Debt based Mutual Fund schemes that invests in fixed income instruments, such as Corporate and Government Bonds are considered to give stable returns and are often proposed as an alternate to Fixed Deposits. In the last post here we saw these funds are also subject to market conditions and can depreciate in value during short periods. This price depreciation is caused by the prevailing interest rates in market, if interest rates increases bonds prices experiences
a drop and thus the funds holding the bonds also drops in value. Similarly if interest rates decreases the debt funds will experience price appreciation.
As an investor just knowing when a price would increase or decrease is not sufficient, we would also like to know by how much. Let’s say we expect that after RBI’s next notification the interest rates would fall by 0.5%, we can deduce that the prices of debt based funds would increase so investing in these funds makes sense. But by how much the value would increase?, will the value of all funds increase by same percent or some bonds will have higher/lower impact? The answers to these questions lie in duration of the bond.
What is Duration?
Duration conceptually is the time the investor takes to recover their invested money in the bond through coupons and principal repayment. For example, consider a four-year bond with a maturity value of ₹ 1,000 and a coupon of ₹ 50 paid annually. The bond pays back principal amount on the final payment. Given this, the following cash flows are expected over the next four years:
Period 1: ₹ 50
Period 2: ₹ 50
Period 3: ₹ 50
Period 4: ₹ 50 + ₹ 1,000 = ₹ 1,050
If the market interest rates are at 7%, the fair value of this bond will be ₹ 932. The Macaulay Duration of this bond when calculated comes out to be 3.72 years. This means an investor who would invest ₹ 932 to buy the bonds will be able to recover their money in 3.72 years using the cashflows and principle payments.
Note: Macaulay Duration is often confused with the maturity period of the bond. For the above bond maturity period is 4 years which is the time when the investor will receive all the investment, Macaulay Duration is instead the period by when the investor will receive the amount they invested which is ₹ 932, the fair value investor paid to buy the bond. Macaulay Duration is thus always less than the maturity duration of the bond as invested amount will be recovered first and then the interest will be recovered.
What are the uses of duration?
The duration is an important concept in bonds market as it defines how sensitive a bond is to fluctuating interest rates. For example the above bond had following characteristics:
Maturity Amount: ₹ 1,000
Coupon: ₹ 50
Maturity Term: 4 years
Market Interest Rates: 7%
Fair Value: ₹ 932
Macaulay Duration: 3.72 years
Coming back to our original quest if an investor wants to know that what will be the fair value of the bond in case of market interest rate fluctuation. The answer is fair value will change approximately by change in interest rate * bond duration.
% Δ fair value = – (Δ Interest Rate * Bond Duration)
If the interest rates increases by 1% bond prices will approximately change by –(1%*3.72) = -3.72%. When calculated mathematically bond price moves to ₹ 901 (-3.5%). In other direction if the rates decreases by 1% bonds prices should change by +3.72% and when calculated mathematically if changes to ₹ 965 (+3.7%).
Conclusion
Duration of the bond can give investors a signal of what will be the impact of in market interest rates to prices of bonds and ultimately the debt mutual funds. The duration of debt mutual funds are generally reported in the fact sheets produced by AMCs which is helpful for investors to take investment decisions. An investor wants immunity from interest rate fluctuation would like to choose a fund with lower duration and investor who wants inflation protection in longer run would choose for fund with higher duration.
Hitesh Gulati, CFA 