Question

Problem D. Take 3 semi-annual coupon paying bonds with face values of $100. They carry D1 percent, D2 percent and D3 percent coupons, mature in ½ year, 1 year, and 1 ½ year, with current market prices of D4, D5, and D6, respectively. Find the “crude” (which does not use regression) term structure of discount factor, spot interest rate and forward interest rate. Assume semi-annual compounding and write your answers for:

23. Half-year discount factor.
24. One-year discount factor.
25. One and half-year discount factor.
26. Half-year spot rate.
27. One-year spot rate.
28. One and half-year spot rate.
29. Forward rate for period (0.5 – 1.0) year.
30. Forward rate for period (1.0 – 1.5) year.
31. What is the current fair price of a 1.5 year bond with face value 100, carrying an annual coupon of 10 percent, paid two times per year?
32. What is the current fair price of a 1 year zero coupon bond with face value 100?
33. What is the current fair price of a 6-month strip with face value 100?

D1 = 11
D2 =14
D3 = 9
D4 = 103
D5 = 107
D6 = 107

Please show work.

Answer 1

Answer:-

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23.To calculate half year discount factor:

Semi annual coupon paying bond face value= $100

Maturity=0.5 Year

Market price= $101.64

We can use following excel formula: DISC(DATE(2018,1,1), DATE(2018,6,30),101.64,100,3)

In this formula, we have taken, 1/1/2018 as settlement date, 6/30/2018 as settlement date to calculate 0.5 year. Then current market price $101.64 and redemption price $100. Basis taken as 3, i.e actual/365

We are getting discount as -0.03326

24. Semi annual coupon paying bond face value= $100

Maturity=1 Year

Market price= $97.18

We can use following excel formula: DISC(DATE(2018,1,1),DATE(2018,12,31), 97.18, 100,3)

In this formula, we have taken, 1/1/2018 as settlement date, 12/31/2018 as settlement date to calculate 1 year. Then current market price $97.18 and redemption price $100. Basis taken as 3, i.e actual/365

We are getting discount as 0.0282

25. Semi annual coupon paying bond face value= $100

Maturity=1.5 Years

Market price= $100.41

We can use following excel formula: DISC(DATE(2018,1,1),DATE(2019,6,30), 100.41,100,3)

In this formula, we have taken, 1/1/2018 as settlement date, 6/30/2019 as settlement date to calculate 1.5 years. Then current market price $100.41 and redemption price $100. Basis taken as 3, i.e actual/365

We are getting discount as -0.0027

26. for six months spot rate, future value will be $(100+3.82) =$103.82, as six months coupon will be 7.64/2=$3.82

Spot rate = 2*( (103.82/100)^(1/(0.5*2))-1) =0.0764 or 7.64%