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Maths Summary Intro: Zero coupon yield curve (Ex 13) TV concept - - PDF document
Maths Summary Intro: Zero coupon yield curve (Ex 13) TV concept - - PDF document
Maths Summary Intro: Zero coupon yield curve (Ex 13) TV concept Yield curve construction calcs (Ex 13) Yield curve prods calcs Stats calcs Intro yield curve AER (%) 10% Risk free 8% Zero coupon 7% Maturities
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TV Concept
John invests R5000 @ 5% NACM. How much interest does he have after:
a) 1 yr (365 days) b) 30 days (1 month) c) 60 days (2 months)?
Assume int. re-invested (=> PMT = 0)
TV Concept
1 YR 1 month 2 months Clear All
AER?255.81 / 5000 x 100 = 5.1162 = 5.12% HP calc: 5 Nom% ; 12 P/YR; Press EFF% = 5.12%NACA
End Mode 5000 +- PV 5 I/YR 12 P/YR 12 N 0 PMT Press FV 5 255.809 Int = FV – PV = 255.81 √ √ √ √ √ √ √ 1 N √ 5 020.83 41.75 √ √ √ √ √ √ √ 2 N √ 5 041.75 20.83
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TV Concept
Calc some AERs AER vs. Annualised
P/Yr N John invests @ 10.5% NACM from 1 Jan11 to 1 Jul12 John invests … NACQ 1 Jan11 to 1 Jul12 John invests … NACSA 1 Jan11 to 1 Jul11 John invests … NACA 1 Jan11 to 1 Jan13 John invests … NACM 1 Jan11 to 1 Oct11
12 4 2 1 12 18 6 1 2 9
TV Concept
Sometimes disc. Rate
- Disc. Rate ≠ i
First convert into yield (= int. rate) Formula (disc. Rate int. rate) 365i (365 – id) Calc see later
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Yield curve construction Ex 13
a)
i)
9.72 Nom%; 365 P/YR; Press EFF% = 10.207%NACA ii) 365 x 9.59/100 (365 – 9.59/100 x 91) = 9.825% NACQ iii) 9.825 Nom%; 4 P/YR; Press EFF% = 10.193%NACA iv) 9.96 EFF%; 2 P/YR; Press NOM% = 9.724% LT rates for prods derived in this way
Yield curve construction Ex 13
a) v) 8.03 NOM%; 2 P/YR; Press EFF% = 8.191%NACA vi) 8.20 NOM%; 2 P/YR; Press EFF% = 8.368%NACA b) See next slide
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Yield curve construction Ex 13
Χ Χ Χ Χ Χ
AER (%) Maturities
1d 91d 182d 2 yr 4 yr 10 9 8
c) Negative – downwards, Lower risk (infl.) in LT d) Lower risk (infl.) in LT e)-5000 PV; 8.191 I/YR;1 P/YR; 2 N; 0 PMT; Press FV = 5852.65
Yield curve construction Ex 13 (f)
Χ Χ Χ Χ Χ
AER (%) Maturities
1d 91d 182d 2 yr 4 yr 10 9 8
?
9.825% 9.724%
Step 1 (1 + 182/365 x 9.724/100) = 1.0484868 Step 2 (1 + 91/365 x 9.825/100) = 1.0244952 (1.0484868/1.0244952) -1) x 365/(182 -91) x 100 = 9.393%
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Yield curve prods calcs
Sign Conventions Fin Calc PV Initial Investment amount PV Loan (Initial amount) Repayment loan (= PMT) Add Regular Investm (=PMT)
- Reg. inv. withdrawals (= PMT)
Loan is pd off; FV =? Loan not pd off (= Residual); FV =? Cap left after reg. inv. withdrawals; FV =?
Inflow = + Outflow = – For below indicate + or – or 0: + – – – + – +
Yield curve prods calcs
Home loan – Mr Kagiso Checklist: FV = PV [1 + i/(P/YR)]
n, PMT
FV = 0 (Pd off) PV = 1 900 000 I/YR = 10 P/YR = 12 N = 240 Press PMT = -18 335.41 If PMT = -20000 How long? Press N = 189.017 IF I/YR = 9 How long? Press N = 166.8268
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Yield curve prods calcs
Car loan (with residual) Checklist: FV = PV [1 + i/(P/YR)]
n, PMT
FV = -60 000 (residual) PV = 180 000 I/YR = 13.5 P/YR = 12 N = 54 Press PMT = -3 652.25
Stats Calcs
Weighted Growth rates
90% of investment yields 21% return 10% of investment yields 5% return Overall % return? (0.9 x 21) + (0.1 x 5) = 19.4%
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Stats Calcs
Std dev
6% Avg Χ Χ Χ Χ 2% 2% 3% 3%
Same Avg, select lower Std dev But if Avg diff, std dev diff?
Stats Calcs
CV
= (std dev) / (Average) x 100 Example 15 Health warning
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