Question

In this exercise, you are going to analyze first the relationship between interest rates and bond prices, and then the effect of time to maturity, interest rates and coupon rates on duration.

a) (5 points) First, consider a 10 year bond with a coupon rate of 7% and annual coupon payments. Draw a graph showing the relationship between the price and the interest on this bond. The price should be on the y- axis and the interest rate on the x-axis. To compute the various prices, consider interest rates between 2% and 12% (use 0.5% increments). So your x-axis should go from 2%, then 2.5% ... until 11.5% and then 12%.

Is the relationship linear (i.e. is the slope constant)? Start at 7%. If interest rates go up or down by 0.5% is the price changing by the same amount? What type of relationship do we observe between prices and interest rates (liner, concave, convex or something else)?

b) (5 points) Now consider the same bond with 10 year maturity, a face value or $1,000, a coupon rate of 7% (coupon is paid annually) and assume that the yield to maturity on the bond is 7%. Compute the duration of this bond.

c) (5 points) Next, we are going to analyze the effect of time to maturity on the duration of the bond. Compute the duration of a bond with a face value of $1,000, a coupon rate of 7% (coupon is paid annually) and a yield to maturity of 7% for maturities of 2 to 18 years in 1-year increments (so here we are going to vary the time to maturity and see how duration changes if N=2, 3 ... etc.). What happens to duration as maturity increases?

d) (5 points) Next, we are going to analyze the effect of the yield to maturity on the duration of the bond. Compute the duration of a bond with a face value of $1,000, a coupon rate of 7% (coupon is paid annually) and a maturity of 10 years as the interest rate (or yield to maturity) on the bond changes from 2% to 12% (consider increments of 1% - so you need to compute the duration for various yields to maturity 2%, 3%, ..., 12%) . What happens to duration as the interest rate increases?

e) (5 points) Finally, we are going to analyze the effect of the coupon payment on the duration of the bond. Compute the duration of a bond with a face value of $1,000, a maturity of 10 years and a yield to maturity of 7%. Compute the duration for coupon rates ranging from 2% to 12% (in increments of 1%). What happens to duration as the coupon rate increases?

TO BE DONE IN EXCEL

you cab jusr do part a if it takes you too long and ill submit the other parts as other questions

Answer 1

Answer to part a

n	10	years
coupon rate	7%	coupon payments=	70
Face Value	$ 1,000.00
Int Rate	2.00%	Price	$     1,449.13
	2.50%		$     1,393.84
	3.00%		$     1,341.21
	3.50%		$     1,291.08
	4.00%		$     1,243.33
	4.50%		$     1,197.82
	5.00%		$     1,154.43
	5.50%		$     1,113.06
	6.00%		$     1,073.60
	6.50%		$     1,035.94
	7.00%		$     1,000.00
	7.50%		$        965.68
	8.00%		$        932.90
	8.50%		$        901.58
	9.00%		$        871.65
	9.50%		$        843.03
	10.00%		$        815.66
	10.50%		$        789.48
	11.00%		$        764.43
	11.50%		$        740.45
	12.00%		$        717.49

Compute =PV(rate,nper,pmt,fv,type) using excel by putting rate=2.00% which increases each round by 0.5%

nper=10 years and do absolute referencing

Pmt = $1000*7%= $70 and do it absolute referencing.

Fv as $1000 and press Enter.

Below is the graph showing int rate on x-axis and price on y-axis.

Calculating the slope from 0.5% increase form 7% we get= (965.68-1000)/(7.50%-7.00%)=-6864.08

Calculating the slope from 0.5%decrease from 7%, we get=(1000-965.68)/(7.00%-7.50%)=-6864.08

Likewise, we can calculate for each 0.5% increase or decrease in interest rate what effect it has on the price

the relationship is Linear and the slope is constant.