# Investment

## Table of Contents

## Definitions

### Words

- ask
- "offers", i.e. what people are willing to sell
- bids
- people willing to buy
- difference between the best
*bid*and best*ask* - basically means "buy / sell X amount at the best possible price,
*right now*", which means that if you're not careful, you might end up buying more than what's available at the price you want and thus buying from the*next*level (asks) - you specify the price and quantity you're willing to buy or sell at

**Dividends** is a sum of money paid regularly (typically annually) by a company to its
shareholders out of its profis (or reserves).

### Alpha

**Alpha** is a measure of the active return on an investment, the performance of that investment compared with a suitable market index.

It takes the volatility (price risk) of a security or fund portfolio and compares its risk-adjusted performance to a benchmark index. The excess return of the investment relative to the return of the benchmark index is its **alpha**.

An **alpha** of 1% means the investment's return on investment (ROI) over a selected period of time was 1% *better* than the market during the same period.

### Beta

**Beta** (coefficient) is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole.

**Beta** is calculated using regression analysis, and you can think of it as the tendency of an investment's return to respond to swings in the market. By definition, the market has a beta of 1.0. Individual security and portfolio values are measured according to how they deviate from the market.

### Sharpe ratio

The **Sharpe ratio** is defined as

where

- is the
*asset*return - is the
*risk-free rate* - is the std. dev. of the
*asset*

### Markets

**Equity market** is the market in which shares are issued and traded, either through exchanges or over-the-counter markets, also known as the *stock market*.

**Credit market** refers to the market through which companies and governments issue debt to investors, such as investment-grade bonds, junk bonds and short-term commercial paper.

Sometimes called the debt market, the credit market also includes:

- debt offerings, e.g. notes
- securitized obligations, including
- mortgage pools
- collateralized debt obligations (CDOs)
- dwarfs
- credit default swaps (CDS)

## Capital Asset Pricing Model (CAPM)

**Capital asset pricing model (CAPM)** is a model used to determine a theoretically appropriate required *rate of return* of an asset, to make decisions about adding assets to a *well-diversified portfolio*.

In CAPM, for individual securities, we make use of the **security characteristic line (SCL)** , which is the regression line, modeling the *performance* of a particular security or portfolio against that of the *market portfolio* at every point in time:

where

- is called the asset's alpha (abnormal return)
- is a
*nondiversifiable*or*systematic risk* - is the non-systematic or diversifiable, non-market or idiosyncratic risk
- is a
*market risk*, or rather the return of the market portfolio - is a
*risk-free rate*(e.g. interest rates from keeping the money in the bank)

Minimizing the RSS (i.e. obtaining the MLE), we get

where we've let and , which is in coherence with the definition of beta as "relative variance / risk wrt. market".

## Volatility

Simply the **variance** of the financial instrument.

## Risk

- Reflects the chance that the
*actual*return on an investment varies from the*expected*return (i.e. mean) - There a multiple measures of risk:
- Variance / std. dev.

## Sharpe Ratio

### Overview

- Measure for computing
*risk-adjusted*return

## Risk-free return

- Theoretical rate of return of an investment with
*zero*risk - Considering risk is a variance metric, I'm assuming the
**risk-free**return is then simply the*expected*or*average*return

## DoM - Depth of Market

Basically about observing the order-book, i.e. the volumes of the bids and sells (both those "scheduled" and those being performed).

## Average Portfolio Allocation to Equities

This is heavily based on this article. It's about how one should look into
using **Average Portfolio Allocation to Equities** as a predictor of
future stock market returns. The definition argued for is the following:

where

- is the
*total return*^{1} - is the
*price return*^{2} - is the
*dividends return*^{3}

Furthermore, we can write the *price return* term as follows:

where:

- is the price return from
*change*in**Aggregate Investor Allocation of Stocks**^{4} - is the price return from
*increase*in**Cash-Bond supply**^{5}, the value of which assumes Aggregeate Investor Allocation of Stocks stays constant

**Why this formula?** It's all explained very well in the article, but to summarize:

- Assuming you can diversify your investments; if the funds spent on stocks goes up,
i.e.
**aggregate investor allocation of stocks**, your return goes up. - If the
**Cash-Bond supply**increases:- if the loaner takes a loan from the bank → money supply expands → investors have more money → (assuming stock allocation for the investor stays constant) investor invests more money into stocks
- if the loaner takes a loan directly from the investor → investor holds the bond → investor now has more bonds than the allocated ratio → need to increase investment in stocks to get back to his/her set stock allocation
**Note:**the average bond trades close to par, so, in aggregate, the value of the liabilies approximates the total market value of the bonds.

## Footnotes:

^{1}

*Total return* is the rate of return of an investment portfolio, including capital
appreciation, interests and divideds.

^{2}

*Price return* is the rate of return on an investment portfolio, where the return measure takes
into account **only** the capital appreciation of the portfolio,
while income generated by the asets in the portfolio, in the form of interest
and dividends, is ignored. This contrasts with the *total return*,
which does take into account the income generated in the portfolio.

^{3}

*Dividends* is a sum of money paid regularly (typically annually) by a company to its
shareholders out of its profis (or reserves).

^{4}

*Aggregate Investor Allocation of Stocks* is the summed up funds to be allocated in the stock market

^{5}

**Cash-Bond supply** is the supply of cash and bonds, i.e. money NOT allocated to
for investments in stocks.