Math Of Finance

NOTES FOR WEEK 1 - JUNE 02, 2007

I. OVERVIEW OF FINANCE

Finance - is an inter-temporal choice between spending today and spending tomorrow.

Investing - is a productive activity

Productive activity can be classified as:

a. Directly - putting up your own a business.

b. Indirectly - if there is an intermediary assigned to take care of your investments such as banks, investment bankers, etc.

Saver Productive activity

Financial instrument

- Claim on cash flows of a productive activity that is being funded

- Needs computation to value the instrument

Types of Financial Instruments:

Debt Equity

Secured Debt Converting Debt

Unsecured Debt Convertible Preferred

Preferred

Common

Tree Model of Finance

- consider the value of the asset

- expected return/yield of the asset

Cow Model of Finance

- Produce same result regardless of scenarios, also known as cash cow model.

Principle of Finance

1. Price and Rate of Return (R) - manifestation of the value of the asset.

- Price is inversely related to Return

- If the Price is low the rate of Return will be very high

2. Risk - possibility to lose value because of market movement

- The higher the risk, the higher the return that should be asked for

Portfolio Theory - some risks cancel each other out when assets are put together.

II. NUMBERS

1. Real numbers

- everything on the number line

a. Rational numbers - numbers that can be expressed in decimal, which are terminating or repeating.

i. integers - positive integers, zero, negative integers

ii. non-integers

b. Irrational numbers- expressed as non-repeating decimals

e.g.

or =SQRT(2)

or =P1()

e or =EXP(1)

- measures the number of radiuses or radii around the circle.

2. Complex numbers

E.g.:

= i

i = "imaginary numbers"

= = = 2i

2.1 Absolute Value

- distance of a number from 0

- without equality will just mean an expression.

To illustrate:

E.g:

(i.) If then =

(ii.) If , then

=1

2.2 Intervals on the red line:

(i.) - open interval

< <

Read as: Sets of all x, such that x is greater than 2 or less than 3

(ii.) - closed interval

Read as: Sets of all x, such that x