Cbonds.Ru Ltd.
Pirogovskaya nab., 21, St. Petersburg
Phone: +7 (812) 336-97-21 http://www.cbonds-group.com
Bond calculator is designed to calculate analytical parameters used in assessment of bonds. The tool allows calculating prices, accrued coupon interest, various types of bond yields, duration, as well as modified duration, curve, PVBP, making it possible to analyze volatility of the debt market instruments and assess how bond price changes with the yield.
Software interface allows viewing key issue parameters and simulating them. It is also possible not only to analyze traded issues, but also to simulate bond cash flows and create user models.
Using the calculator
Terms and Definitions
,
,
Designations
Calculated Values
Yield to Maturity
Effective Yield to Maturity
Nominal Yield to Maturity
Simple Yield to Maturity
Yield to Offer
Yield to the Next Coupon
Current Yield
Adjusted Current Yield
Years to Maturity
Macaulay Duration
Modified Duration
Price Value of Basis Point (PVBP)
Convexity (Conv)
References and Contact details
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To continue working with the calculator, you need to load the issue from the database or create a bond model.
Loading Issues from Cbonds Database
1.
Enter either the issuer, or the issue registration number, or ISIN in the search bar, and click
"Search".
2.
Select a bond issue from the opened list and press "Load".
Creating a Bond Model
1.
Click the button "Create a Model" and choose the type of the bond you want to create (coupon bond / discount bond).
2.
Fill in the issue parameters.
Calculating Bond Parameters
The calculator allows computing analytical parameters either based on the known bond price, or based on the given yield. Price of the bond is the input value by default. To calculate bond parameters based on the given yield, click "Calculate Price from Yield".
Bond price can be shown as a percentage of face value, or directly in units of face value. You can make your calculations based on the known "net price" of the bond (price excluding ACI), or "dirty price"
(including ACI). By default, calculations are made from the net price shown as percentage of face value.
Using the Constructor Mode
In our calculator, you can edit parameters of an existing bond model. To edit the bond cash flow (or create a new one), use the buttons underneath it.
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With "Constructor" button, you can create a chart of coupon payments on the bond.
Enter the period, for which the cash flow will be filled, frequency of coupon payment (by default, these parameters are filled based on the issue terms you have already entered), coupon rate and payment amount.
Payment amount is optional - you can just click on
"Automatic Calculation", and coupon payments will be calculated automatically.
Use "Add" button to add coupon payments to an existing coupon chart.
Cash flow on the bond can be edited directly in the table (you can change the date, coupon rate, coupon payment and redemption amount). After editing the cash flow parameters, select respective lines in the stream and click "Update". The system will then recalculate the coupon payments based on your edit.
To delete lines from the "Cash Flow" table, select the lines and click the "Delete" button.
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The lite-version of the calculator is available for all website profiles via the menu item "Bond
Calculator (Lite)". The functionality does not require a flash-player support and works in all browsers.
The basic version of the calculator allows computation of yield by price and price by yield for any date. In the list of calculated indicators various types of prices, yields, ACI and duration are displayed.
There is the function to model simple coupon-bearing and discount bonds, which allows you to quickly assess the price or yield of bonds according to the input parameters.
To continue working with the calculator, you need to load the issue from the database.
Loading Issues from Cbonds Database
1.
Enter either the issuer, or the issue registration number, or ISIN in the search bar.
2.
Select a bond issue from the opened list and click.
Calculating Bond Parameters
The calculator allows computing analytical parameters either based on the known bond price, or based on the given yield. Price of the bond is the input value by default. To calculate bond parameters based on the given yield, click "Calculate Price from Yield".
Bond price can be shown as a percentage of face value, or directly in units of face value. You can make your calculations based on the known "net price" of the bond (price excluding ACI), or "dirty price"
(including ACI). By default, calculations are made from the net price shown as percentage of face value.
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Using the "Issue model"
To model the issue enter the "Maturity",
"Coupon rate", "The frequency of coupon paymwnts (per year)". At least one of the fields
"Current price" or "Yield to maturity" is also required for calculation.
Press the button "Calculate" to view all other calculating parameters.
In the example we create the model of shortterm zero-coupon bond with current price 100% and maturity 100 days. Also we create the model of 3-year coupon bond with current price 100% and coupon rate 10%.
We use bond basis 365 days per year to calculate all parameters.
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Bond is a security bearing an obligation of the issuer to pay its holder (lender) the face value or an equivalent in property at the end of the tenor. A bond may also include the holder's right to receive a percentage of the face value stipulated therein, or other property rights.
Eurobond is a security issued in external (international, offshore) bond market with the following characteristics: international syndicates act as the underwriters; bonds are simultaneously placed with investors from different countries; bonds are issued outside the jurisdiction of any specific country and do not have to be registered. Securities issued both in the domestic and external markets are called global bonds.
Foreign bonds are bonds issued in the domestic market of another country. Issuers of the foreign bond market are not officially registered in the country, where the bond is issued and traded.
Depending on the sector:
1.
Government
2.
Municipal
3.
Corporate
Depending on the method of interest payment:
1.
Interest bearing bonds:
coupon bonds (bonds with periodic coupon payments)
accrual bonds (at maturity investors are paid the bond's face value together with the accrued coupon interest)
2.
Zero-coupon bonds (bonds paying no coupon interest). Investors in zero-coupon bonds, as a rule, earn on the difference between the placement price and the face value.
Depending on the method of income generation:
1.
Fixed permanent coupon bonds
2.
Fixed variable coupon bonds
3.
Floating rate bonds
4.
Index-linked bonds
By method of face value repayment:
1.
Bonds with redemption of face value in one payment in the end of tenor
2.
Bonds with repayment in installments distributed over time (amortization)
Depending on early redemption terms:
1. Bonds without an option of early redemption
2. Bonds with a call option (redemption is initiated by the issuer). The issuer has the right to fully or partially repay the debt before the maturity date.
3. Bonds with a put option, including: a) bonds with an option of early redemption initiated by the investor
The holder has the right for redemption of the bond at a predetermined price on the agreed date. b) bonds with an option of resale (early repurchase) initiated by the investor (Russian analogue is the bond with irrevocable offer, which can be traded after the sale). Holder of such bonds has the right to sell them back to the issuer at a predetermined price on an agreed date.
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Depending on the maturity:
1.
Term bonds
2.
Perpetual:
with a call option
with a put option
Face value of a bond is par value set by the issuer and is usually indicated directly on the security.
The notion of outstanding face value applies to bonds structured with amortization. It is a part of the face value remaining after partial repayments of par over the life of the bond. Analytical indicators on such bonds are calculated based on the outstanding face value.
Lot of multiplicity (denomination increment, trading lot increment) is the minimum number of securities at face value, with which settlement and depository operations are performed.
Minimum denomination (minimum trading lot, minimum trading volume) is a parameter of a certificated bearer Eurobond. The borrower determines the total size of the issue at face value, the lowest denomination and denomination increment Depositary can register trade and settlement transactions only if the amount of securities exceeds the minimum denomination (for example, USD 100,000) and is a multiple of the denomination (e.g., USD 1,000).
Minimum trading lot is the minimum amount of securities at face value, available for sale. Cash flow on the bond is calculated from the minimum trading lot.
Coupon is a periodic interest payment made during the life of the bond. Coupon is calculated as a percentage (per annum) of face value and/or an amount payable to bondholders.
Accrued coupon interest (ACI) is a value measured in monetary units, and characterizing the part of coupon income, which has "accrued" from the beginning of the coupon period. Coupon on the bonds is paid periodically, usually once every quarter, six months or a year. Accordingly, when one coupon is paid and the next coupon period begins, the coupon begins to "accrue". On the coupon due date, investors receive a coupon payment for the respective coupon period, and ACI is zero.
Calculating this indicator is important due to the fact that in most markets, bonds are traded at so-called "net price" excluding the ACI (there are exceptions, however: for example, in the bond market of Ukraine bonds are quoted at full price). Thus, in order to get the full price payable by the bond buyer to the seller (also known as "gross" price), one needs to add ACI to the net price.
A

C i t t
0 i
 t i

1
 t i

1
ACI may also be expressed as coupon rate in percentage points (usually these are the formulas given in issue prospectus), rather than the coupon size in monetary units. Then the ACI formula will be as follows:
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A
(%)

C i (%) t
0
 t i

1
B
For zero-coupon bonds, ACI index is not calculated.
Days calculation method determines the formula used to calculate the notional number of days between the starting and ending dates of the ACI period, and the notional number of days in a year
(calculation basis). The choice of method affects the discount value when calculating analytical parameters of the bond.
For Russian bonds, the generally used method is Actual/365F; for Ukrainian bonds, we usually use methods
30/360 or Actual/365F; 30E/360 is the most commonly used method for Eurobonds.
30/360 Methods
Starting date: D1.M1.Y1 (day.month.year)
Ending date D2.M2.Y2 (day.month.year)
Difference between the dates (Day count) = (Y2-Y1)*360+(M2-M1)*30+(D2-D1)
30/360 German (o ther names: 30E/360 ISDA )
Source: 2006 ISDA Definitions (Section 4.16(h))
D1 and D2 adjustment rules:
• if D1=31, then D1=30
• if D2=31, then D2=30
• if D1 is the last day of February, then D1=30
• if D2 is the last day of February, then D2=30
The last day of February : February 29 in any leap year, February 28 in any non-leap year.
30/360 ISDA (30/360) (other names: Bond Basis, 30-360 U.S. Municipal )
Source: 2006 ISDA Definitions (Section 4.16(f))
D1and D2 adjustment rules:
• if D1=31, then D1=30
• if D2=31 and D1=30, then D2=30
30/360 US (other names: 30U/360, 30US/360 )
1
D1 and D2 adjustment rules:
• if D1=31, then D1=30
• if D2=31 and D1=31, then D2=30
• if D1 is the last day of February, then D1=30
• if D1 is the last day of February and D2 is the last day of February, then D2=30
Last day of February: February 29 in any leap year, February 28 in any non-leap year.
30E+/360
1
D1 and D2 adjustment rules:
• if D1=31, then D1=30
• if D2=31, then D2.M2.Y2 is the first day of the following month ((D2=1; Y2=Y2+integral part((M2+1)/12); M2 =
((M2 +1) mod 12) – remainder of dividing (M2+1) by 12)
30E/360 (other names: 30/360 Eurobond, 30/360 ISMA, 30/360 European, 30S/360 Special German, Eurobond
Basis )
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Source: 2006 ISDA Definitions (Section 4.16(g))
D1 and D2 adjustment rules:
• if D1=31, then D1=30
• if D2=31, then D2=30
Actual Methods
Actual/360 (other names: Act/360, French )
Source: 2006 ISDA Definitions (Section 4.16(e))
Number of days in the period is calculated as the difference between the dates without any adjustments, based on 360day year. Calculation basis = 360.
Actual/365A (other names: Actual/365 Actual )
Source: The Actual-Actual Day Count Fraction (1999)(Section 2 (с))
Number of days in the period is calculated as the difference between the dates without any date adjustments.
Calculation basis = 366, if the leap day (February 29) falls on the period, otherwise ACI calculation basis = 365.
Actual/365F (other names: Actual/365 Fixed, English )
Source: 2006 ISDA Definitions (Section 4.16(d))
Number of days in the period is calculated as the difference between the dates without any date adjustments.
Calculation basis = 365.
Actual/365L (other names: Actual/365 Leap year )
1
Number of days in the period is calculated as the difference between the dates without any date adjustments.
Calculation basis = 366, if the end date of the period falls on a leap year, otherwise ACI calculation basis = 365.
Actual/Actual (other names: Act/Act, Actual/Actual (ISDA))
Sources: 2006 ISDA Definitions (Section 4.16(b), The Actual-Actual Day Count Fraction (1999)(Section 2 (a))
Fractional number of days = (Number of days in the period, which falls on a leap year) / 366 + + (number of days in the period, which falls on a non-leap year) / 365.
Actual/Actual (ISMA) (other names: Actual/Actual (ICMA))
Sources: 2006 ISDA Definitions (Section 4.16(c), ISMA Rule Book (Rule 251.1 (iii)) , The Actual-Actual Day Count
Fraction (1999)(Section 2 (b))
In this method, all coupon payments are always the same size. ACI is the same for every day of the coupon period.
Size of the coupon payment is equal to the annual coupon rate divided by payment frequency per year and multiplied by face value of the bond. Number of days in the period is calculated as the difference between the dates without any date adjustments.
Fractional number of days = Number of days in the period / ((number of days in the current coupon period)*(number of payments per year)).
Actual/364 - instance Actual/Actual (ISMA), when the coupon period is 91 or 182 days. Used for some short-term securities. Calculation basis = 364.
NL/365 (other names: Actual/365 No Leap year, NL 365 )
1
Number of days in the period is calculated as the difference between the dates without any date adjustments.
1 is deducted from the number of days in the period, if the leap day (February 29) falls on this period. Calculation basis = 365.
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Calculation basis - Notional number of days in the year.
Fractional number of days means the number of days in the period divided by the number of days in the year (ACI calculation basis). Depends on the ACI Calculation Method applied.
Parameter Definition
Y effective yield, % p.a.
Y n
Y s
CY
ACY nominal yield, % p.a. simple yield, % p.a. current yield, % p.a. adjusted current yield, % p.a.
A accrued coupon interest, ACI, units of face value
"net price" of the bonds excluding ACI (Clean Price), units of face value
P
(%)
"net price" of the bonds excluding ACI (Clean Price), % of face value
P+A, P d
"gross price" of the bonds including ACI (Dirty Price), units of face value
C
(%) coupon rate, % p.a.
C
N i size of i-th coupon payment, units of face value face value of the bond, units of currency
N
P
(%) face value of the bond, %
N i the i-th payment of the debt face value (including redemption of principal under offer, amortization payments, full repayment), units of face value t n m t i t
0 m
B coupon frequency number of coupon payments redemption date of the i-th coupon, face value etc. current date or calculation date maturity date number of days in a year taken for calculation purposes, calculation basis duration (Macaulay), days (years) D
MD
Tm
PVBP
Conv modified duration years to maturity price value of a basis point convexity
__
1 – we used prospectuses, expert opinions and site deltaquants.com to describe the method
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Yield to Maturity
Yield to maturity is the rate of return on investments in bonds, provided that the investor holds them until maturity. It is usually shown as percentage per annum. Yield to maturity can be calculated either including reinvestment of coupon payments over the course of the year (effective yield), or excluding reinvestment of coupon payments over the course of the year (nominal yield). It should be noted that yield to maturity is only an ESTIMATE of the return investors will get from the bond, as calculation of the yield to maturity takes into account reinvestment of coupons at the same interest rate. In reality, this assumption can not be true, which is why the actual yield will differ from the estimated yield to maturity. However, yield to maturity is the most frequently used method of assessing bonds.
Effective Yield to Maturity
Effective yield to maturity (YTM) is yield to maturity calculated based on reinvestment of coupon payments during the year at the rate of the initial investment. Effective yield to maturity is an internal rate of return on the bond cash flow.
Effective yield is the root of the equation:
P

A
 i m 

1
C
( 1
 i

Y )
N t i i
 t
0
B and represents a discount rate, at which the "dirty" price of a bond is equal to the current cost of payment flows on the bond. The calculator computes the effective yield using Newton's method (also known as the tangent method).
Effective yield of zero-coupon bonds is calculated with the equation (a special case of the equation to calculate the effective yield when A = 0 and C i
= 0):
P

N
( 1

Y ) t m
 t
0
B
Methodologically, effective yield is a more correct measure than the nominal yield. However, nominal yield is traditionally in wider use in many developed bond markets. In Russia, effective yield is used more commonly, while in Ukraine both nominal and effective yields are in use.
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Nominal Yield to Maturity
Nominal yield to maturity is the yield to maturity, which does not include reinvestment of coupon payments during the year. If the paper is being placed at par, at the time of placement nominal yield will be equal to the coupon rate. For example, a bond with semiannual coupons of 10% would have a nominal yield to maturity of 10%, while the effective yield would be 10.25%.
Nominal yield is calculated using effective yield and based on the following equation:
1

Y

( 1

Y m n ) m
Nominal yield to maturity is a commonly used indicator in financial markets of most developed countries.
This is largely due to tradition, has to do with relative simplicity of this indicator. In Russia, nominal yield is official in calculation of yields in the short-term government bond (GKO) market and is generally accepted in the promissory note market.
For a zero-coupon bond, nominal yield to maturity is calculated with the formula:
Y n

N
P


1
 t i
B
 t
0
Simple Yield to Maturity
Simple yield to maturity is the yield to maturity, which does not take into account reinvestment of coupon payments during the year. It is calculated from the ratio:
Y n

(

C i

N i
)

P d ( покупки )
P d ( покупки ) t i
B
 t
0
Yield to Offer
Yield to put (put option) is the rate, at which the discounted value of cash flows received before the expected date of compulsory re-purchase by the issuer, as well as the put price on that date (as per the schedule), together are equal to the price of the bond.
Yield to call (call option) is the rate, at which the discounted value of cash flows received before the expected date of possible re-purchase by the issuer, as well as the call price on that date (as per the schedule), are together equal to the price of the bond.
In our calculator, yield to put and yield to call are designated as "yield to offer".
In contrast to yield to maturity, yield to offer takes account only of those payments (including redemption of face value), which will be made before the offer date. Method for calculation of effective, simple and nominal yields to offer is similar to computation of the respective yields to maturity.
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Only yield to put (and not yield to maturity) is calculated for bonds with a put/call option, which has not been exercised, and with a cash flow that has not been set until maturity date. In this case, calculations are made to the date of the last known coupon preceding the expected offer date.
Yield to the Next Coupon
Yield to the next coupon is the interest rate, at which the discounted value of cash flows received before the date of the next coupon, are in aggregate equal to the price of the bond. In calculations, it is assumed that the remaining outstanding face value is repaid on the date of the next coupon. Such yield is calculated for bonds, for which only the next coupon rate is known, and the subsequent cash flow is not defined.
Current Yield
Current yield (CY) is the bond yield based on the current coupon period only. It is assumed that the net price of the bond will remain unchanged during this period. The calculator uses the following formula to determine the current yield:
CY

C
* 100
P
For example, let us assume that the bond price is 90% of face value, with an annual coupon of 9% p.a. In this case the current yield will be 9/90 = 10%. And the yield to maturity of such bonds will undoubtedly be higher, since the price will tend to face value as the tenor decreases. In contrast, for bonds trading above par the current yield will be higher than the yield to maturity, as potential reduction in prices will not be taken into account. With this in view, current yield is not the best indicator of the bond's investment appeal.
Thanks to its simplicity, however, this value is often calculated as an additional parameter.
Adjusted Current Yield
Adjusted current yield is the yield on a bond that takes into account possible purchase of bonds at a premium or a discount. The calculator uses the following formula to determine the adjusted current yield:
ACY

CY

100

T m
P
(%)
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To understand the price volatility as reaction to interest rates, one needs a tool to measure volatility.
Dependence of the price on the yield in case of a yield change only: a convex curve. Key factors affecting the calculation: coupon (cash flow) and tenor.
Prices may also change due to a shift in perceptions of credit quality, approaching maturity date, changes in market rates.
Objective: being able to quickly assess the price change following the change in yield.
Years to Maturity
This parameter represents the time (in years) remaining until maturity of the bond.
Macaulay Duration
Macaulay duration is an estimate of the average tenor of payment flows on the bond, taking into account discounting the cost of certain payments. Thus, duration will always be less than or equal to the term to maturity of the bond, and it will be equal to the term to maturity of zero-coupon bonds only. The formula for calculating of duration is as follows:
D
 i m 

1
( t i
 t
0
)
P
( 1
C i

Y

)
( t i
N
 t i
0
)

A
B
Duration is a measure of the bond price elasticity to the interest rate, and characterizes the risk of changes in bond prices following a change in interest rates. From this view point, duration can be conceived of as:
D
  dP d
P d
: d ( 1

Y )
1

Y
, where dP d
- minor change in bond gross price, dY - minor change in bond yield, dP d
P d d ( 1

1

- percentage change in bond gross price,
Y
Y )
- percentage change in bond yield.
From the formula it follows that: dP d
P d
 
D dY
1

Y
.
This formula is used for approximate calculation of the relative price change based on given change in yield and given duration.
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Using only duration when calculating the relative price change does not give a very accurate estimate of the percentage change in the bond price. The more the yield to maturity changes, the less accurate the estimate will be. The error of result occurs because the duration is a linear estimate of the percentage change in bond price.
Irrespective of the yield change, the tangent line always lies below the price/yield curve, thus duration always undervalues the actual bond price.
Duration is usually measured in years, but in the Russian and Ukrainian markets, it is often specified in days.
Let us assume that the bond tenor is 3 years, annual coupon of 10%, effective yield is 10% p.a., and the bond is trading at par. Then the duration of this paper will be:
D

100 * 1 /( 1 .
1 )

100 * 2 /( 1 .
1 )
1000
2 
1100 * 3 /( 1 .
1 )
3

2 .
74
Duration properties:
1.
Macaulay duration of a zero-coupon bond remains the same until maturity. When yield to maturity changes, its duration remains unchanged.
2.
The higher the rate, the lower the cost of later payments compared to the short-term ones, and the smaller the duration; and visa versa - the lower the rate, the longer the duration of the payment flow.
3.
When yield to maturity grows, duration decreases; when yield to maturity shrinks, duration grows.
4.
The longer the time to maturity, the greater the duration. However, longer tenor of the bond does not automatically mean an increase in duration.
5.
The higher the coupon frequency, the shorter the duration, as more payments are scheduled closer to the starting point.
6.
Regardless of the coupon size, duration of a coupon bond, increasing the time until maturity tens to a limit equal to
1

1
Y
Duration not only shows the average tenor of payment flows on the bond, but is a good measure of price sensitivity to changing interest rates. The higher the duration, the greater the volatility of interest rates in
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relation to price changes. The phrase "bond duration is three years" means that the bond in question has the same price sensitivity to interest rates changes as a three-year zero-coupon bond.
Modified Duration
Modified duration is an indicator characterizing reaction of the bond's price to changes in the yield to maturity, linear approximation. In terms of mathematics, it is the first derived function of price from yield.
It is important to note that modified duration shows volatility of the full price including ACI. It is the value, by which the "dirty" price changes when the yield changes by 100 bp.
Modified duration is connected to the duration value through the following formula:
MD

D
1

Y
In terms of derivatives: MD
 
( P d
)
' y
P d
In case of small values, the following equality applies:

P d  
MD *

Y
P d
Modified duration is the relative change in the bond price occurring when the yield changes by one percent, provided that values of the expected cash flows on the bond remain the constant when the yield changes.
Modified duration provides a more accurate estimate of the percentage change in bond price, compared to
Macaulay duration.
Characteristics:
1.
Modified duration of a zero-coupon bond is less than the time before its maturity. In this case, the modified duration equals MD

T m
1

Y
2.
shrinks.
Modified duration decreases as the yield to maturity grows, and increases when the yield
Let us assume that the modified duration is 4, the bond is trading at a price of 90% with a yield of 8%, ACI is zero. How does the price change, if the yield rises to 8.5% (a change of 0.005).
The price change can be calculated as follows: -4*0.005*90=-1.8. Thus, the bond price will fall by 1.8 to
88.2%.
Price Value of Basis Point (PVBP)
In contrast to the modified duration, which is a relative value, PVBP indicates the absolute value of a bond price change following the change in the yield by one basis point.
MD ( P

PVBP

A )
100 100
%
Let us assume that the modified duration is 4, the bond is trading at a price of 90% with a yield of 8%, ACI is zero.
© Cbonds.ru
PVBP

4 90
100 100

0 .
036
16

If the price is 90% of par, estimated change in the bond's monetary value following the change in its yield by one bp is 0.036 currency units (per 100 nominal currency units).
Convexity (Conv)
Convexity is an indicator of the curve-shape relationship between the bond price and yield, which shows how the modified duration changes when the yield shifts by 100 bp. It gives a much better approximation of price change due to yield change.
Conv
 i m 

1
( C i

N i
( 1

Y
) t ( t
) t

2

1 )
P

A
, where t
 t i
 t
0
B
In terms of derivatives: Conv

( P d
)
" y
P d
Price approximation:

P d
P d
 
MD *

Y

1
2
Conv (

Y )
2
Use of modified duration and convexity allow a rather accurate estimation of the percentage change in the bond price due to a significant change in the yield to maturity.
Convexity properties:
1.
Value of convexity grows along with decreasing yield to maturity, and shrinks along with a raise in the yield.
2.
With duration grows, convexity grows faster than duration. This is a consequence of the quadratic dependence of convexity on duration.
3.
At a given value of yield to maturity and time of redemption, the value of convexity is greater for bonds with lower coupon.
4.
For the given level of yield to maturity and coupon, convexity increases along with the tenor.
5.
For a zero-coupon bond
Conv

( t
1
( t


Y
1
)
)
2
2
6.
Convexity of a perpetual bond is
Y
2
Let us assume that the bond tenor is 3 years, annual coupon of 10%, effective yield is 10% p.a., and the bond is trading at par. Then the value of convexity for such bond will be equal to:
Conv

100 * 1 * 2 /( 1 .
1 ) 3 
100 * 2 * 3 /( 1 .
1 )
1000
4 
1100 * 3 * 4 /( 1 .
1 ) 5

22 .
4
How will the price change, if the yield grows to 11% (change of 0.01), MD = 2.5.
The price change can be calculated as follows:
(-2.5*0.01+0.5*22.4*(0.01)
2
)*100 = - 2.4%.
Thus, the bond price will fall 2.4% to 97.6%.
© Cbonds.ru 17

© Cbonds.ru
The current version of the calculator allows computing G-spreads and T-spreads.
G-spread is calculated as the difference between the issue yield and the yield for the point on G-curve with the same duration. G-spread can only be calculated for Russian ruble-denominated bonds. Results of Gspreads computation are published daily in the ruble bond trading results of the Trading Floor Quotes section. The archive of spreads is calculated starting from 2003.
*Zero coupon yield curve for government securities (G-curve) is a zero coupon yield curve defined based on bond transactions in the market of short-term zero-coupon government bonds (GKO) and federal loan bonds
(OFZ). Zero coupon yield curve for government securities is calculated by the Moscow Exchange. G-curve is calculated in real time following transactions with bonds included in the calculation data base.
T-spread is calculated as the difference between the issue yield and the yield on government securities of the USA, Great Britain and Germany in the corresponding issue currency and with comparable modified duration (the calculations are based on the effective yields only). The value is computed only for issues in
USD, EUR, GBP. "Benchmark T-spread" field displays the issue, against which the T-spread is computed on the day of calculation. Issues with floating coupon rate and kinds of issues like STRIPS are excluded from the total amount of benchmarks. In the search for a benchmark for T-spread calculation, data from
Cbonds Valuation floor is used.
Results of T-spreads computation are published daily in the USD bond trading results of the Trading Floor
Quotes section. The archive of spreads for issues in USD is calculated starting from 2013, for issues in EUR,
GBP – from September 2013.
18

References
1.
O.V. Lomatidze, M.I. Lvova, A.V. Bolotin Basic Course of Securities Market. - Moscow: KNORUS,
2010.
2.
F. Fabozzi, S. Mann. The Handbook of Fixed Income Securities, seventh edition, volume 1-2. -
Moscow: "I.D. Williams", 2008
3.
A.N. Burenin Duration and Convexity in Bond Portfolio Management. - Moscow: Scientific and
Technical Society named after Vavilov, 2009
Contact details
Konstantin G. Vasilyev, Partner, Head of Department at Cbonds, Ph.D.
Ph./fax: +7 (812) 336 9721, ext.105. e-mail: kv@cbonds.info
Elena Skurikhina, Head of Projects
Ph./fax: (812) 336 9721, ext.118. e-mail : sea@cbonds.info
© Cbonds.ru 19