Quantopian Lecture Series

This lecture series can be found on the Quantopian website, and is free for anyone to follow (though you may have to sign up). The lectures are in the form of jupyter notebooks, but most are accompanied by youtube videos. I think it’s a great introduction to quant finance – it puts a lot of emphasis on common pitfalls that must be avoided.

Contents

Mean and variance

Statistical moments

\[Sk = E \left[ \left( \frac{X - \mu}{\sigma}\right)^3 \right]\] \[K_E \approx \frac 1 n \frac{\sum (x_i - \mu)^4}{\sigma^4} -3\]

Correlation

\[\rho = \frac{Cov(X,Y)}{\sigma_X \sigma_Y}\]

Instability of parameters

Linear regression

Hypothesis testing

  1. State $H_0$ and $H_A$
  2. Identify an appropriate test statistic (and check the assumptions)
  3. Compute the critical value from the significance level $\alpha$.
  4. Compute the test statistic and compare with the critical value.

p-hacking

Estimating the covariance matrix

\[\hat{S} = (1-\delta) S + \delta F\]

Volume, slippage and liquidity

Market impact models

\[\text{cost} = 0.5 \gamma \sigma \frac X V \left(\frac \Phi V \right)^{1/4} + \eta \sigma \left| \frac{X}{VT}\right|^{3/5}\] \[\text{impact} \propto \sigma_m \cdot (\text{participation rate})^\beta\] \[\text{cost} = 0.1 \left| \frac{X}{VT}\right|^2\]

The Capital Asset Pricing Model (CAPM)

\[E(R_i) = R_F + \beta(E(R_M) - R_F)\] \[E(R_i) = R_F + b_1\lambda_1 + \ldots + b_k \lambda_k\]

Factor Models

\[FMCAR_j = \frac{b_j \sum_{i=1}^k b_i Cov(F_j, F_i)}{(\text{active risk})^2}\]

Principal Component Analysis (PCA)

Long-Short Equity strategies

Hedging Beta and Sector Exposure

\[BR = \frac{N}{1+ \rho (N-1)}\] \[\sigma_\pi^2 = w^TBFB^Tw + w^T D w\]

Value-at-Risk

\[VaR_\alpha = \mu - \sigma \Phi^{-1}(\alpha)\] \[ES_\alpha = \frac{1}{1-\alpha} \int_0^{1-\alpha} VaR_\gamma(X) d\gamma\]

Integration, Cointegration and Stationarity

Pairs trading

Auto-regressive models

\[x_t = b_0 + b_1 x_{t-1} + \epsilon_t\] \[x_t = b_0 + b_1 x_{t-1} + \cdots + b_p x_{t-p} + \epsilon_t\] \[\rho_k = \frac{Cov(x_t, x_{t-k})}{\sigma_x^2}\]

ARCH and GARCH Models

\[\sigma_t^2 = a_0 + a_1x_{t-1}^2 + b_1 \sigma_{t-1}^2\] \[x_t^2 = a_0 + a_1 x_{t-1}^2 + \ldots + a_p x_{t-p}^2\]

Kalman Filters

Futures