Features of coupon and discount bonds. What are bonds
In this article I will analyze the concept of discount bonds, what kind of profit discount bonds can give to an investor, i.e. their yield, as well as the cost (price) and maturity of discount bonds.
Discount bonds - price, yield
Discount bonds - This is one of the types of ordinary bonds. Discount bonds are often referred to as zero-coupon bonds or zero-coupon bonds. Since, in comparison with traditional bonds, coupons are not paid at all, hence the corresponding name.
Lenders extract income from a discount bond through deep discounting, which implies a discounted face value at the time of purchase. The vast majority of discount bonds can be purchased on the secondary market. The cost of selling zero-coupon bonds is much less than the face value, sometimes 2-3 times, with the expectation of compensating for the lack of coupons. As the maturity date of a discount bond approaches, its market price begins to rise rapidly.
The bonds are redeemed at par value, which gives the investor (bond holder) actual income.
Let me give you an example to make it easier to understand investing in discount bonds:
Let's say a discount bond was purchased for 1,150 rubles, and its maturity is set at 1 year. The nominal value of this discount bond is 1,300 rubles. Of course, there is no coupon. Based on our initial data, we find that the discount is 150 rubles (1300-1150=150). As a result, we get that the income is 150 rubles. Now let's calculate the yield in % per annum.
To do this, divide the yield of a discount bond by its cost at the time of purchase and multiply by 100%. We get 150/1150*100% = 13.04%. If the maturity of this discount bond were six months, then the annual yield would already be equal to 26.08%. But if the maturity of the bond was a couple of years, then the yield would be much lower (2 times) - 6.52% (13.04/2=6.52%).
By the way, between a standard coupon bond and a zero-coupon (discount) bond there is a so-called transitional option - a bond with a deep discount.
The most well-known discount (zero) bonds include short-term debt obligations of the governments of the UK and the USA.
Our Russian government short-term obligations (bonds) or simply GKOs were issued using the same model, but this was so long ago, even before the crisis year of 1998. The issuer of these securities was the Ministry of Finance of the Russian Federation, and the Central Bank of the Russian Federation acted as the General Agent for servicing the issue of government short-term zero-coupon bonds.
But August 17, 1998 came, and the government announced a technical default on GKOs. Literally a few days before the announcement of default, the yield on GKOs skyrocketed - right up to 135-140% per annum. As a result, the severe economic crisis of 1998 completely devalued investments in state bonds, again in US dollars by more than 3 times, and the country’s government stopped all payments until the spring of next year.
Differences between stocks and bonds.
The right to participate in the management of a joint stock company.
Property rights of shareholders (except for the right to receive dividends).
A JSC can be liquidated voluntarily or by court decision.
Priority: Payments on preferred shares; Payments to holders of common shares.
Property rights include the right to receive annual profit in the form of dividends and the right to receive part of the JSC's property. In the event of its liquidation, if after satisfying the claims of creditors, there remains property for distribution among shareholders.
Only those who were included in the list of shareholders on the date established by the Board of Directors have the right to participate in the general meeting of shareholders. Regardless of whether the Register data has subsequently changed, the right to vote at the announced meeting is given to those shareholders who were registered on the day the List was compiled.
Right to participate in management:
The right to be elected to the management bodies of the joint-stock company (board of directors, audit commission);
The right to make contributions to the agenda of the general meeting, to nominate candidates to the board of directors (at least 2% of voting shares);
The right to demand an extraordinary general meeting (at least 10% voting shares);
Block the decision of the general meeting (more than 25% who take part in the meeting);
Make decisions at the general meeting, except for issues on changing the charter, liquidation, and major transactions (more than 50%).
Types of bonds depending on the type of income:
●Coupon bonds (they periodically pay interest on coupons, coupon).
●Discount bonds (Discount income is the difference between the face value and the purchase price) They generate discount income upon maturity.
There are types of coupon bonds:
1) With a constant coupon rate - when issuing bonds, the same coupon rate is established for all coupon periods
2) Fixed coupon rate. (Increasing over the years of the loan, Decreasing over the years of the loan) - when issuing bonds, a fixed coupon rate is established for each coupon period.
3) Variable coupon rate - when issuing a bond, the rules for calculating coupon income are established, but the coupon rate is not fixed. Example: coupon rate = Fixed part + non-fixed part (coupon rate = 3% + official inflation rate for the year).
For bonds of this type, a maturity date and par value are established. Coupon income is not accrued or paid. That's why such bonds are called zero coupon or zero coupon bonds (zero coupon bond).
Zero-coupon bonds generate income only if they are purchased at a price below par or, what is the same, at a rate below 100. In this regard, these bonds are also called discount bonds.
In Russia, securities of this type are government short-term zero-coupon bonds (GKOs), which have been issued since 1993.
Since there is only one payment - repayment of the face value N, then the bond price is determined by:
Where n - time of holding the bond (in years) until maturity (value n not necessarily an integer number of years). The bond rate is determined by the ratio:
(21)
If the price of a zero-coupon bond or its exchange rate is known, then the bond's yield to maturity is equal to:
(22)
As can be seen from the last relationship, the yield of a bond is positive if the bond price is below par or the rate is less than 100.
If the bond's term is less than a year or market rates are low, the bond's yield is determined by a simple interest rate:
(23)
The last relationship is consistent with the general ideology of simple interest rates: the numerator (23) is income ,
received by the owner for the entire period of ownership of the bond. Dividing the income by the price of the bond, we get the yield for the entire period. If we now divide the last return by the term n, then you get the annual yield of the bond.
Example 8. The bond will be repaid in 5 years and 3 months. Current rate is 45.64. Find the yield to maturity.
Solution: The yield to maturity is found using relation (23):
, or
Example 9. There are 1.5 years left until the zero-coupon discount bond matures. Find the market rate of the bond if the discount rate is 15%.
Solution: In accordance with relation (21), the bond rate is equal to:
Example 10. Find the yield to maturity of a zero-coupon bond, if the market price today is 790 rubles, the bond is redeemed at a par value of 1000 rubles. in 2 years 2 months or 2.167 years.
What is the simple rate of return?
Solution: The yield of a bond (complex and simple) is determined using relations (22), (23):
or
,
or
Bonds with interest and par value payment at maturity
Such bonds provide the accrual of coupon income (at a compound interest rate g),
however, no ongoing coupon payments are made. The accumulated coupon income is paid at maturity along with the face value. Thus, the owner of the bond at the end of the term receives an amount equal to .
If n
-
Bond holding period in years (P- not necessarily an integer number of years), then the price of the bond and its exchange rate are related to the yield to maturity by the following relationships:
,
. (24)
Yield to maturity:
. (25)
Example 11. The bond accrues 15% per annum with payment at the end of the term. The bond was purchased at an exchange rate of 75. The maturity date is 5 years. Determine the yield to maturity.
Solution: In accordance with (25)
or
.
Example 12. The bond accrues 3% quarterly. Interest is paid when the bond matures. The bond was purchased at an exchange rate of 120. The maturity period is 6 years. Find the yield to maturity.
Solution: Nominal interest ratej=12%, interest is calculated t=4 times a year. The effective interest rate according to (11) is equal to:
The yield of a bond is determined according to (25):
or
.
Example 13. Determine the market value of a bond that pays 12% annually with interest paid at the end of the term. The discount rate is 14%, the par value of the bond is 2000 rubles, the term is 6 years.
Solution: Using relation (24), we find the cost of the bond:
The income on which is paid in the form of , that is, the difference between the purchase and the amount that the investor will receive at the end of the security’s circulation period.
A discount bond is a bond whose owner receives income by purchasing the bond at a price below par and receiving the par value at maturity. The discount bond does not provide for other payments (coupons). Discount bonds that do not pay interest are called zero coupon bonds.
For example, a bond with a maturity of one year was purchased for 900 rubles. Denomination 1,000 rubles. No coupon. Then the discount size is 1,000 minus 900 equals 100 rubles. The investor's discount income for the year from such a security will be 100 rubles divided by the purchase price of 900 and multiplied by 100% equals 11.11% per annum. If the same security had a maturity of not one, but two years, then the annual yield would be equal to, accordingly, half the calculated yield, or 5.55%. And if it were six months, then in annual terms it would be 22.22% per annum.
Discount bonds first appeared in the United States in the 1960s as a result of investors discovering several loopholes in the country's tax laws that did not allow for the accumulation of interest, particularly compound interest, over several years. They became widespread by the 1980s. When the loopholes were hastily closed by the US government, long duration zero-duration bonds became the predominant use of . Since zero bonds do not have coupons, it is not the coupon that is subject to federal tax each year, but the positive difference between the denominations of the bond itself at the beginning and end of the year, that is, its accumulated value. Thus, if the bond goes up in price (standard case), the accumulated value of the bond is taxed; if the bond becomes cheaper, creditors do not pay taxes. The debtor (company) taking out the loan, in turn, deducts the accumulated value from its pre-tax income, thus reducing the tax burden. Nil bonds are not subject to additional state and municipal taxes if the lender resides in the state where the nil bond is issued. They appeared in the Russian Federation and CIS countries in the 1990s.
Classic examples of discount bonds include short-term debt obligations of the US government (T-notes), UK (T-bonds). It was in this form that until 1998 Russian state short-term obligations – GKOs – were issued.
The yield on a bond is what the investor buys the bond for. The income depends on: if it is coupon, then the holder of the bond will be paid a coupon - a percentage of the face value. The bond can be zero-coupon, then its income will be a discount - the difference between the par value and the purchase price.
Bond yield
is a security indicating the debt of the issuer to the investor. When the bond is repaid, the issuer returns the principal amount of the loan ( face value) and reward as a percentage ( coupon) for using money.
The coupon is announced per year, but payments usually occur 1-2 times a year. The more often the payment, the more profitable it is for the investor; the money received can be reinvested.
For example, the par value of the bond is 1,000 rubles, the coupon is 20%. Let's calculate the coupon value in rubles: 1,000 x 20/100 = 200 rubles. If payments occur twice a year, then the investor will receive 100 rubles every six months; if payments are quarterly, then for each quarter there will be a payment of 50 rubles.
Coupon bonds
Previously, when all bonds were paper forms, coupons looked like coupons that were cut out from a special sheet. The sheet was integral with the bond or was attached to it. The coupon indicated the income that the investor was supposed to receive.
The number of coupons was equal to the number of income payments. When the payment was due, it was necessary to cut 1 coupon (the expression “cut coupons”) and exchange it for a cash payment.
The coupon income on a bond depends on issuer reliability: the lower the risk, the lower the interest (for example, government bonds). The lower the issuer's rating and the greater the risk, the higher the income.
The coupon depends not only on the stability of the issuer, but also bond maturity : the longer the term, the higher the interest should be.
Coupon payments are:
- fixed annual;
- indexed annual;
- repaid at the same time as the principal amount of the loan.
Zero coupon bonds
A coupon is not the only income from a bond; there are zero-coupon bonds, they are also called “zero coupon bonds,” “pure discount bonds,” or simply “discount bonds.”
The return to a zero-coupon bond investor is discount, discount or dizagio– a positive difference between the redemption price (face value) and its acquisition price.
For example, a zero-coupon bond has a par value of 100 thousand, but it sells for 80 thousand, the discount is 20 thousand. When the bond is redeemed, the investor's income will be 20 thousand.
The yield on a zero coupon bond is the amount of the discount.
The income from a bond with a coupon consists of coupon payments and the amount of the discount or premium. Prize or agio– this is the negative difference between the redemption price (face value) and the sale price, that is, the bond was purchased at a price higher than the face value. The premium reduces the yield on the bond.
For example, a coupon bond has a par value of 100 thousand and a 20% coupon, maturity in a year, purchased by an investor for 110 thousand. After a year, the income on the bond will be: coupon 20 thousand (100 * 20%) - premium 10 thousand (100 thousand . – 110 thousand) = 10 thousand.
Nina Polonskaya
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