IRC

IRC

1 Currencies for which actual/365 is used are GBP, NZD, AUD, SGD, CAD, HKD, ZAR

2 Tokyo Overnight Average Rate

3 The convention for terms longer than four weeks in the money market is modified following.

4 The End of Month (EOM) convention should be used here.

5 In this case the End of Month convention should be used.

6 The convention for short-dates is Following.

7 0.045 bond basis is equivalent to 0.045 x 360/365 = 0.0444 money market basis. And 0.0444 semi-annual is equivalent to ((1 + 0.0444 - 1 )^0.5 -1) x 2 = 0.0449

8 360/ 365 x 0.0308= 0.0304

9 (1 + 0.0508/2)^2 - 1 = 0.0514

10 0.0445 actual/360 is equivalent with 365/360 x 0.0445 = 0.0451 bond basis. And 0.0451 annual - (1.0451^2-1) x 2 = 0.0446 semi-annual

11 2.87% bond basis is equivelant with 360/365 x 2.87% = 2.83% actual/360. And 2.85% annual is (1.0285^0.5 - 1) x 2 = 2.81% semi-annual

12 3.60% + 0.15% x 10/30 = 3.65%

1 Interest Rate Calculations - IRC

IRC

13 3.10% + 20/90 x (3.55% - 3.10%) = 3.20%

14 Yield = 0.0254 / ( 1 - 61/360 x 0.0254) = 0.0255

15 PV = 5,000,000 / ( 1 + 87 / 360 x 0.0426) = 4,949,050

16 Holding period return = 31,250 / 10,000,000 x 360 / 45 = 0.025

17 The interest for financial instruments with a term over 1 year is always paid annually.

18 ((1 + 31/360 x 0.0456) x ( 1 + 60/360 x 0.0471) - 1 ) x 360/91 = 0.0467

19 (1 + 62/365 x 0.0265) x (1 + 78/365 x 0.0287) x (1 + 93/365 x 0.0304) - 1) x 365 / (62 + 78 + 93) = 0.0290

20 The curve stays normal but becomes less steep.

21 Market Segmentation Theory is a modern theory stating that that there is no necessary relationship between long and short-term interest rates & and that investors have fixed maturity preferences. It is also called segmented markets theory. Supporters of Market Segmentation Theory maintain that short-term and long-term rates are distinct markets, each with its own buyers and sellers, and are not easily substituted for each other.

22 rb = 4,20% + 20/30 ? 0.30 = 4,40%

23 50M x ( 1+31/360 x 0.0367) = 50,158,013.90

24 100,000 / 15,500,000 x 360/91 = 0.0255

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IRC

25 Equivalent annual yield: (1 + 0.0275/2)^2 -1 = 0.0277 and bond basis: 0.0277 x 365/360 = 0.0281

26 ((1 + 31/360 x 0.0178) x (1 + 60/360 x 0.0198) - 1 ) x 360 / 91 = 0.0191

27 12th June is Saturday. According to the modified following convention: Monday 14 June

28 According to the end of month (EOM) convention, the 3 month value date is Tuesday 31th May.

29 Spot is 30th April. Regular 6 months date would be Saturday 30th October. According to the modified following convention: Friday 29 October because Monday would be 1 November and the value date should not exceed a month ultimo.

30 2.20% + 20/30 x 0.30% = 2.40%

31 rb = 4,20% + 20/30 ? 0.30 = 4,40%

32 200,000/31,000,000 x 360/91 = 0.0255

33 29,275 / 50,000,000 x 360/91 = 0.0232

34 ( 1 + 0.042 / 2)2 - 1 = 0.0424

35 ((1.0287)^0.5 - 1) x 2 = 0.0285. Next, convert from actual/ 360 to bond basis: 0.0285% x 365/360 = 0.0289.

36 0.025/ ( 1 - 180/360 x 0.025) = 0.0253

3 Interest Rate Calculations - IRC

IRC

37 The equation to be used is

Yield = ----------------------P----D-----R-----------------------1 ? # days / 360 ? PDR

Yield = -------------------0---.--0---3---5-------------------- = 0.0361 1 ? 316 / 360 ? 0.035

38

Present value

=

--N-----O----K------2---0---,-0----0---0---,-0---0---0--1 + 60/360 x 0.035

=

NOK 19,884,009.94

39 Price (present value) = -----------S---E----K-------2---0----m-----i-o------------ = SEK 19,887,305.27

1 + 0,017 ? 120 / 360

40 Price = USD 5 mio ? (1 ? 0.04 ? 90 / 360) = USD 4,950,000

41

Discounted amount= USD 10,000,000 x ( 1 - 90/360 x 0.025) = USD 9,937,500

42 ((1 + 180/360 x 0.0575)/(1 + 90/360 x 0.055625) - 1) x 360/(180-90)

43 ((1 + 91/360 x 0.0205)/(1 + 31/360 x 0.0175) - 1) x 360/(91-31)

44

rfw

=

1-----+-----0---,-0---2---7---3-----?-----1---8---0----/---3---6---01 + 0,0257 ? 90 / 360

?

1

? 360 / 90

=

--1---,-0---1---3----6--5--1,006425

?

1

?4

=

0,0287

45

The general to calculate a forward rate in the money market is:

rfw Here

=

-1----+-----r---l--?-----d---l---/--3---6---0-1 + rs ? ds / 360

?

1

? 360 / (dl ? ds)

rfw

=

1-----+-----0---.-0---1---6-----?-----2---7---3----/---3---6---01 + 0.015 ? 182 / 360

?

1

? 360 / 91

=

0.0179

46 The equation to calculate a forward rate in the money market is:

rfw

=

-1-----+----r---l--?-----d---l---/---3---6---51 + rs ? ds / 365

?

1

? 360 / (dl ? ds)

Here

4 Interest Rate Calculations - IRC

IRC rfw = -1-1---+--+---0-0--.-.0--0-0--0-8--7-0--0---?-?----1-6--5-2--4---/-/-3--3-6--6-5--5- ? 1 ? 360 / 92 = 0.0087

47 ((1 + 31/360 x 0.0234) x (1 + 60/360 x 0.0255) x ( 1 + 92 /360 x 0.0262) - 1) x 360/183

5 Interest Rate Calculations - IRC

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