Fixed Income Security: Bonds

Introduction

This post aims to introduce the basic concepts related to bond, which will be used to understand the deeper concepts related to the bond market. In this topic review, we will start with understanding how significant role bonds play in the global capital market. Then we will see basic concepts like coupon, face value, covenant, indenture related to bonds, lastly, we will examine various types of bonds.

Role of Bonds in Global capital market

Bonds are the prominent source of raising capital by the borrower, and it far surpasses equity as a source of raising capital. The use of bonds as a source of capital over the year can be seen in the below image.

From the above data, we could see that in 2018 outstanding bond was valued at about $102 trillion far outstripping equity which stood at $74 trillion. 

Various concepts related to bonds

Bonds are fixed income security which promises a fixed stream of cash flows to the bond holder in the form of a coupon at regular interval for a fixed period and face value at maturity.

Face value: Face value of the bond is the amount that issuer promises to pay once the bond matures. It is mentioned in the bonds contract. Face value is also called par value. It is important to note that the market value of a bond can be different from the face value depending on the prevailing interest rate in the market and return demanded by investors. We will discuss in detail the difference between the two in the next post.

Term to maturity: It refers to the length of time remaining for which the bondholder will receive regular payment and at the end of this period bond will mature, and the issuer will pay the face value and redeem the bond.

Coupon: Coupon is the regular cash or payment a bondholder receives. It is mostly annual or semiannual payment. The coupon is defined as a percentage of the face value of the bond, and the mentioned rate is in terms of per annum.

Let's take an example: A corporation wants to raise $1 million for 5 years. The corporation decides to raise this amount by issuing a bond with a par value of $1000 having 6% coupon paid semiannually for 5 years.

Now, Face value = $1000 (Note: This may or may not be market value)

          Term to maturity = 5 years

           coupon =  6%*1000 = $60

Note: Coupon mentioned above is an annual payment because the coupon rate is always mentioned annually. But, since issuer has promised to pay coupon semiannually, the investor will receive $30 every six months or (6%/2)*1000.

Bond Indenture: Bond is a contract between issuer and borrower, and as in any contract issuer and borrower has certain rights and obligation. All these right and obligations mentioned in the form of contract is called a bond indenture. The indenture also includes specific details related to bonds, like some bonds have call option attached to it. 

Covenants: There is always a  credit risk associated with bonds apart from bonds issued by the government in the domestic currency, which is almost credit risk-free. To protect the investor from these risks which may be credit risk or some other risk, certain provisions related to the borrower are included in the indenture. These provisions are called covenants. 

There are basically two types of covenants:

Negative covenants: These provisions mention the action that borrower cannot take. Like taking further secured debt, selling the asset which has been pledged.

Affirmative covenants: These provisions mention the action that borrower needs to perform on its part. Like maintaining certain financial ration above the threshold, proper maintenance of pledged collateral.

Types of Bond

Apart from the bond whose example was given above, a straight bond, there are various other types of bonds as mentioned below.

Zero-coupon bond: These bonds don't pay coupon, the interest earned on these bond is because these bonds are issued at a discount to face value. When the bond matures investor gets face value of the bond.

Let say a zero-coupon bond is issued at 10% per annum for 5 years having a face value of $1000.

Now since this bond will not pay any coupon and only $1000 at the end of 5th year, to earn 10% per annum, the bond will be issued at $620.92 to the investor.

Dual currency bond: These type of bond pays principal in one currency and interest in other currency. This type of bond is used to raise money in one currency and pay interest in other currency.

Like a bond issued in euro but pays interest in us dollars.

Currency option bond: These type of bond generally gives the investor an option to decide in which of the currency, generally among two currency choices, they want payment in. This option is both for coupon and principal.

Step-up notes: In this type of security coupon rate increase over the period at a given rate.

Domestic bond: These are the bond issued by the firm present in the same country where the bond is traded and denominated in the same country currency.

U.S firm issuing the bond denominated in U.S dollar and traded in the U.S bond market.

Foreign bond: These bonds are issued by the firm outside the country in whose currency the bond is denominated and traded in the market of denominated currency. The foreign bonds have unique names like samurai bond, it is the bond issued in Japan by a non-Japanese company.

Eurobond: These are the bond issue by a firm outside its domiciled country, and the bond is denominated in a currency different from both the home country of the firm or the country in which it is traded. Like a bond issued by Japanese firm is the U.S denominated in yuan. 

Most of the Eurobonds are bearer bond, i.e. the ownership is with the person holding bond as it is not registered. It is important to understand that Eurobonds are not named in such a way because it was issued in Europe or denominated in euro.

Eurobond denominated in U.S dollar is called Eurodollar.

Deferred-coupon bond: These are the bond in which initial coupon payments are deferred for some time in future, the accrued coupon payments are paid at the end of the deferred period. The bonds are issued when certain project supporting the coupon payment are expected to generate cash flows in the future period.

Apart from these bonds, there are various other types of bonds which we learn about and understand as we move along our journey to understand fixed income securities.

 

Compound Interest

“Compound interest is the 8^th wonder of the world. He who understands it, earns it; he who doesn't, pays it.”
       - Albert Einstein 

Introduction

In this topic, we will first see the impact of compounding, then we will understand what compound interest means, and how to calculate it next we will understand compounding frequency and how to convert one compounding frequency into another. In the end, we will understand the effective annual interest rate.

Impact of compound interest 

  

Compounding creates an exponential effect on the interest earned, and the best way to understand its impact is visually.

From the above figure we see how over the time compound interest grows exponentially, and this is the kind of impact compounding has in the long run.

Compound Interest

Compound interest can be understood as interest earned on interest. Let say we have INR 1000 and we invested it to earn 10% per annum compounded annually. Now using the below formula we calculated the total amount after 2 years.

             A = p*(1 +r/100)^n
  
             A = amount after 2-year
             p = initial amount invested
             n = number of year
             r = interest rate
So, A = 1000*(1 + 10/100)^2
          =  1210
      C.I( compound interest) = A-p
                                             = 1210-1000
                                             =  210
Now if we expand the equation a little
        A = 1000*(1 + 10/100)*(1 + 10/100) 
the underlined portion shows interest earned in the first year, and the bold portion shows interest earned in the second year. As can be seen from the bold part of the equation, second-year interest is not only earned on the principal but also interest earned in the first year. So, let's further simplify it.

CI = interest earned on the principal in the first year +  interest earned on (principal + first-year        interest) in the second year
     = 100 + (1000 + 100)*10/100
     = 100 + 110
     = 210
The same logic can be extended to n>2 also.

Compounding Frequency 

In the financial world, we encounter statements like x % per annum compounded semiannually. So, what is compounded semiannually means, it is what we called compounding frequency. It basically means how many times we pay interest in a year. Here compounding semiannually means interest will be paid 2 times a year. So, here compounding frequency is 2. Similarly, it could be quarterly, monthly or daily. Now, how we incorporate this into our earlier formula.

        

          A = p*( 1 + r/100*m)^n*m

           

          r = rate of interest given per annum

          n = no of year 

          m = compounding frequency

So, if it is given that INR 1000 is invested at 10% per annum compounded quarterly for 3 years, then

          A =1000*( 1 + 10/100*4)^4*3

              = 1344.88

Continuous compounding

 When compounding frequency becomes very small i.e compounding takes place every moment then it is called continuous compounding. For continuous compounding we use formula.

         A = p*e^rn

         

         r = rate of interest given continuously compounded

         n = number of year

Converting on compounding frequency to another 

Let say we are given interest rate as 10% per annum compounded semiannually, and we need to find an equivalent rate for quarterly compounding i.e a quarterly compounded interest rate which will give us equivalent output for the same initial investment after

So if we desire the same output assuming an initial investment of INR 1000 for 2 years.

         1000*(1 + 0.10/2)^2*2  =  1000*( 1 + r/100*4)^4*2

solving for r we get 9.87%

We could generalise the above formula

         A*( 1 + rp/100*p)^p*n = A*( 1 + rq/100*q)^q*n

         n = number of year

         p,q = componding frequencies 

         rp = interest rate with compounding frequency p

         rq = interest rate with compounding frequency q

  

Important point: one thing to observe above is the equivalent r for quarterly compounded is lower than semiannually compounded rate. So, as we increase the compounding frequency equivalent compounding rate will decrease.

Effective annual interest rate

When we convert a rate with a given compounding frequency to the equivalent rate for compounding frequency of 1, the equivalent rate is called an effective annual interest rate. Effective annual interest rate basically tells the actual interest earned as a result of compounding over the period. To find an effective annual interest rate we use the above formula and put p = 2 and q = 1

      

          1000*(1 + 0.10/2)^2*2 = 1000*(1 + r/100)^2

EAIR = 10.25%

Important point: From the above image we can note that as the compounding frequency increases for the given interest rate EAIR increases. Similarly, we can say that for a given EAIR equivalent compounded rate decrease as compounding frequency increases.

This ends our discussion on compound interest. For any doubt please comment.

   

Why this blog?

Financial freedom is essential for everyone, whether the person is an investment banker or a person without any financial understanding. It is vital for me too, and when I started my journey toward it, I had no financial knowledge. I committed mistakes that could have been avoided with a better understanding of the basic know-how of the financial world. There started my journey to understand the details of the financial world working, and to provide that knowledge and understanding to everyone out there looking to understand this world.

That being said, the aim is to provide a comprehensive understanding of the financial world, which I hope will help people with make informed investment choices and understand financial opportunities around us even in difficult times. Now, remember we will keep on making mistakes, it is in the nature of humans to make mistakes, but the aim is to reduce the frequency and cost of these mistakes. 

This blog starts from very basic of various aspects of the financial world, like Financial statement analysis, Corporate Finance, Fixed Income, Derivatives, Equity, Valuations, and various others, and build on these basic concepts to dive in more details. Efforts will be to introduce the concepts in layman terms and then use it to understand practical scenarios.