Effective Convexity Calculator

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✖Price of Bond When Yield is Decreased refers to the new price of the bond after a hypothetical reduction in the yield or interest rate.ⓘ Price of Bond When Yield is Decreased [PV_-]			+10% -10%
✖Price of Bond When Yield is Increased refers to the new price of the bond after a hypothetical increase in the yield or interest rate.ⓘ Price of Bond When Yield is Increased [PV₊]			+10% -10%
✖Initial Price of Bond is the price of the bond at the beginning of the fiscal year.ⓘ Initial Price of Bond [P_o]			+10% -10%
✖Change in Curve refers to movements or shifts in the yield curve, which is a graphical representation of the relationship between interest rates and different maturities of debt securities.ⓘ Change in Curve [ΔC]			+10% -10%

✖Effective Convexity is a measure used in bond investing to assess the sensitivity of a bond's duration to changes in interest rates.ⓘ Effective Convexity [EC]

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Effective Convexity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Effective Convexity = (Price of Bond When Yield is Decreased+Price of Bond When Yield is Increased-(2*Initial Price of Bond))/((Change in Curve)^2*Initial Price of Bond)
EC = (PV_-+PV₊-(2*P_o))/((ΔC)^2*P_o)
This formula uses 5 Variables

Variables Used

Effective Convexity - Effective Convexity is a measure used in bond investing to assess the sensitivity of a bond's duration to changes in interest rates.
Price of Bond When Yield is Decreased - Price of Bond When Yield is Decreased refers to the new price of the bond after a hypothetical reduction in the yield or interest rate.
Price of Bond When Yield is Increased - Price of Bond When Yield is Increased refers to the new price of the bond after a hypothetical increase in the yield or interest rate.
Initial Price of Bond - Initial Price of Bond is the price of the bond at the beginning of the fiscal year.
Change in Curve - Change in Curve refers to movements or shifts in the yield curve, which is a graphical representation of the relationship between interest rates and different maturities of debt securities.

STEP 1: Convert Input(s) to Base Unit

Price of Bond When Yield is Decreased: 19405 --> No Conversion Required
Price of Bond When Yield is Increased: 470 --> No Conversion Required
Initial Price of Bond: 135 --> No Conversion Required
Change in Curve: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

EC = (PV_-+PV₊-(2*P_o))/((ΔC)^2*P_o) --> (19405+470-(2*135))/((10)^2*135)

Evaluating ... ...

EC = 1.45222222222222

STEP 3: Convert Result to Output's Unit

1.45222222222222 --> No Conversion Required

FINAL ANSWER

1.45222222222222 ≈ 1.452222 <-- Effective Convexity

(Calculation completed in 00.004 seconds)

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Created by Aashna

IGNOU (IGNOU), India

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Indian Institute of Technology, Indian School of mines, Dhanbad (IIT ISM Dhanbad), Dhanbad

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Effective Convexity Formula

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What is Effective Convexity ?

Effective Convexity metric helps investors understand how the bond's duration (interest rate sensitivity) changes as interest rates change. It provides a more accurate reflection of the bond’s price volatility compared to traditional convexity measures by taking into account the potential changes in cash flows due to these options. Effective Convexity helps in understanding the interest rate risk of bonds with embedded options, which can have non-linear price movements in response to yield changes. It aids in more accurate pricing and valuation of bonds, especially those with call or put options, by considering how cash flows change with interest rates. In summary, effective convexity is a crucial metric in fixed income investing, providing a comprehensive measure of interest rate risk for bonds with embedded options by accounting for the potential changes in cash flows due to these options.

How to Calculate Effective Convexity?

Effective Convexity calculator uses Effective Convexity = (Price of Bond When Yield is Decreased+Price of Bond When Yield is Increased-(2*Initial Price of Bond))/((Change in Curve)^2*Initial Price of Bond) to calculate the Effective Convexity, Effective Convexity measures the curvature of the relationship between a bond's price and interest rates, considering changes in cash flows due to embedded options. Effective Convexity is denoted by EC symbol.

How to calculate Effective Convexity using this online calculator? To use this online calculator for Effective Convexity, enter Price of Bond When Yield is Decreased (PV_-), Price of Bond When Yield is Increased (PV₊), Initial Price of Bond (P_o) & Change in Curve (ΔC) and hit the calculate button. Here is how the Effective Convexity calculation can be explained with given input values -> 1.452222 = (19405+470-(2*135))/((10)^2*135).

FAQ

What is Effective Convexity?

Effective Convexity measures the curvature of the relationship between a bond's price and interest rates, considering changes in cash flows due to embedded options and is represented as EC = (PV_-+PV₊-(2*P_o))/((ΔC)^2*P_o) or Effective Convexity = (Price of Bond When Yield is Decreased+Price of Bond When Yield is Increased-(2*Initial Price of Bond))/((Change in Curve)^2*Initial Price of Bond). Price of Bond When Yield is Decreased refers to the new price of the bond after a hypothetical reduction in the yield or interest rate, Price of Bond When Yield is Increased refers to the new price of the bond after a hypothetical increase in the yield or interest rate, Initial Price of Bond is the price of the bond at the beginning of the fiscal year & Change in Curve refers to movements or shifts in the yield curve, which is a graphical representation of the relationship between interest rates and different maturities of debt securities.

How to calculate Effective Convexity?

Effective Convexity measures the curvature of the relationship between a bond's price and interest rates, considering changes in cash flows due to embedded options is calculated using Effective Convexity = (Price of Bond When Yield is Decreased+Price of Bond When Yield is Increased-(2*Initial Price of Bond))/((Change in Curve)^2*Initial Price of Bond). To calculate Effective Convexity, you need Price of Bond When Yield is Decreased (PV_-), Price of Bond When Yield is Increased (PV₊), Initial Price of Bond (P_o) & Change in Curve (ΔC). With our tool, you need to enter the respective value for Price of Bond When Yield is Decreased, Price of Bond When Yield is Increased, Initial Price of Bond & Change in Curve 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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