T1 - Financial Maths.ppt - Investment Management Financial Mathematics www.bournemouth.ac.uk Topics • Percentages • Investment returns(and risk •

T1 - Financial Maths.ppt - Investment Management Financial...

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Investment Management Financial Mathematics
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2 Topics Percentages Investment returns (and risk) Compounding and discounting The internal rate of return Statistics Formulae and Excel functions Linear regression and correlation The normal distribution
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3 Percentages (1) To convert percentages to decimals: Divide by 100 Convert 20% to a decimal: 20 ÷ 100 = 0.2 To convert decimals to percentages: Multiply by 100 Convert 0.2 to a percentage: 0.2 x 100 = 20% To calculate a percentage change: Deduct old value from new value, divide by old value and convert to percentage £50 increases to £60: (60 - 50) ÷ 50 => 10 ÷ 50 => +20% £50 decreases to £40: (40 - 50) ÷ 50 => -10 ÷ 50 = -20%
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4 Percentages (2) To increase by a percentage: Convert percentage to decimal, add result to 1 and multiply by the number Increase £50 by 20%: (1 + (20 ÷ 100)) x 50 => 1.2 x 50 = £60 To decrease by a percentage: Convert percentage to decimal, subtract result from 1 and multiply by the number Decrease £50 by 20%: (1 – (20 ÷ 100)) x 50 => 0.8 x 50 = £40 Percentages are strictly multiplicative not additive Increase £50 by 20% then decrease by 20%: 1.2 x 0.8 x 50 = £48 Decrease £50 by 20% then increase by 20%: 0.8 x 1.2 x 50 = £48
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5 Investment Return (and Risk) Investment Returns: Percentage rate Historic (in the past) Expected (in the future) Nominal (actual) Real (inflation adjusted) (Total) Risk: Percentage Volatility (standard deviation) Historic = expected
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6 Nominal and Real Rates of Return Nominal rates of return (r n ) are in actual money terms Inflation (i) erodes purchasing power over time Real rates of return (r r ) are adjusted for inflation and therefore of primary importance to investors The Fisher equation is used to convert nominal rates to real rates and vice versa: r r = ((1 + r n ) ÷ (1 + i)) - 1 Calculate the real rate of return of an investment whose price rose by 10% in a year when inflation was 2% r r = ((1 + 0.1) ÷ (1 + 0.02)) -1 r r = (1.1 ÷ 1.02) - 1 r r = 1.078 - 1 = +7.8%
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7 Compounding - Discrete The future value (FV) of a present value (PV) which is compounded at a constant annual rate (r) for (t) years when there are (n) compounding periods per annum Discrete compounding formula: FV = PV (1 + (r ÷ n)) nt Compound £100 at 10% for 2 years if there is one compounding period p.a.
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  • Winter '18
  • Spencer Barnet

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