Question

Case 3:

We find the data for a municipal bond issued by the Illinois state government.

The bond’s “last trade date” (i.e., settlement date) is June 05, 2019.

The bond’s “maturity date” is March 14, 2054.

The bond’s “coupon rate” is fixed as “5.000%” per year.

The bond’s coupon “payment frequency” is “semi-annual”.

The bond’s “last trade yield” (i.e., yield-to-maturity) is quoted as “4.280%” per year.    

(a) Based on the aforementioned settlement date, maturity date, coupon rate, coupon payment frequency and yield to maturity, what shall be the corresponding bond PRICE (relative to redemption par of 100)?

(b) Assumes that the Fed suddenly tightens its monetary policy now, causing interest rates to rise across financial markets. The aforementioned IL municipal bond’s yield-to-maturity also rises from 4.280% to “5.280%” per year. Will the bond PRICE go up or go down then? By how much?

(c) Assumes that the Fed suddenly loosens its monetary policy now, causing interest rates to rise across financial markets. The aforementioned IL municipal bond’s yield-to-maturity also drops from 4.280% to “3.280%” per year. Will the bond PRICE go up or go down then? By how much?

(d) Based on your answers to (b) and (c), is there a positive, negative or zero association between bond YIELD and its PRICE? (Hint: Positive association means “moving in the same direction”, negative association means “moving in the opposite directions”, while zero association means “one moves but the other does not get affected”.)

Answer 1

Interest days are calculated as per MSRB Rule G-33 , ie. Every month has 30 days& year, 360 days
Interest due to the seller :
Mar 15-June 4
15	Mar
30	Apr
30	May
4	June
79

a..Price of the bond
Accrued Interest upto 4th june	2.5%*100*79/360	0.5486
PV of (35*2)=70 semi-annual coupons at the semi annual yield	2.5*(1-1.0214^-70)/0.0214	90.2876
PV of face value at maturity at the s/a yield rate	100/1.0214^70=	22.7138
bond PRICE		113.55
b.yield-to-maturity rises from 4.280% to “5.280%”
Price of the bond
Accrued Interest upto 4th june	2.5%*100*79/360	0.5486
PV of (35*2)=70 semi-annual coupons at the s/a yield	2.5*(1-1.0264^-70)/0.0264	90.2876
PV of face value at maturity at the s/a yield rate	100/1.0264^70=	16.1375
bond PRICE		106.97
the bond PRICE goes down By 113.55-106.97=
6.58
c.bond’s yield-to-maturity drops from 4.280% to “3.280%”
Accrued Interest upto 4th june	2.5%*100*79/360	0.5486
PV of (35*2)=70 semi-annual coupons at the s/a yield	2.5*(1-1.0164^-70)/0.0164	103.6221
PV of face value at maturity at the s/a yield rate	100/1.0164^70=	32.0239
bond PRICE		136.19
the bond PRICE goes up By 136.19-113.55=
22.64
d. There is a negative association between bond YIELD and its PRICE
Yield rises , price falls
Yield falls, price rises