computational_invest

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Definitions

Daily Returns:

(1)
\begin{align} \frac{value[i]}{value[i-1]} \end{align}

Measures of Risk:

1.Volatility: is related to the dispersion (e.g., standard deviation) of returns. Commonly, the higher the volatility, the riskier the security.
2. Draw down: measures the relative drop of a portfolio value.


Sharpe Ratio: The most important metric for return and risk combination of assets, which basically measures "How much reward are you getting for your risk?":

(2)
\begin{align} S=\frac{E[R-R_{f}]}{\sigma_{R}} \end{align}

, where $R$ is daily return, $\sigma$ is the standard deviation of daily returns, and $R_{f}$ is risk free return.
Sharpe ratio is usually estimated as

(3)
\begin{align} S=\frac{K \bar{R}}{\sigma_{R}} \end{align}

, where $K=\sqrt{250}$ (250 financial days in one financial year) or $K=\sqrt{12}$ in the case of using monthly return.


Types of Orders:

1. market order: buy or sell at whatever the current price of stock is
2. limit order: buying or selling is depending to a threshold which define by seller or buyer.
3. Sell Short: You predict that the price of a stock will go down, you borrow stock from someone and sell it and if it went down you buy the shares back and return to the lender. Obviously if the price goes up you will lose money.
4. Stop limit


The Order Book: A list of thresholds for limit buyers and sellers



Value of a Company

  • Intrinsic Value: is the sum of a Geometric series. i.e.,
(4)
\begin{align} \sum_{i=1}^{\infty} dividend * \gamma ^i &=\frac{dividend }{1-\gamma} \end{align}

Where $\gamma (<1)$ is the discount rate.

  • Book Value: is total asset minus intangible assets and liabilities.

Capital Assets Pricing Model (CAPM)

(5)
\begin{align} r_i =\beta_i r_M + \alpha_i \end{align}

$r_i$ is the return of stock "i", $r_M$ is the return of the market and $\alpha_i$ is the residual of stock "i".
$\beta_i r_M$ is the systematic (or risk free) part of the return and $\alpha_i$ is the excess return. The expected value of $\alpha_i$ is zero (i.e.,$<\alpha_i>=0$ )

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