Answer  : DURATION OF BONDS

Bond Duration is a measure of bond price volatility, which captures both price and reinvestment risk and which is used to indicate how a bond will react in different interest rate environments. The duration of a bond represents the length of time that elapses before the average rupee of present value from the bond is received. Thus duration of a bond is the weighted average maturity of cash flow stream, where the weights are proportional to the present value of cash flows. Formally, it is defined as:

Duration = D = {PV (C1) x 1 + PV (C2) x 2+ —– PV (Can) x n} / Current Price of the bond

Where PV (Chi) is the present values of cash flow at time I.

Steps in calculating duration:

Step 1 : Find present value of each coupon or principal payment.

Step 2 : Multiply this present value by the year in which the cash flow is to be received.

Step 3 : Repeat steps 1 & 2 for each year in the life of the bond.

Step 4 : Add the values obtained in step 2 and divide by the price of the bond to get the

value of Duration.

Example: Calculate the duration of an 8% annual coupon 5 year bond that is priced to

yield 10% (i.e. YTM = 10%). The face value of the bond is Rs.1000.

Annual coupon payment = 8% x Rs. 1000 = Rs. 80

At the end of 5 years, the principal of Rs. 1000 will be returned to the investor. Therefore cash flows in year 1-4= Rs. 80.

Cash flow in year 5= Principal + Interest = Rs. 1000 + Rs. 80 = Rs. 1080

(t)	Annual Cash flow	PVIF @10%	Present Value of Annual Cash Flow PV(Ct)	Explanation	Time x PV of cash flow	Explanation
1	80	0.90909	72.73	= 80 x 0.90909	72.73	= 1 x 72.73
2	80	0.82645	66.12	= 80 x 0.82645	132.24	= 2 x 66.12
3	80	0.75131	60.10	= 80 x 0.75131	180.3	= 3 x 60.1
4	80	0.68301	54.64	= 80 x 0.68301	218.56	= 4 x 54.64
5	1080	0.62092	670.59	= 1080 x 0.62092	3352.95	= 5 x 670.59
Total			924.18		3956.78

 

Price of the bond= Rs 924.18

The proportional change in the price of a bond:

(ΔP/P) = – {D/ (1+ YTM)} x Δ y

Where Δ y =change in Yield, and YTM is the yield-to-maturity.

The term D / (1+YTM) is also known as Modified Duration. The modified duration for the bond in the example above = 4.28 / (1+10%) = 3.89 years. This implies that the price of the bond will decrease by 3.89 x 1% = 3.89% for a 1% increase in the interest rates.

 

 

Q.2 Using financial ratios, study the financial performance of any particular company of your interest.

Q.3 Show with the help of an example how portfolio diversification reduces risk.

Q.4 Differentiate between ADRs and GDRs

Q.5 Study the performance of any emerging market of your choice.

 

Q.6 As an investor how would you select an equity mutual fund scheme?