Skip to main content

What is Convexity with diagram?


 Convexity: Duration is a linear line which measures the changes in bond price in relation to changes in interest rate. But it does not determine the accurate bond price changes if there is large change in yield rate. On the other hand convexity is measure of the non-linear relationship of bond price in relation to changes in interest rate. It measures the changes in duration in relation to changes in interest rate to determine the accurate bond price.
Formula:
Convexity = 1 / P * (1+y) 2Ʃ Tt=1 [CF / (1+y) 2 (t 2 + t)]
Where,
P = bond price
Y = yield to maturity
CF = Cash flow
T = maturity period
Or
Convexity = P (i decreases) + P (i increases) – 2P0/ 2P0* ∆Y 2
Convexity adjustment = Convexity*100*∆y 2
Change in bond price in percentage with the help of modified duration:
∆p% = -D*p *∆y
Change in bond price in percentage with the help of modified duration and convexity:
∆p% = -D*p *∆y + 0.5*C*∆y 2
Where,
∆p %= change on bond price in percentage
D = duration
P = Initial price of bond
∆y = Change in yield rate
C = convexity

A convexity adjustment is a difference between forward interest rate and future interest rate. It is used to measure the accurate price of a bond because convexity is a non-linear relationship between changes in bond price and yield rate.

In above diagram the straight line shows the modified duration and the curve shows the convexity. It shows in a diagram that small changes can easily measured by duration like yield rate increases by 1 % then the bond price will decreases by Rs. 1. But large change in yield rate does not measured by duration. For large change in interest rate in relation to bond price is measure by convexity by forming a curve in above diagram. The gap between duration line and curve is a duration error and it shows that duration is insufficient to measure the accurate price of a bond.

The convexity can be positive or negative. The negative convexity means the duration increases with increase in yield rate. In negative convexity the bond price will increase as increase in yield rate or price decrease with decease in yield rate. We can say that there is a direct relationship between yield rate and duration. An example of negative convexity is callable bond.
In positive convexity the duration will increases when there is a fall in yield rate. In simple way there is a negative correlation between duration and yield rate. It means the bond price increases when there is a fall in yield rate. An example of positive convexity is non- callable bonds.
The degree of convexity is either higher or lower is depend on coupon rate of a bond. If the coupon rate is high then there is low degree of convexity. So, on the basis of that there is a high degree of convexity of a zero coupon bond.
If there is a two bond, Bond Q and Bond P and both the bond has same duration then select the bond which has lower convexity than the other. Lower convexity decreases the effect of changes in interest rate.


Comments

Post a Comment

Popular posts from this blog

How to calculate Cost of Preference Share Capital?

Cost of Preference Share Capital:  An amount paid by company as dividend to preference shareholder is known as Cost of Preference Share Capital. Preference share is a small unit of a company’s capital which bears fixed rate of dividend and holder of it gets dividend when company earn profit. Dividend payable is not a tax deductible amount. So, there is no tax adjustments required for comparing with cost of debt. Formula for Cost of Preference Share: Irredeemable Preference Share Redeemable Preference Share K p  = Dp/NP K p  = D p +((RV-NP)/n )/ (RV+NP)/2 Where, K p  = Cost of Preference Share D p  = Dividend on preference share NP = Net proceeds from issue of preference share (Issue price – Flotation cost) RV = Redemption Value N = Period of preference share Example:  A company issues 20,000 irredeemable preference share at 8% whose face value is Rs.50 each at 4% discount. Find out the Cost of ...
89 comments
Read more

What is the difference between Cheque book and Pass book?

 Cheque book is issued by bank in customers / account holder request. With the help of this book account holder can withdraw cash from his/her account. Bank does not charge any fee to issued cheque book to its customer. But afterward bank charges some amount for using bank facility like cheque book, Debit card etc.So, Automatic some definite amount deducted from customer bank account. Pass book is  also issued by bank to its customer. It helps to record all the bank related activity according to date that is withdrawal and deposit. It is recorded by bank but the book is kept by customer to know the current balance of  his /her account.  Point of difference Pass book Cheque book What is the meaning of pass book and cheque book? Passbook is a book in which all withdrawal and deposit against customer account is recorded.   Cheque book is a book of cheques which are used to withdrawal the money to b...
Post a Comment
Read more

What is Working Capital Leverage (WCL)?

Working capital leverage: It shows the sensitivity of the return on investment with change in current assets. As we all know the working capital is difference between current assets and current liabilities. And the working capital is use for meeting day to day capital requirements in business operations. With the help of working capital leverage we will find out how productivity or profitability of a business is affected by change in current assets. Formula: Working Capital Leverage (WCL) = % ∆ ROE / % ∆ CA Or If % decreases in current assets: WCL= CA / TA - ∆ CA If % increases in current assets: WCL = CA / TA + ∆ CA Where, CA = current assets TA = total assets ROE = return of capital employed or return on investment ∆ CA = change in current assets Example: Company A total assets are Rs. 17, 60, 800 and the current assets are Rs. 6, 00,000. The fixed assets are Rs. 11, 60, 800. Find out the working capital leverage if the current asset increases by 15...
2 comments
Read more