You appreciate an umbrella in a rainy day more, notwithstanding you bought it to save yourself from the sun. Life is like that so are the seasons. Let us not “lo and behold” the season we are in and move on to learn something in between. Actually, in a first month of my new job in the new role of DCM guy, I have been told to find out the Average Maturity of a couple of bonds, which desk was weighing out for prospective trades. The ‘Umbrella’ in the case in point is a simple excel which calculates average maturity.
I had learnt this calculation in the context of loan, as a Project Finance guy, to find out whether the loan structure is eligible for Reserve Bank of India (RBI) approved External Commercial Borrowing (ECB).Typically for an ECB facility, the Average Maturity of the loan should be less than 5 years. However, I used the same excel for structuring few bond proposals to enhance the returns using Duration play. So before we move on to the most important chapter of a book called-Bond, we should get acquainted with basic fundamentals of the game.
Interest Rate – Bond Price-Yield trinity decoded
So we all agree that the interest rates and price of bonds are interlinked. When interest rates move down, the prices of the bond move up. Hmm.. Okay… But is it well understood why this is so? Let me try. My answer is simple:
- Bond is a fixed coupon instrument. The coupon factors the existing interest rate, so at the time of issuance the coupon is at par with the interest rate. However when interest rate changes (let us assumes falls), the security holder starts enjoying an interest rate arbitrage at the expense of Issuer. As we know that an arbitrage cannot exist forever, so other guys jumps in to buy that security as it will continue to service the pre fixed coupon. This tilts the demand supply scenario in the favour of the seller and hence the price of bond rises.
- As a corollary, hence yields also falls as by definition it is inversely proportion to the price.
Yield=Coupon/Price
The image above summarizes the motions. On the other hand, when the interest rates move up, the prices of bond move down. Why??Now you can guess.
- As the interest rates goes up the coupon is lesser than the prevalent market interest rate, so the returns on the bond perishes, which leads to investors selling the bonds, which ultimately leads to oversupply of bonds and hence the price of the bond goes down.
Duration Play and How Bond traders play on Duration?
Duration is defined as the measure of sensitivity of Bond price to a change in the interest rate. Besides Interest rate, Duration also gets impacted by Coupon rate and hence yields. Bonds with high coupon rate have lower duration and vice-versa. Why is it so? It is very common-sensical. Look it from a bond investor’s point of view.
- If, I am receiving higher time bound coupon, so why on earth I would be bothered about what is happening to interest rate (knowing I have got enough).Henceforth the price of the bond would be slightly immune to the deltas in interest rate.
- Since yield follows coupon, so yield would also be inversely proportional to Duration.
Now the below mentioned diagram which depicts the motions of these variables, would make complete sense to you.
Let me draw a simile here. People, who invest in stock market, know the term called Beta. Beta is the measure of price volatility of a stock with a change in the market as a whole. Duration is its bond counterpart in many ways.
When Keynes famously said:” In the long term we all are dead”. He also meant one more thing. Longer the tenor, closer you are to death so higher the risk of death. And as the death is the mother of all risks. The risk perception and hence volatility of bond price goes up, ceterus paribus, when we increase the tenor of a bond. If the coupon rate and the bond’s initial price are constant, the bond with a longer term to maturity will display higher price volatility and a bond with a shorter term to maturity will display lower price volatility.
Show me the Moolah
So when the desk has a firm view about movements of interest rate, then it takes a conscious call to play on bond’s duration. It translates into buying high duration papers and holding it for some time till the anticipated rate change occurs. To summarize the discussion so far, the secret sauce here is:
- An investor who predicts that interest rates will decline would best potentially capitalize on a bond with low coupon payments and a long term to maturity (longer average maturity), since these factors would magnify a bond’s price increase.
Let us move on to how to execute this money spinner concept. Average maturity is the lever through which a trader can play on Duration.
Average Maturity of a Loan
Let’s go back in time and open the umbrella first. The excel below helps a commercial banker to find out the average maturity of loan in RBI approved format.
- A loan of 400 has been taken and it has a 10 years repayment schedule.
| Date of Disbursement (drawal)/Repayment | Drawdown amount | Repayment amount | Outstanding Balance | No of days balance with Borrower | Product |
|---|---|---|---|---|---|
|
01-04-2015 |
100 |
100 |
90 |
0.06 |
|
|
01-07-2015 |
100 |
200 |
90 |
0.13 |
|
|
01-10-2015 |
100 |
300 |
90 |
0.19 |
|
|
01-01-2016 |
100 |
400 |
360 |
1.00 |
|
|
31-12-2016 |
40 |
360 |
360 |
0.90 |
|
|
31-12-2017 |
40 |
320 |
360 |
0.80 |
|
|
31-12-2018 |
40 |
280 |
360 |
0.70 |
|
|
31-12-2019 |
40 |
240 |
360 |
0.60 |
|
|
31-12-2020 |
40 |
200 |
360 |
0.50 |
|
|
31-12-2021 |
40 |
160 |
360 |
0.40 |
|
|
31-12-2022 |
40 |
120 |
360 |
0.30 |
|
|
31-12-2023 |
40 |
80 |
360 |
0.20 |
|
|
31-12-2024 |
40 |
40 |
360 |
0.10 |
|
|
31-12-2025 |
40 |
0 |
0 |
||
|
Average Maturity |
5.88 |
||||
- Tip: Use DAYS360 function to find out the No of days balance with Borrower. Product Column is a product of ‘No of days balance with Borrower’ and Outstanding.
Average Maturity of a Bond
- It tells the investors how sensitive a bond is to change in interest rates. Average maturity of a Zero Coupon Bond is the tenor.
- For coupon paying bonds, the average maturity is similar to the calculation of average maturity of loan minusDAY360 function. The no of days balance with borrower is simply calculated as difference between two dates of drawal/repayment.
Structuring of bond to suit the Duration Play
It can be done using the excel below. The excel is the redemption schedule, which has reduced the Average Maturity of the 400 Face Value,10 year tenor bond to 9 years.
| Date of Disbursement (drawal)/Repayment | Drawdown amount | Repayment amount | Outstanding Balance | No of days balance with Borrower | Product |
|---|---|---|---|---|---|
|
01-01-2015 |
400 |
400 |
364 |
1.00 |
|
|
31-12-2015 |
0 |
400 |
366 |
1.00 |
|
|
31-12-2016 |
0 |
400 |
365 |
1.00 |
|
|
31-12-2017 |
0 |
400 |
365 |
1.00 |
|
|
31-12-2018 |
0 |
400 |
365 |
1.00 |
|
|
31-12-2019 |
0 |
400 |
366 |
1.00 |
|
|
31-12-2020 |
100 |
300 |
365 |
0.75 |
|
|
31-12-2021 |
0 |
300 |
365 |
0.75 |
|
|
31-12-2022 |
100 |
200 |
365 |
0.50 |
|
|
31-12-2023 |
0 |
200 |
366 |
0.50 |
|
|
31-12-2024 |
0 |
200 |
365 |
0.50 |
|
|
31-12-2025 |
200 |
0 |
0 |
||
|
Average Maturity |
9.0 |
||||
- If the portfolio of a debt fund is loaded with long-term bonds i.e. high average maturity bonds, it will be highly sensitivity to interest rates movements. So this card needs to be played with a lot of conviction and gumption to load the portfolio with high duration bonds.
Conclusion
So the final answer to the captioned question for a person who strongly feels that interest rate is going to go down is: Invest in a bond with low coupon payments and a long term to maturity. Period.
Sadhan 