Mathematics Investing
Mathematics Investing
Mathematics Investing
Investing
Franklin Templeton
Learning Academy
FV = PV(1 + r)n
FV = Future Value
PV = Present Value
r = Rate of Return/ Coupon Rate
n = No. of compounding periods
Ms. Aishwarya invested Rs.1 crore in a noload mutual fund scheme in their IPO, four
years ago.
According to the latest fact sheet, the scheme
has shown a CAGR since inception of 10%
p.a.
How much is Ms. Aishwarya's investment
worth today?
FV = PV (1 + r)n
FV = 1 (1 + 10%)4
FV = Rs.1.464 crore
1/4
-1
FV = PV(1 + r)n
Applications aside, what do you think this
equation really signifies?
The essence of how to create wealth!
n
PV
r
FV = PV (1 + r)
The more you
save, makes a
difference
The more
you earn,
makes a
difference
The sooner
you start,
makes a
difference
Total Amount
Saved
Value after
25 years
5,000
1,500,000
4,073,986
3,000
900,000
2,444,391
1,500
450,000
1,222,196
1,000
300,000
814,797
Total Amount
Saved
Value at the
age of 60
25
420,000
1,811,561
30
360,000
1,227,087
35
300,000
814,797
40
240,000
523,965
Starting Age
Value after 10
years
Value after
25 years
6%
164,699
696,459
8%
184,166
957,367
10%
206,552
1,337,890
12%
232,339
1,897,635
Growth Rate
FV = CF1(1+r)n +
CF2(1+r)(n-1)+ .. +
CFn(1+r)
CF=Cash flow
Description
Present Value
No. of compounding periods
Payment made/ received each period
Rate of return/ interest rate per period
Future Value
Points to remember
Denote outflows with a negative (-) sign
Be consistent about the units
Mr. Ganguly has retired at the age of 60. His total investments
as on that date are worth Rs.10 lakhs.
lakhs.
He receives a pension of Rs.5000 p.m. and needs to draw
another Rs.10000 p.m. from his investments.
Assuming he lives till the age of 75 years, and is not keen on
leaving any money to his family, how much return should his
investments earn to help him achieve his objectives?
Situation
Function best
suited
IRR
XIRR
1000
12
83.333
1000
15
66.667
1000
111.111
1000
12
83.333
TOTAL
4000
48
344.444
1
2
3
4
TOTAL
Total
Value
Rs.
1000
2000
3000
4000
NAV
Units to own
Existing
Units
Units to
buy
Amount
Rs.
12
15
9
12
48
83.33
133.33
333.33
333.33
0
83.33
133.33
333.33
83.33
50.00
200.00
0.00
1000
750
1800
0
3550
Standard Deviation
It is a statistical measure of historic volatility
of a fund/ portfolio.
It measures the dispersion of a fund's
periodic returns (often based on 36 months
of monthly returns).
The wider the dispersions, the larger the
standard deviation and the higher the risk.
Beta
R-squared
Sharpe Ratio
Return Risk free Return
Standard Deviation
Duration
It is the weighted average of the
maturities of a bond's cashflows
It measures the sensitivity of the bond
price to changes in interest rates
Markowitz: Portfolio
Selection, 1952:
Key conclusion:
Dividing a portfolio
over asset classes
that do not move
up/ down at the
same time helps
bring down the risk
of the portfolio.
Markowitz: Portfolio
Selection, 1952:
Key conclusion:
Dividing a portfolio
over asset classes
that do not move
up/ down at the
same time helps
bring down the risk
of the portfolio.
Markowitz: Portfolio
Selection, 1952:
Key conclusion:
Dividing a portfolio
over asset classes
that do not move
up/ down at the
same time helps
bring down the risk
of the portfolio.
Correlation
Correlation measures the extent to which the
returns of a group of investment options have
moved together over time. It ranges from 1
to +1
9 +1 = the movement of two funds has been
exactly the same i.e. perfect positive correlation.
9 -1 = the two funds have moved in diametrically
opposite directions i.e. perfect negative
correlation.
Asset Allocation
Derived from Return
Growth
Funds
40%
45%
40%
Income
Funds
60%
55%
60%