Fundamental financial concepts
Introduction to Financial Concepts in Python
Dakota Wixom
Quantitative Finance Analyst
Course objectives
- The Time Value of Money
- Compound Interest
- Discounting and Projecting Cash Flows
- Making Rational Economic Decisions
- Mortgage Structures
- Interest and Equity
- The Cost of Capital
- Wealth Accumulation
Calculating Return on Investment (% Gain)
$$ \text{Return (\% Gain) } = \frac{v_{t_2} - v_{t_1}}{v_{t_1}} = r$$
- $v_{t_1}$: The initial value of the investment at time
- $v_{t_2}$: The final value of the investment at time
Example
- You invest $10,000 at time = year 1
- At time = 2, your investment is worth $11,000
$$ \frac{\$11,000 - \$10,000}{\$10,000} * 100 = \text{10\% annual return (gain) on your investment} $$
Calculating Return on Investment (Dollar Value)
$$ v_{t_2} = v_{t_1} * (1 + r) $$
- $v_{t_1}$: The initial value of the investment at time
- $v_{t_2}$: The final value of the investment at time
- $r$: The rate of return of the investment per period t
Example
- Annual rate of return = 10% = 10/100
- You invest $10,000 at time = year 1
$$ \text{\$10,000} * (1 + \frac{10}{100}) = \text{\$11,000} $$
Cumulative growth (or depreciation)
- r: The investment's expected rate of return (growth rate)
- t: The lifespan of the investment (time)
- $v_{t_0}$: The initial value of the investment at time 0
$$ \text{Investment Value} = v_{t_0}*(1 + r)^t $$
If the growth rate $r$ is negative, the investment's value will depreciate (shrink) over time.
Discount factors
$$ df = \frac{1}{(1 + r)^t} $$
$$ v = fv*df $$
- $df$: Discount factor
- $r$: The rate of depreciation per period $t$
- $t$: Time periods
- $v$: Initial value of the investment
- $fv$: Future value of the investment
Compound interest
$$ \text{Investment Value} = v_{t_0}*(1 + \frac{r}{c})^{t*c} $$
- r: The investment's annual expected rate of return (growth rate)
- t: The lifespan of the investment
- $v_{t_0}$: The initial value of the investment at time 0
- c: The number of compounding periods per year
The power of compounding returns
Consider a $1,000 investment with a 10% annual return, compounded quarterly (every 3 months, 4 times per year):
$$ \$1,000*( 1 + \frac{0.10}{4} )^{1*4} = \$1,103.81 $$
Compare this with no compounding:
$$ \$1,000*( 1 + \frac{0.10}{1} )^{1*1} = \$1,100.00 $$
Notice the extra $3.81 due to the quarterly compounding?
Exponential growth
Compounded Quarterly Over 30 Years:
$$ \$1,000*(1 + \frac{0.10}{4})^{30*4} = \$19,358.15 $$
Compounded Annually Over 30 Years:
$$ \$1,000*(1 + \frac{0.10}{1})^{30*1} = \$17,449.40 $$
Compounding quarterly generates an extra $1,908.75 over 30 years
Let's practice!
Introduction to Financial Concepts in Python
