Ryangineer

Artificial Intelligence Fundamentals

Expert Systems

• Weak Methods

  "[G]eneral-purpose search mechanism trying to string together elementary reasoning steps to find complete solutions." (Russell, p. 22)

Finance Fundamentals

Data Processing

Market data is temporal in nature → a series of trading events that will happen in a moment of time.

• Technical Indicators

• Constant Threshold (CT)

$\mathrm{CT\; =\; |\; price\; -\; average\; |\; >\; x\; dollars}$

• Fraction Threshold (FT)

$\mathrm{FT\; =\; }\frac{\mathrm{|\; price\; -\; average\; |}}{\mathrm{price}} \; >\; \mathrm{x\; percent}$

• Fundamental Information

• Sales Per Share

$\mathrm{SPS\; =\; }\frac{\mathrm{revenue}}{\mathrm{\#\; of\; shares}}$

• Earnings Per Share

$\mathrm{EPS\; =\; }\frac{\mathrm{revenue\; -\; costs}}{\mathrm{\#\; of\; shares}}$

• Dividends Per Share

$\mathrm{DPS\; =\; }\frac{\mathrm{dividends}}{\mathrm{\#\; of\; shares}}$

• Price to Earnings Ratio (PE ratio)

$\mathrm{PE\; ratio\; =\; }\frac{\mathrm{current\; mkt\; price}}{\mathrm{most\; recent\; EPS}}$

• Stock Returns

• Returns (aka Linear, Percentage, Raw, Simple)

$\mathrm{r\; =\; }\frac{p_{\mathrm{t}}-p_{\mathrm{t\; -\; 1}}}{p_{\mathrm{t\; -\; 1}}}$

• Log Return

$R=\ln \left(\frac{p_{\mathrm{t}}}{p_{\mathrm{t\; -\; 1}}}\right)$

• Convert between raw returns & log returns

$R=\mathrm{ln(r\; +\; 1)}$
$r=e^{\mathrm{R}}-1$

• Rates of Compounding

• Straightforward Yearly Interest

  $\mathrm{Future\; Value} \; =\; \mathrm{Deposit\; Amount} \; *\; \left(\mathrm{1\; +\; Annual\; Interest\; Rate}\right)$

• Continuous Compounding

  $p_{\mathrm{t}} \; =\; p_{\mathrm{t\; -\; 1}}\left(\mathrm{1\; +}\frac{r}{n}\right){}^{\mathrm{n}}$

• Calculus for Limit

  ${\lim }_{\mathrm{n\; \to \; \infty }}(1\; +\; \frac{r}{n}){}^{\mathrm{n}} \; =\; e^{\mathrm{r}}$
    ↳ where:
      $\mathrm{ \; r} \; =\; \mathrm{continuously\; compounded\; annual\; return}$
  $\; \; \; r \; =\; \ln \left(\frac{p_{\mathrm{t}}}{p_{\mathrm{t\; -\; 1}}}\right)\mathrm{ \; \Rightarrow \; }\mathrm{log\; return}$

• Trading Strategy

• Mean Monthly Return

  $\mathrm{x̄}\mathrm{ \; =\; }\frac{1}{n}$Σx_i
    ↳ where:
    n = # of monthly returns in the sample

• Standard Deviation

  $s\mathrm{ \; =\; }\sqrt{\frac{1}{\mathrm{n\; -\; 1}}\Sigma (x_{\mathrm{i}} \; -\; \mathrm{x̄}){}^2}$

• t-Statistic

  Way of testing probability getting as large of mean with correct assumptions made to build our model of strategy returns

  $t \; =\; \frac{\mathrm{x̄}}{{\mathrm{SE}}_{\mathrm{x̄}}}$

• Standard Error of the Mean

  $s_{\mathrm{x̄}} \; =\; \frac{s}{\sqrt{n}}$

• Regression

  • Probability Density Function (PDF)

    An equation that defines a probability distribution; for every number from negative infinity to positive infinity, the PDF gives a probability that this number will be generated

    $\mathrm{X\; ~\; D}$
      ↳ Random variable 'X' follows a probability distribution 'D'
    $\mathrm{P(x|D)\; =\; p(x)}$

  • Standard Normal Distribution (X ~ N)

    $f\left(x\right|\mathrm{\mu , }{\sigma }^2) \; =\; \frac{1}{\sqrt{2\pi }}{e}^{\frac{-{\mathrm{(x\; -\; \mu )}}^2}{{\mathrm{2\sigma }}^2}}$

  • Box-Cox Transformation

    Way to make our data normally distributed & homoscedastic (same over time); a monotonic transformation that changes the value of the dataset, but preserves their relative order

    $T\left(x\right)=\frac{(x^{\mathrm{\lambda }}-1)}{\lambda }$

Macroeconomics

"The branch of economics that deals with the structure, performance, behavior, and decision-making of the whole, or aggregate, economy. The two main areas of macroeconomic research are long-term economic growth and shorter-term business cycles." Investopedia

Inequality

• Gini Coefficient

  "A single number that demonstrates a degree of inequality in a distribution of income/wealth." Wikipedia

  $\mathit{Gini} \; =\; \frac{A}{(A \; -\; B)}$
    ↳ where:
     A = area above the curve
     B = area below the curve

• Kuznets Curve

  "[E]xpresses a hypothesis advanced by economist Simon Kuznets in the 1950s & 1960s. According to this hypothesis, as an economy develops, market forces first increase and then decrease economic inequality." Wikipedia

  

Positively Brilliant References

• Koshy, T.   (2003).   Discrete Mathematics & Its Applications.   Academic Press.

• Massaron, L.   (2016).   Regression Analysis with Python.   Packt Publishing.

• Russell, S. & Norvig, P.   (2021).   Artificial Intelligence: A Modern Approach.   Pearson.

• Ryan, M. (2016).   Calculus for Dummies.   For Dummies.

• Schneider, M. (1994).   A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, & Science.   HarperCollins Publishers.

About Ryan L Buchanan

I am re-skilling as a Data Analyst & Machine Learning Engineer.  I am currently enrolled in a Masters in Data Analytics.  I am also acquiring certifications as an ML Engineer & Algorithmic Trader from Udacity.   I have an MBA & an MS in Instructional Design.

I have a multi-displinary background including military intelligence, psychology, linguistics, economics, virtual reality & educational technology.  I have worked abroad for ten years with military, universities & vocational schools.   I have working knowledge of Arabic, Chinese & French.  I am very mobile, able to relocate quickly, adapt easily to diverse working conditions & have a current passport.

I have a passion for mathematics, statistics & artificial intelligence.  I am enthusiastic, highly self-motivated & enjoy presenting informative data to decision makers.  I am eager to work with dynamic teams to create high quality products & services.