Bond Convexity Approximation Calculator

✖Bond Price when Incremented refers to how the price of a bond changes when certain factors are incremented or increased.ⓘ Bond Price when Incremented [P₊]			+10% -10%
✖Bond Price when Decremented refers to the impact on the price of a bond when the yield (interest rate) decreases.ⓘ Bond Price when Decremented [P_-]			+10% -10%
✖Bond Value refers to the current worth or price of a bond in the financial markets.ⓘ Bond Value [P₀]			+10% -10%
✖Change in Interest Rate refers to the difference between the new interest rate and the previous interest rate.ⓘ Change in Interest Rate [Δ_y]			+10% -10%

✖Bond Convexity Approximation is an approximation measure of the sensitivity of the duration of a bond to changes in interest rates.ⓘ Bond Convexity Approximation [BC_A]

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Formula

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Bond Convexity Approximation

Formula

`"BC"_{"A"} = ("P"_{"+"}+"P"_{"-"}-2*("P"_{"0"}))/(2*"P"_{"0"}*("Δ"_{"y"})^2)`

Example

`"13750"=("35"+"30"-2*("5"))/(2*"5"*("0.02")^2)`

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Bond Convexity Approximation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bond Convexity Approximation = (Bond Price when Incremented+Bond Price when Decremented-2*(Bond Value))/(2*Bond Value*(Change in Interest Rate)^2)
BC_A = (P₊+P_--2*(P₀))/(2*P₀*(Δ_y)^2)
This formula uses 5 Variables

Variables Used

Bond Convexity Approximation - Bond Convexity Approximation is an approximation measure of the sensitivity of the duration of a bond to changes in interest rates.
Bond Price when Incremented - Bond Price when Incremented refers to how the price of a bond changes when certain factors are incremented or increased.
Bond Price when Decremented - Bond Price when Decremented refers to the impact on the price of a bond when the yield (interest rate) decreases.
Bond Value - Bond Value refers to the current worth or price of a bond in the financial markets.
Change in Interest Rate - Change in Interest Rate refers to the difference between the new interest rate and the previous interest rate.

STEP 1: Convert Input(s) to Base Unit

Bond Price when Incremented: 35 --> No Conversion Required
Bond Price when Decremented: 30 --> No Conversion Required
Bond Value: 5 --> No Conversion Required
Change in Interest Rate: 0.02 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

BC_A = (P₊+P_--2*(P₀))/(2*P₀*(Δ_y)^2) --> (35+30-2*(5))/(2*5*(0.02)^2)

Evaluating ... ...

BC_A = 13750

STEP 3: Convert Result to Output's Unit

13750 --> No Conversion Required

FINAL ANSWER

13750 <-- Bond Convexity Approximation

(Calculation completed in 00.004 seconds)

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Created by Vishnu K

BMS College of Engineering (BMSCE), Bangalore

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Satyawati College (DU), New Delhi

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< 10+ Bond Yield Calculators

Coupon Bond Valuation

Go Coupon Bond = Annual Coupon Rate*((1-(1+Yield to Maturity (YTM))^(-Number of Payments Per Year))/(Yield to Maturity (YTM)))+(Par Value at Maturity/(1+Yield to Maturity (YTM))^(Number of Payments Per Year))

Yield to Call for Callable Bond

Go Yield to Call = ((Coupon Payment+(Theoretical Price of Call Option-Current Bond Price)/Number of Years to Track Growth)/((Theoretical Price of Call Option+Current Bond Price)/2))

Bond Convexity Approximation

Go Bond Convexity Approximation = (Bond Price when Incremented+Bond Price when Decremented-2*(Bond Value))/(2*Bond Value*(Change in Interest Rate)^2)

Yield to Maturity

Go Yield to Maturity (YTM) = (Coupon Payment+((Face Value-Price)/Years to Maturity))/((Face Value+Price)/2)

Holding Period Yield

Go Holding Period Yield = (Interest Paid+Face Value-Purchase Price)/Face Value

Zero Coupon Bond Effective Yield

Go Zero Coupon Bond Effective Yield = (Face Value/Present Value)^(1/Number of Periods)-1

Zero Coupon Bond Value

Go Zero Coupon Bond Value = Face Value/(1+Rate of Return/100)^Time to Maturity

Bank Discount Yield

Go Bank Discount Yield = (Discount/Face Value)*(360/Days to Maturity)*100

Money Market Yield

Go Money Market Yield = Holding Period Yield*360/Time till Maturity

Current Bond Yield

Go Current Bond Yield = Coupon Payment/Current Bond Price

Bond Convexity Approximation Formula

Bond Convexity Approximation = (Bond Price when Incremented+Bond Price when Decremented-2*(Bond Value))/(2*Bond Value*(Change in Interest Rate)^2)
BC_A = (P₊+P_--2*(P₀))/(2*P₀*(Δ_y)^2)

What is Bond Convexity Approximity?

Bond convexity is a measure of the sensitivity of a bond's duration to changes in interest rates. It provides additional information beyond what is captured by duration alone, particularly in the case of non-linear changes in bond prices due to interest rate fluctuations. Convexity helps investors better understand the potential price changes of a bond when interest rates change.
The concept of convexity stems from the shape of the price-yield curve. When plotted, the relationship between bond prices and yields generally exhibits a curved shape, particularly for bonds with coupon payments. Convexity measures this curvature and helps investors assess how much the bond's price will change when yields move.

How to Calculate Bond Convexity Approximation?

Bond Convexity Approximation calculator uses Bond Convexity Approximation = (Bond Price when Incremented+Bond Price when Decremented-2*(Bond Value))/(2*Bond Value*(Change in Interest Rate)^2) to calculate the Bond Convexity Approximation, The Bond Convexity Approximation formula is defined as a measure of the sensitivity of the duration of a bond to changes in interest rates. Bond Convexity Approximation is denoted by BC_A symbol.

How to calculate Bond Convexity Approximation using this online calculator? To use this online calculator for Bond Convexity Approximation, enter Bond Price when Incremented (P₊), Bond Price when Decremented (P_-), Bond Value (P₀) & Change in Interest Rate (Δ_y) and hit the calculate button. Here is how the Bond Convexity Approximation calculation can be explained with given input values -> 13750 = (35+30-2*(5))/(2*5*(0.02)^2).

FAQ

What is Bond Convexity Approximation?

The Bond Convexity Approximation formula is defined as a measure of the sensitivity of the duration of a bond to changes in interest rates and is represented as BC_A = (P₊+P_--2*(P₀))/(2*P₀*(Δ_y)^2) or Bond Convexity Approximation = (Bond Price when Incremented+Bond Price when Decremented-2*(Bond Value))/(2*Bond Value*(Change in Interest Rate)^2). Bond Price when Incremented refers to how the price of a bond changes when certain factors are incremented or increased, Bond Price when Decremented refers to the impact on the price of a bond when the yield (interest rate) decreases, Bond Value refers to the current worth or price of a bond in the financial markets & Change in Interest Rate refers to the difference between the new interest rate and the previous interest rate.

How to calculate Bond Convexity Approximation?

The Bond Convexity Approximation formula is defined as a measure of the sensitivity of the duration of a bond to changes in interest rates is calculated using Bond Convexity Approximation = (Bond Price when Incremented+Bond Price when Decremented-2*(Bond Value))/(2*Bond Value*(Change in Interest Rate)^2). To calculate Bond Convexity Approximation, you need Bond Price when Incremented (P₊), Bond Price when Decremented (P_-), Bond Value (P₀) & Change in Interest Rate (Δ_y). With our tool, you need to enter the respective value for Bond Price when Incremented, Bond Price when Decremented, Bond Value & Change in Interest Rate and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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