Convexity of a bond

 

Modified duration comes from first order derivative of present value of future cash flows from a bond. For small changes in yield the first order derivative is adequate, however, for large changes in yield, it gives inaccurate results.

It’s evident from the formula of duration that it’s not a static property of a bond but depends on time and change in yield. Since the price-yield relationship is not linear but convex (slope or duration is different at different points in the curve), larger the change in yield larger the error in estimating the impact on price of a bond using modified duration. Read more

June 21, 2008 | Filed Under Bonds | Leave a Comment 

Dollar Value of a Basis Point

 Amount of change in price of a bond in response to 1 basis point change in yield is Dollar value of a basis point (DVBP) or Dollar value of one basis point change (DV01).

A basis point is a one hundredth percentage i.e. 0.01%. The term basis point is used in fixed income market to measure change in interest rates.

Calculating DVBP

Going back to the formula that we derived for price sensitivity of a bond, Read more

June 15, 2008 | Filed Under Bonds | Leave a Comment 

Relation between Duration and Price Sensitivity

As we already discussed, price of a bond can be given by present value of its future cash flows.
P = CF1/(1+r)1 + CF2/(1+r)2 + …….+ CFn/(1+r)tn

From the above formula, it’s evident that r, the market yield or discount rate, affects price of a bond in a big way. Now let’s examine how prices change in response to a small change in yield (r).

Differentiate the above equation with respect to r

dP/dr = -CF1/(1+r)2 -2*CF2/(1+r)3 -3*CF3/(1+r)4 -………-n*CFn/(1+r)n+1

The above equation can be written as

dP/dr = -1/(1+r) [CF1/(1+r) + 2*CF2/(1+r)2 + ….+ n*CFn/(1+r)n ] Read more

June 14, 2008 | Filed Under Bonds | Leave a Comment 

Duration of a Bond

 

Duration of a bond refers to its weighted average life. Bond duration is a measurement of how long in years it takes for the price of a bond to be repaid by its internal cash flows. The duration is always lesser than its maturity period for coupon paying bonds as the coupons received can be reinvested and money can be generated. The more frequent the coupon payments the lesser will be the effective life of a bond. For a zero coupon bond there are no intermittent coupon payment and hence the duration and maturity period are same.

Let’s us discuss duration with a simple example. Read more

June 14, 2008 | Filed Under Bonds | Leave a Comment 

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