Answer the following questions on bond valuation and duration. part b info: Face value of $1000 Five years to maturity Coupon rate of 11%, paid semi-annually Current price of $970 (Hint: The effective annual yield should be 12.1604%.) part b information Macaulay Duration=[(t1 X FV)(C)/(m X PV)(1+Y)T]+...+[(tn X FV)(C)/(mXPV)(1+YTM/m)mtn X (tnXFV)/(PV) (1+YTM/m)mtn.Macaulay Duration=[(t1 X FV)(C)/(m X PV)(1+Y)T]+...+[(tn X FV)(C)/(mXPV)(1+YTM/m)mtn X (tnXFV)/(PV) (1+YTM/m)mtn. T = Total time = 5; C = Coupon payment = 1,000 X (0.11/2) = $55; Y = Yield = 12.1604%/2 = 0.0607; N = No. of periods = 2; M = Maturity = 5 years; and Bond Price = $970. Macaulay Duration = [(0.5 X $1,000) ($55)/(5 X $670)(1+0.0607)2X0.5]+ [(1 X $1,000) ($55)/(5 X $670)(1+0.0607)2X1] + [(1.5 X $1,000) ($55)/(5 X $670)(1+0.0607)2X1.5]+....+ [(10 X $1,000) ($55)/(5 X $670)(1+0.0607)2X10]] X [(10 X $1,000)/($970)(1+0.0607)2X10].Macaulay Duration = [(0.5 X $1,000) ($55)/(5 X $670)(1+0.0607)2X0.5]+ [(1 X $1,000) ($55)/(5 X $670)(1+0.0607)2X1] + [(1.5 X $1,000) ($55)/(5 X $670)(1+0.0607)2X1.5]+....+ [(10 X $1,000) ($55)/(5 X $670)(1+0.0607)2X10]] X [(10 X $1,000)/($970)(1+0.0607)2X10]. Macaulay duration = 3.95 years.Macaulay duration = 3.95 years. Modified Duration = Macaulay Duration/(1+YTM/m) Modified Duration = 3.95/(1+0.1216/2) Modified Duration = 3.72 years. Macaulay duration of the bond is3.95 years and modified duration is 3.72 years. c. Duration is a measure of interest rate risk. Specifically, it measures the approximate percentage change in bond price given a small percentage change in interest rate (% bond price change / % interest rate change). For example, for a bond with a duration of five years, a 0.1% change in interest rate would change the bond’s price by 5 * 0.1% = 0.5%, approximately. Suppose that the interest rates on all bonds increase uniformly by 0.1% (this is what is commonly called a “parallel upward shift in yields of 10 basis points”). What is the percentage change in the price on the coupon bond in part (b)? What is the approximate coupon bond price? Note that bond yield and bond price
A2 9c
with info from b.
May I please have it in formula version and not excel. thx:)
Answer the following questions on bond valuation and duration.
9. Answer the following questions on bond valuation and duration.
part b info:
Face value of $1000
Five years to maturity
Coupon rate of 11%, paid semi-annually
Current price of $970
(Hint: The effective annual yield should be 12.1604%.)
part b information
Macaulay Duration=[(t1 X FV)(C)/(m X PV)(1+Y)T]+...+[(tn X FV)(C)/(mXPV)(1+YTM/m)mtn X (tnXFV)/(PV) (1+YTM/m)mtn.Macaulay Duration=[(t1 X FV)(C)/(m X PV)(1+Y)T]+...+[(tn X FV)(C)/(mXPV)(1+YTM/m)mtn X (tnXFV)/(PV) (1+YTM/m)mtn.
T = Total time = 5; C = Coupon payment = 1,000 X (0.11/2) = $55; Y = Yield = 12.1604%/2 = 0.0607;
N = No. of periods = 2; M = Maturity = 5 years; and
Macaulay Duration = [(0.5 X $1,000) ($55)/(5 X $670)(1+0.0607)2X0.5]+ [(1 X $1,000) ($55)/(5 X $670)(1+0.0607)2X1] + [(1.5 X $1,000) ($55)/(5 X $670)(1+0.0607)2X1.5]+....+ [(10 X $1,000) ($55)/(5 X $670)(1+0.0607)2X10]] X [(10 X $1,000)/($970)(1+0.0607)2X10].Macaulay Duration = [(0.5 X $1,000) ($55)/(5 X $670)(1+0.0607)2X0.5]+ [(1 X $1,000) ($55)/(5 X $670)(1+0.0607)2X1] + [(1.5 X $1,000) ($55)/(5 X $670)(1+0.0607)2X1.5]+....+ [(10 X $1,000) ($55)/(5 X $670)(1+0.0607)2X10]] X [(10 X $1,000)/($970)(1+0.0607)2X10].
Macaulay duration = 3.95 years.Macaulay duration = 3.95 years.
Modified Duration = Macaulay Duration/(1+YTM/m)
Modified Duration = 3.95/(1+0.1216/2)
Modified Duration = 3.72 years.
Macaulay duration of the bond is3.95 years and modified duration is 3.72 years.
c. Duration is a measure of interest rate risk. Specifically, it measures the approximate percentage change in bond price given a small percentage change in interest rate (% bond price change / % interest rate change). For example, for a bond with a duration of five years, a 0.1% change in interest rate would change the bond’s price by 5 * 0.1% = 0.5%, approximately.
Suppose that the interest rates on all bonds increase uniformly by 0.1% (this is what is commonly called a “parallel upward shift in yields of 10 basis points”). What is the percentage change in the price on the coupon bond in part (b)? What is the approximate coupon bond price? Note that bond yield and bond price are inversely related to each other (i.e., an increase in yield should lead to a decrease in bond price).
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