##### October 25, 2016

### Important Factors for Bonds Evaluation

###### Kishorkumar Balpalli

###### Founder & CEO myMoneySage an award-winning Fin-Tech startup

**3 Important Factors for Bonds Evaluation**

As an advisor, I am sure you will agree with me that bonds have a place in every portfolio and evaluating bonds may not be as simple as it is perceived to be. While investing in bonds, you may have given coupon rates an in-depth thought. But apart from that, there are other critical factors that should be taken care of. You need to compare the bonds by price because it ultimately helps in assessing the bond yields. Needless to explain that prices are affected by the fluctuating interest rate regime thereby influencing the yields. Then, duration becomes another significant concern wherein you analyse the bond by the years taken by it to repay the purchase price.

For an in-depth understanding, let me take you through a detailed analysis of each of these factors in a practical manner:

**1. Bond Price**

As you know, price forms a primary consideration in all kinds of investment decisions. In the case of bonds also, price helps you to ascertain the overall position of the bonds on interest rates. Usually, a bond sells at a premium when it offers a higher coupon rate than the prevailing interest rates. Conversely, when the coupon rate of the bond is lower than the current rates, then the bond price is lowered to attract the investors.

So, it becomes vital for you to know how to determine the price of the bond. The basic assumption underlying the bond price estimation is that the coupon payments are reinvested at the same interest rate upon receipt. Using the following formula, in case of annual coupon payments, you may arrive at the correct bond price:

In case you receive coupon payments more than once in a year, then use the formula below:

Sometimes, you may purchase Zero-coupon bonds which are issued at deep discounts and redeemed at par value. Instead of regular coupon payments, what you earn is the difference between the issue price and face value. To calculate the price of Zero-coupon bonds, use the formula below:

**2. Yield **

After determining the price of the bond that you are willing to pay, it’s time to determine what returns you are going to earn out of the entire investment. You refer to the current yield at the time of purchasing a bond from amongst competitive offerings similar maturity and credit quality. Current Yield comprises the regular Coupon payments along with gradual gain/ loss on account of fluctuations in the bond prices in the open market. It is computed as follows:

When you purchase the bond at face value, the yield is equal to the interest rate. As the price of the bond changes, the yield also changes. Suppose you buy a bond of 10% coupon rate at Rs 1000. The yield on the bond will be 10% (i.e. Rs 100/Rs 1000). If the price of the bond rises to Rs 1500, the yield would fall to 6.67% (i.e. Rs100/Rs1500)

At this juncture, it becomes pertinent to discuss the relationship between bond yields & prices. There is an inverse relationship between bond prices and yield. As the price of the bond increases, the bond yield decreases and vice-versa. Accordingly, the graphical representation shows a negative curve as shown below:

In case you plan to hold the bond until maturity, then you need to calculate YTM. The calculation of YTM is a much sophisticated process. It consists of all the interest payments that you will receive assuming that the same will be reinvested at the current yield on the bond, par value and any gain. You may use the formula shown below to calculate YTM:

Yield to Maturity is a very useful tool that not only helps to assess the returns earned on particular bond but also enables bond selection when faced with bonds of similar maturities and coupon rates.

Imagine a situation when you want to make a choice between 2 five-year bonds having a coupon rate of 6%. In such a scenario, you need to use YTM as a selection criterion. The bond with a higher YTM should be chosen over bond with a lower YTM.

**3. Duration**

After bond prices and yields, duration becomes yet another criterion to be included in the investigation. Duration explains to a large extent the volatility inherent in bonds. Bonds with longer duration are more vulnerable to interest rate fluctuations as compared to bonds with shorter duration. Longer duration bonds will take more time to repay the purchase price using its internal cash flows.

The concept of duration is applied distinctly in the case of zero-coupon bonds and ordinary/vanilla bonds. The duration in case of zero-coupon bonds is equal to the maturity date because the entire cash flow is received at maturity. Conversely, the duration for ordinary bonds is shorter than the maturity date because the coupon payments received at regular intervals are reinvested at the current yield causing the realisation process to speed up. Apart from coupon payments, the coupon rate also affects the duration of the bond. A bond having a higher coupon rate would take lesser time to repay the price of the security as compared to a bond having a lower coupon rate.

You can make use of the duration concept to decide upon an appropriate bond that should be purchased from amongst a number of similar securities being offered in the market. The basic duration of a bond is known as Macaulay Duration. It assumes that the coupon payments received at regular intervals are being reinvested at the same interest rate. It is calculated by using the following formula:

Suppose you hold a five-year bond of Rs 1000 par value and coupon rate of 5%. Consider that coupon is paid annually and interest rates are 5%. The Macaulay Duration is calculated as follows:

It implies that 4.55 years would take to recover the price paid towards the purchase of the bond.

As you know, fluctuations in the interest rate regime lead to a change in the yield of the bond as a result of a change in the prices. So, in reality, there’s always a risk of not being able to reinvest the coupon payments at the same interest rate. It is known as Reinvestment Risk. Automatically, the duration of the bond would change owing to interest rate fluctuations. But this circumstance is not addressed by the Macaulay Duration.

You need to use Modified Duration in such a scenario which takes into account the changing interest rates. It shows you that in the case of bonds without embedded features, for every 1% change in the bond yield, the quantum of duration would change. You may calculate Modified Duration as given below:

Continuing with the above example, suppose if your bond is selling at par i.e. Rs 1000, then the yield to maturity would be 5%. Substituting these values into the formula gives the following modified duration:

Modified Duration = [4.55/(1+0.05/1)] = 4.33 years

It means that if the yield of the bond rises from 5% to 6%, then the duration of the bond falls from 4.55 years to 4.33 years. It enables you to gauge the volatility of the bond.

**Impact of Volatility**

Volatility implies a change in the bond price as a result of movement of the interest rates in the economy which in turn leads to fluctuation in the bond yield. As a prudent advisor, you would desire to buy a bond which would be relatively less vulnerable to volatility. By combining three factors namely; coupon rates, duration and yield to maturity; you would be able to select a bond that would give returns countering volatility effectively. A bond with a higher coupon rate, shorter duration and higher YTM would be less volatile as compared to a bond with lower coupon rate, longer duration and lower YTM.

**Final Words**

Being fixed-income security bonds hold vital importance as regards asset allocation in your portfolio. Before making your decision, ensure that you evaluate the competitive offerings regarding price, yield, duration and volatility. These factors would facilitate in capitalising on interest rate movements and would help to protect your portfolio against unwarranted risks.

## Leave a Reply