Essay About Positive Integers And Portfolio Theory

Math Of Finance
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NOTES FOR WEEK 1 – JUNE 02, 2007
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:
Directly – putting up your own a business.
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:
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
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
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.
NUMBERS
Real numbers
– everything on the number line
Rational numbers – numbers that can be expressed in decimal, which are terminating or repeating.
integers – positive integers, zero, negative integers
non-integers
Irrational numbers- expressed as non-repeating decimals
e.g.
=SQRT(2)
=P1()
=EXP(1)
– measures the number of radiuses or radii around the circle.
Complex numbers
E.g.:
= i
i = “imaginary numbers”
= = = 2i
Absolute Value
– distance of a number from 0
– without equality will just mean an expression.
To illustrate:
E.g:
If then =
(ii.)
If , then
=1
Intervals on the red line:
– 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