Investment Management
Financial Mathematics

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

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%

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

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

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%

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