measured by duration. In other words, duration measures the price sensitivity of a bond with interest rate movements. The measurement is based on the average time to maturity of its interest and principal cash flows. Before delving in further, it is essential to differentiate between the average maturity of a portfolio and its duration. The average maturity and duration of a bond fund are simply the weighted averages of individual security's maturities and durations respectively. By average maturity, we understand that it represents the amount of time remaining for the bond to mature. The longer the maturity of a bond more is the interest rate risk as probability of volatility in bond prices is more. Having said that, the maturity does not take into account the coupon rates of different bonds while comparing them. Hence, it is a deficient measure for comparison of bonds. Two ten year bonds having same face value and coupon of 5% and 7% respectively will thus have the same maturity. However, we require a measure which considers both the coupon and principal cash flows as bond with 5% coupon will be more sensitive to interest rate changes than the 7% coupon bond. Duration is an appropriate measure here as it enables one to compare the bonds with different coupons and maturities. Duration of 4 would mean that the bond prices would rise 4% for every 1% decline in interest rates and would fall 4% for every 1% rise in interest rates.Fixed income portfolio managers can earn above average returns by capitalizing on the duration parameter while comparing bonds. Effective duration, Macaulay duration and Modified Duration Effective duration is the ratio of percentage change in bond price to change in yield in percent. Mathematically, Effective duration= -(percentage change in bond price)/ change in yield in percent From this relationship, we can easily approximate the change in bond price when there is a change in the interest rates. If the duration of a bond is 4.5 and its current price is 980 an increase in the interest rates by 2% will change the bond price by Price change= -4.5*0.02*980= -88.2 Thus we see that an increase in interest rates by 2% brings down the price of the bond by Rs. 88.2 Here it would be appropriate to introduce the concept of convexity. It has been observed that for a plain vanilla bond, the price change in response to rising rates is smaller than the price change in response to the falling rates. In other words, an option free bond is more sensitive to decrease in interest rates than to an increase in the interest rates. For accounting of this fact, we modify the formula for effective duration as: Effective duration=(bond price when yields fall-bond price when yields rise)/(2*initial price of bond*change in yield in decimal form) Two other adaptations of duration are Macaulay duration and Modified duration. Macaulay duration simply estimates the interest rate sensitivity of a bond until the cash flows arrive. It is calculated in years. For instance, a 3 year zero coupon bond will have Macaulay duration of 3 as its cash flows will arrive only after 3 years. A fall in yield by 1% will entail a 3% rise in price for this bond. While Macaulay duration is based on the expected cash flows, modified duration is a slightly refined versionas it takes the current yield to maturity into account and discounts the cash flows to arrive at duration. Thus Modified duration can be expressed as: Modified duration= Macaulay duration/ (1+periodic market yield) One drawback of modified and Macaulay duration is that they consider cash flows to be constant. This is suitable only for a plain vanilla bond and not bonds with embedded options. Effective duration is the preferred measure as it gives interest sensitivity measure suitable for both option free and bonds with embedded options. Fund managers increase the average duration of the portfolio when they expect a decline in the interest rates so as to profit from the corresponding increase in the bond prices. When they expect interest rates to increase, they reduce the average duration of the portfolio to minimize the effect of decline in the bond prices. Factors affecting duration Coupon rate: The bond with high coupon has lesser duration. This is because high coupon is accompanied with low volatility while lower the coupon, higher the volatility. A higher coupon bond provides higher coupon cash flows to the bond holder and he recovers his original cost faster than the lower coupon bond holder. Time to maturity: A longer maturity bond will have higher duration as it has high price volatility and it will take longer time for the bondholder to recover his original cost. Similarly, a lower term to maturity implies lower price volatility and lower duration. In general, it would be advantageous for fund managers to advise their clients to hold bonds with higher coupon and lowerterm to maturity as the cash flows would be higher and quicker and duration of the portfolio will be lower. This is the case when bondholders plan to hold the investment till maturity. However, interest rates play a bigger role when we consider the bond prices. This is why the fund managers should recommend shorter duration portfolio to the investors when they foresee a rise in the interest rates. On the contrary, if fund managers anticipate a decline in the interest rates, they should recommend lower coupon and longer term bonds to the investor. A higher duration bond in such a scenario would lead to increase in the bond prices and hence benefit the investors. This is the case when investors are not really planning to hold the investment till maturity and may look for speculating opportunities to take advantages of increase in bond prices and interest rate movements.

 

 

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