Bonds and their dirtiness
Introduction
So we are talking about bonds as a fixed income instrument which is a potential source of income from the debt category.
What differentiates bond from equity is that bond does NOT entitle the bond holder with any kind of ownership in the company. That being said they are not eligible for dividends and they are also not eligible to vote in the annual general meetings. A positive outcome though is that in cases of bankruptcy, the bond holders are to be paid first , so the principal amount is certainly secured.
On a high level , bonds are classified as government bonds and corporate bonds. A large number of governments issue bonds in order to raise capital for projects that span long years. To encourage people participation, governments sometimes waive off the tax on the income generated from bond sale and resulting accrued coupons. In a similar manner , corporates also issue bonds in order to raise capital and in case if they would not want to provide an ownership in the form of stocks.
Bond earnings are typically in the form of coupons. The coupons are paid out over a fixed defined interval which could be annual, semi-annual , quarterly or monthly.
Each day the investor holds the bond , a daily coupon amount gets accrued. This daily accrued amount is a fraction of the coupon amount that will be paid out at the end of coupon payment cycle.
Clean and Dirty
An important concept that one would come across while dealing with bonds is that of clean and dirty prices.
Clean price - is the market price at which a bond is traded. This value could be :
1. Same as the face value.
2. Higher than face value (called as premium)
3. Lesser than face value (discounted)
When a bond exchanges hands in the middle of a coupon payment cycle , the seller is entitled to a coupon share amounting to the days for which he held the bond. The purchaser of the bond has to pay out to the seller the accrued coupon amount. This amount is usually piggy backed over the clean price divided per share. Thus we get an amount which is the sum of clean market price and the coupon accrual per share(referred to as a dirty accrual).
This price which is the sum of clean price plus the dirty accrual per share is what is called as a dirty price.
Formula
The coupon is derived using below formula:
Coupon = FV x coupon rate x accrued days/ days in period
Bond Gains
An interesting thing to note is that the coupon amount is calculated based on the face value amount. Hence whether or not a certain user will derive a profit out of the bond is subject to the coupon percentage and the difference between face value and the current market price.
To understand this , we will take the help of some examples.
Case 1 : Clean price same as face value (FV)
Consider a bond trading at 100 INR clean price and which is also the FV. We will assume the following:
Face value or bond notional =100
Coupon - 5%
Term - annual
Lot size - 1
Hence coupon amount for 1 year (assuming full period will be 360 days) will be as follows -
Coupon = 100 x 0.05 x 1 = 5
If the buyer sells his bond after 1 year at fv , his gain will be 5. This is the most plain vanilla case.
Gain = selling price - purchase price + coupon
Hence gain = 100 - 100 + 5 = 5
Case 2: Clean price higher than face value
Consider a bond trading at 105 INR and having a face value of 100. We will assume the same bond characteristics as before.
Face value or bond notional =100
Coupon - 5%
Term - annual
Lot size - 1
Hence coupon amount for 1 year (assuming full period will be 360 days) will be as follows -
Coupon = 100 x 0.05 x 1 = 5
However, if the buyer sells his bond after 1 year , his coupon would just offset his market price at which he purchased the bond at premium.
I.e. Gain = Selling price - purchase price + coupon i.e = 100- 105 + 5 = 0
Remember, the bond will always be sold at the FV price irrespective of the market price. Hence in this case , in order to offset the market price and earn a profit , buyer has to hold the bond for more than a year.
Case 3 : Market price lesser than face value
This is usually the case if the bond does not have a great demand and thus being available at a discounted price. Keeping the economics same and considering we still get a coupon amount of 5INR at the end of the year, let's have a look at the gain from a discounted bond.
For our case , let's assume the buyer purchased bond at 95 INR. Thus the gain will be
Gain = Selling price - Purchase price + coupon = 100 - 95 + 5 = 10
Therefore when deciding to invest in a bond , it's imperative to check if the bond Gains are able to cover the buying costs. This is also known as a bond yield.
Calculation of accrued days
While this might seem a trivial case of a calculation , it is important to note that the accrued days will differ based on the selection of the day count convention.
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