\part{Fundamentals}
## Financial market

\chapter{Basics}

We give a brief introduction to the basis layout of a financial system on a personal and corporate scale. We avoid discussing concepts in a mathematical sense, this will come later.
entity
- individual
- company
- trust; contract where a settlor transfers a collection of assets to a trustee, which they then manage and distribute to beneficiaries


income
- wage
- salary
- profit
- interest
	- Simple interest
	- Compound interest
- rent
- dividends

Superannuation/401k; savings account for an individual which is usually accessible after retirement. The savings of ones superannuation are placed in a superfund, with the intent for the savings to accrue by the time it is withdrawn.
Salary sacrifice


asset
Position; quantity of an asset owned by an entity



financial instrument; monetary contract between entities
- equity instrument
	- stock
- debt instrument
	- bond
	- loan; Money is lent to an entity that gradually pays the money back plus an extra fee (interest)
- currency instrument
	- cryptocurrency
	- fiat currency
- commodity instrument
- derivative; instrument stating right/obligation to buy/sell some security (underlying assset) at some time and price
	- option
	- future
	- swap


The word security is generally used to refer to financial instruments, however legal definitions may be more restrictive depending on the juristiction.

Over-The-Counter (OTC) trading
Exchage Traded Fund (ETF)

primary market; market where new securities are issued
- Initial Public Offering (IPO)
secondary market; market where securities are traded
- NASDAQ
- ASX

short selling




BSB; Standard for electronic billing from financial instistutions to clients
BSB Number



Broker

Capital gain; profit obtained by selling an asset at a higher price than what it was obtained at.

\chapter{Assets}

Stock
Contract assigning ownership of some portion of a company
intrinsic value; true,inherent value of an asset as opposed to its current market price
- Dividends; Share of profits paid to a stockholder
- market order; buying stock at market's calculated value
- limit order; buying stock that is sold at or below some desired price
- Blue chip stock

share buyback
company buying back its own public shares

public float

outstanding share
share issued from company to public entities

restricted share
share owned by insider (company or entity tied to company)

golden share
share that has priority voting rights for company decisions









Hedge; Investment actioned as a way to offset losses from another investment, a form of insurance


Index






## Derivatives

##Option
Contract giving the holder the right to buy (call) or sell (put) an underlying asset at or before specific time; the specific details are determined by the option's style as 
- Call; Option offering the right to buy
- Put; Option offering the right to sell 

### exercizing
### expiration

###Option styles
- European; Option with a fixed strike price payoff that is actioned on expiry
- American; Option with a fixed strike price payoff that is actioned on or before expiry
- Asian; Ooption with a payoff being the average price over a period of time
### moneyness
- in-the-money; option would make a profit if exercised
- at-the-money; option would make no profit if exercised
- out-of-the-money; option would make debt if exercised

Payoff; profit from exercising an option
strike price;





### squeeze
-delta squeeze; increased sale of call options leading to share buybacks to create demand for stock, leading to high share prices


\chapter{Trading assets}
Order book;
List of buy and sell orders that 'crosses' once there exists a buy order and sell order for the ame product such that the buy price is greater than or equal to the sell price

Priority;
Orders on orderbooks are crossed based on highest buy price, or if these are equal, oldest order

\chapter{Fundamental analysis}

## fundamental analysis; evaluating company value by their financial statements, assets and liablilities and the current economic environement

Price-to-earnings (P/E) ratio; ratio of a company's market value to their earnings
Price-to-book (P/B) ratio; ratio of a company's market value to their 'book value' (assets minus liabilities)

\chapter{Technical analysis}

## Technical analysis; forecasting company value by previous stock price and volume

### Diversification
mixing portfolio to minimize risk

### Liquidity
measure of ease of turning an assets/instruments into currency



\chapter{Tax minimization}

Franking credits; credits for tax deduction on dividends when the company has already paid tax on their profit



\part{Asset Pricing Theory}


\chapter{Capital asset pricning model}
alpha
beta
Risk-free rate; Rate of return on a hypothetical investment with zero risk
security characteristic line


risk-neutral measure
$\mathrm{Q} \sim \mathrm{Pr}$

\chapter{Black-Scholes model}
draws from the theory of stochastic differential equations

the greeks
Partial derivatives that measure risk
V	value of option
S	price of underlying asset
\sigma	volatility
t	time

\Theta = -\frac{\partial V}{\partial t}
\mathcal{V} = \frac{\partial V}{\partial \sigma}
\Delta = \frac{\partial V}{\partial S}
\Gamma =  \frac{\partial \Delta}{\partial S}
black-scholes equation

fundamental theorems of asset pricing




\part{Modern Portfolio Theory}

\chapter{Markowitz model}

It essentially uses probability theory to form a mathematical optimization problem, which can then be solved by numerical analysis.
The Markowitz model was the first model of  makes assumptions based on th



\begin{itemize}
\item Risk of the portfolio is defined as the variance of returns from said portfolio
\item Investors are risk averse
\item Investors prefer to increase consumption
\item Investors have a concave, increasing utility function
\item A single time period of investment is considered
\item Investors seek to either minimize risk given an expected return or maximize the expected return given a level of risk
\item Investors are rational
\end{itemize}

 the Markowitz model focuses on a portfolios that are static for a given time interval (the portfolio cannot vary during the investment period), and it assumes that as investors, we want to minimize risk and maximize expected returns.



Given $n$ different stocks, we can represent the return on some portfolio $p$ as the following RV.
\[R_p = \sum^{n}_{i=1} w_i R_i\]
\[ \sum^{n}_{i=1} w_i = 1\]

Alternatively, the notation of linear algebra may be used.

\[R_p = \mathbf{w}^{\intercal}\mathbf{r}\]
\[ \sum^{n}_{i=1} \mathbf{w}_i = 1\]

In one sense, the RV $R_p$ is spanned by $n$ RVs.

\section{Optimization problems}

THe Markowitz model leverages its assumptions to culminate the problem of designing a portfolio to a problem in mathematical optimization.
Recall that the Markowitz model operates under the assumption that we seek to either minimize risk given an expected return or maximize the expected return given a level of risk.
We first consider the , let $\mu$ be the expected return desired.


$(\mathrm{Var}(R_p),X,\min)$
$X= \{ \mathbf{w} \in \mathbb{R}^n : \sum^{n}_{i=1} \mathbf{w}_i = 1 \land \mathrm{E}(R_p)=\mu \}$


If we instead fix $\sigma^2$ as the risk (variance), we obtain the following.
$(\mathrm{E}(R_p),X,\max)$
$X= \{ \mathbf{w} \in \mathbb{R}^n : \sum^{n}_{i=1} \mathbf{w}_i = 1 \land \mathrm{Var}(R_p)=\sigma^2 \}$


The feasible region in this context is called the Markowitz bullet (due to it looking geometrically like a ellipsoid bullet in the case of 2 or 3 assets), and the optimal solution is called the efficiency frontier (the boundary of the markowitz bullet).

These can be solved by the method of Langrage multipliers of the critical line method.

Two mutual fund theorem
Mutual fund separation theorem


\chapter{Black-Litterman model}
In practice
