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A few months back, we started a series on **debt mutual fund investments**. Many retail investors avoid debt funds because they do not understand the risk / return characteristics of these investments well. The learning objective of this series is for readers to understand how debt funds work. Debt funds provide a range of solutions to a wide spectrum of investing needs across risk profiles and investment tenures. We had discussed in the first part of this series, Make Debt Funds your friend: Basics of fixed income investing Yield Curve, we had discussed the term structure of interest rates, for fixed income securities of different maturities. While the term structure of interest rates (or **yield curve**) is usually upward sloping (fixed income securities of longer maturities have higher interest rates and vice versa), the yield curve can assume different shapes. If you have not read the first post, we urge you to read it, because the yield curve has important implications on debt funds. In this post, we will discuss how **bonds, the building block of most debt funds**, work.

Bond is essentially a loan given by the investor to a company or the Government. In its most basic form, bond is a type of promissory note, where the borrower promises to repay the money loaned by you on a specified date in the future, known as the bond maturity. When you lend money to someone, unless it is to family members or close friends, you expect to receive interest from the borrower on your loan, just like you pay interest to the bank for loans (e.g. car loan, home loan etc) taken by you. Similarly if you invest in a bond, the borrower (**or debtor or the bond issuer**) promises to pay you interest (also known as **coupon**) at a certain frequency (e.g. annual, semi-annual etc).

Some readers may ask, **what is the difference between a bond and a bank fixed deposit**? There are a number of similarities and differences, which we will explain later. When you make a fixed deposit (or term deposit), you are essentially giving a loan to the bank. The bank will pay back your money at the end of the term (as specified on your fixed deposit certificate) just like the bond issuer will pay you back the investment made by you (at face value). The bank will also pay you interest at some frequency, like coupon payments.

However, there are differences between bonds and fixed deposits. Unlike fixed deposits, bonds are traded in capital markets. Since bonds can be traded, you can buy or sell bonds of different coupons and maturities at any point of time in capital market. Let us understand the implication of this a little better. Suppose the current bank FD rate is 7%. Even if you want an interest rate of 8%, no bank will offer you 8% because interest rates have fallen; however, in the case of a bond, if you want an 8% coupon, you can buy a bond issued when interest rate was 8%, from the market, provided you find a seller.

You may think why would an investor want to sell 8% coupon bond, when the current interest rate is only 7%? The investor of the 8% bond will sell, if he or she needs the money and if he or she gets the right **price**. Surely, you cannot expect to buy a 7% 5-year bond at the same price as an 8% 4-year bond. The **price of a bond** is therefore, an important concept in fixed income. The price of a bond is dynamic, based on several factors (primarily interest rates), but it is also quite scientific, unlike stock prices.

In this post, we will discuss the two most important concepts of **bond investing – the income and price**. These two concepts are also related to two important fixed income strategies, accruals and duration. Hopefully, by end of this post, you will be able to understand how debt fund managers make money for their investors.

Bond pricing is quite mathematical, depending on two factors – the interest rate and the credit risk (we will discuss credit risk in a different post), and anyway, for Government bonds there is no credit risk). For benefit of readers, who are not mathematically inclined, we will try to avoid the mathematics to a bare minimum, as much as possible; understanding mathematical equations is not important, if you have a good conceptual grasp on fixed income pricing. Price of a bond is inversely related to interest rates. If interest rate increases the price of a bond falls and if interest rates decreases, the price of a bond rises.

Why bond prices are inversely related to interest rates? It is quite intuitive, really. Remember, the bond issuer (debtor) will pay you coupons at the rate promised to you. If you are a bond investor and interest rate goes down, you will get higher return on your investment compared to investors who are looking to invest in debt because banks and new bond issuers will pay investors lesser interest rate. Naturally, the value of your bond will increase if interest rates decrease and since bonds are traded in the market you can make a profit by selling your bonds. Similarly, if interest rates increase, then the value (price) of your bond will fall.

Investors should understand that, by interest rate, here we **do not mean the repo rate set by the RBI**. By interest rate we mean the relevant (maturity specific) interest rate **on the yield curve**. **Yield curve**, as discussed in our earlier post, Make Debt Funds your friend: Basics of fixed income investing Yield Curve, is a graph, which plots interest rate or yields of Government bonds of different maturities. The RBI repo rate has a direct impact on yields, but it depends on a variety of other macro factors like, fiscal deficit, inflation, demand and supply of credit etc.

Income from bonds is the **coupon** (interest) you receive from the bond issuer (debtor). We had discussed in the previous section that, price of a bond is inversely related to interest rates. However, if you plan to hold the bond till maturity, the price changes of the bond do not matter to you. Irrespective of what the bond price is, in the market, you will continue to receive coupon payments from the issuer (as promised by the issuer) and on maturity of the bond you will get the face value (as promised by the issuer).

At this stage, we must mention that, the bond issuers may not always keep their promise, but this topic is for another post. For the purpose of this post, you should know that the Government, as bond issuer, will never default; also, if the credit rating of a bond issuer (debtor) is very high, there is very little chance that they will default. Therefore, if you are simply looking for income from your bond, all you have to do is to buy a bond of high credit quality and hold it till maturity. It is important to understand price and income from a bond, because that is how your debt fund managers make money for you.

Debt fund managers usually employ two strategies:-

### Hold till Maturity:

This is also known as accrual strategy, by which the fund invests in certain types of fixed income securities (or bonds) and hold them till maturity of the bond, earning the interest offered by the bond over the maturity period.### Duration Calls:

Using this strategy the fund manager, takes a view on the trajectory of interest rates and gain in terms of capital appreciation.

The **debt fund** managers specify the type of investment strategy in the scheme information documents and therefore, investors should read the documents carefully, in order to take an informed investment decision. Readers should note that, the price sensitivity of a bond is directly related to the maturity of the bond. Bonds of shorter maturity are less sensitive to interest rate changes, while bonds of longer maturity are more sensitive. There are two important bond concepts that investors should understand to get a **quantitative** understanding of the **risk / return characteristics** associated with these two investment strategies.

### Yield to Maturity:

Yield to maturity (YTM) is the return which a bond investor will get by holding the bond to maturity. For a debt fund, it is the return which the fund will get by holding the securities in its portfolio to maturity. For example if a debt fund’s portfolio has a YTM of 10% and a duration of 2 years, it means that, assuming no change to the portfolio, the fund will give 10% returns, as long as it holds the securities in its portfolio till they mature, i.e. for 2 years.### Modified Duration:

Let us first understand what**duration**is. Duration is the measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows of the bond. Remember there are two kinds of cash flows in a bond, interest payments and principal payment.

Some bonds pay the interest along with the principal on the maturity of bond. These are known as zero coupon bonds. Zero coupon bonds in India are issued at a discount to face value and you will get the face value on maturity. The duration of a zero coupon bond is the same as the maturity of the bond. However, there are some bonds which make interest payments also known as coupon payments to the investors at fixed interval, e.g. yearly and the principal is repaid on maturity. These bonds are known as vanilla bonds. Since a vanilla bond makes coupon payments on a regular basis to the investor, the investor recovers his investment well before the maturity of the bond. Let us assume you invested~~र~~100 in 20 year 10% coupon bond. If your bond pays 10% coupon, in other words, interest of~~र~~10 every year, you will recover your investment in 10 years, much before the maturity of the bond.

The**duration**of a vanilla bond is less than the maturity of the bond. However, you should understand that duration of the bond in the above example is not 10 years. The concept of**duration**factors in the time value of money. Simply put, the interest payment received next year is not equivalent to the interest received after 5 years, because the value of money goes down with time. This concept of duration in finance lingo is known as**Macaulay duration**.

Let us now understand what**modified duration**is.**Modified duration**, is simply the price sensitivity of a bond to changes in yields or interest rates, in other words modified duration is the change in the price of a bond with a change of 1% in interest rate. So if the modified duration of a bond is 10 years and interest rates go down by 1%, then the bond price will increase by 10%. It is as simple as that!

You must be wondering why we went into such a long explanation of duration, if modified duration is such a simple concept. The concept is simple, but the calculation of modified duration is not simple. The calculation of Modified Duration is very similar to Macaulay Duration. Even the numerical values are close. However, you should note that, while they are close, they are not the same. The calculations of Macaulay and Modified Durations are a little complicated, but as mutual fund investors you should worry about the calculations, because the fund fact sheets and various research websites have information on the Modified Duration of a fund. Simply remember, that if you expect interest rates to change a certain percentage, you can multiply the percentage change in interest rates with the modified duration to see how much the NAV will change.

If we combine the two concepts, Yield to Maturity (YTM) and Modified Duration, we can come up with a quantitative construct to calculative *indicative returns* based on certain assumptions. Suppose you invest ~~र~~ 100,000 in a Debt Fund portfolio which has a Yield to Maturity of 8% and Modified Duration of 10 years (you can find this information in fact sheet). Your investment horizon is 3 years. You assume that in the next 3 years, interest rates or yields will decline by 2%. The expected return will be:-

On an annualized basis, in percentage terms, the return will be around 13%. However, please note that this is only a rough approximation of returns. You obviously need to deduct the expense ratio of the fund from the gross returns, to get the actual net returns. Further, the YTM and modified duration of fund portfolio may change over time.

Finally, the actual trajectory of yields may be different from what was expected. For example, if the change in yields was only 1% instead of the expected 2%, returns will be lower (you can do the calculations yourself, based on the suggested equation). Now, what if interest rates rose by 1%, instead of falling by 2%? You would still get a positive return after 3 years. What if interest rates rose by 2%, instead of falling 2%? Your gross returns, before expense ratio, will still be positive.

**Conclusion**

Bonds are the most common type of securities in the portfolio of **debt mutual funds**. Apart from bonds, commercial papers (CP) and certificates of deposits (CDs) are the two other types of securities that **debt mutual funds invest in**. Usually, liquid funds and ultra short term debt funds, invest in the majority of their corpus in these securities. CPs and CDs are also fixed income securities like bonds paying interest and face value on maturity. However, unlike bonds, these securities have short maturities (less than a year) and instead of paying interest on a regular frequency like bonds, these securities are issued at discount to the face value. In this post, we have discussed how **bonds, the building block of most debt funds**, work. In this post, we focused on the income from bonds and their price sensitivity to interest rates. In our next post, we will discuss the credit risk of bonds and their impact on prices. Please stay tuned.

**Mutual Fund Investments are subject to market risk, read all scheme related documents carefully**.

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Dwaipayan leads content production and mutual fund research in Advisorkhoj.com. He is actively involved in business development strategy, driving revenue growth and profitability, delivering superior customer satisfaction and talent development in Advisorkhoj. An alumnus of IIM Ahmedabad, Dwaipayan is a Finance and Consulting professional, with nearly 17 years of management and consulting experience in financial services domain across several geographies. In his previous corporate role, Dwaipayan was the Chief Financial Officer of American Express Global Business Services in India. He also co-founded a boutique consulting start-up to advice companies on business restructuring initiatives like private equity funding, mergers & acquisitions, divestitures, outsourcing and organizational restructuring. Dwaipayan has a strong track record of driving superior financial performance and developing talent in the organizations he has been involved with. He can be followed on his Twitter handle @DBadvisorkhoj.

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