## 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*Po))/((ΔC)^2*Po)
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*Po))/((ΔC)^2*Po) --> (19405+470-(2*135))/((10)^2*135)
Evaluating ... ...
EC = 1.45222222222222
STEP 3: Convert Result to Output's Unit
1.45222222222222 --> No Conversion Required
1.45222222222222 1.452222 <-- Effective Convexity
(Calculation completed in 00.004 seconds)
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## < 18 Strategic Financial Management Calculators

Money Market Discount Rate
Money Market Discount Rate = (Year/Days of Maturity)*(Face Value of Money Market Instrument-Present Value of Money Market Instrument)/Face Value of Money Market Instrument
Effective Convexity
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)
Add on Rate = ((Year/Days)*((Amount Paid at Maturity Including Interest)-Present Value of Money Market Instrument)/(Amount Paid at Maturity Including Interest))
Change in Price of Full Bond
Percentage Change in Price of Bond = (-Annual Modified Duration*Change in Yield)+(1/2*Annual Convexity*(Change in Yield)^2)
Value of Right using New Shares
Value of Right = Number of New Shares*(Market Price-Issue Price of New Share)/Total Number of All Shares
Single Month Mortality
Single Month Morality = Prepayment for a Month/(Beginning Mortgage Balance for Month-Scheduled Principal Repayment for Month)
Value of Right
Value of Right per Share = (Stock Price-Right Subscription Price)/Number of Rights to Buy a Share
Cost of Equity
Cost of Equity = ((Dividend in Next Period/Current Share Price)+(Dividend Growth Rate*0.01))*100
Unlevered Beta
Unlevered Beta = Levered Beta/(1+((1-Tax Rate)*(Debt/Equity)))
Levered Beta
Levered Beta = Unlevered Beta*(1+((1-Tax Rate)*(Debt/Equity)))
Price Value of Basis Point
Price Value of Basis Point = (Price of Bond When Yield is Decreased-Price of Bond When Yield is Increased)/2
Price of Bond
Price of Bond = Face Value*(1+Implied Discount Rate)^Holding Period
Approximate Macaulay Duration
Approximate Macaulay Duration = Approximate Modified Duration*(1+Rate of Interest)
Conversion Parity Price
Conversion Parity Price = Value of Convertible Security/Conversion Ratio
Share Exchange Ratio
Exchange Ratio = Offer Price for Target's Share/Acquirer's Share Price
Earnings Yield
Earnings Yield = (Earnings per Share/Market Price per Share)*100
Dividend Rate
Dividend Rate = (Dividend per Share/Current Share Price)*100
Earnings Yield using PE Ratio
Earnings Yield = (1/Price-Earnings (PE) Ratio)*100

## Effective Convexity Formula

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*Po))/((ΔC)^2*Po)

## 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 (Po) & 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*Po))/((ΔC)^2*Po) 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 (Po) & 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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