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Quantitative Finance Primer

Focused on data-driven trading & risk concepts: instruments, math, modeling, infrastructure.

1. Market Microstructure

Concept Note
Bid / Ask Best buy / sell quotes
Spread Ask - Bid; liquidity proxy
Order Types Market, Limit, Stop, IOC, FOK
Slippage Execution vs expected price gap
Latency Time from signal to execution

Order book snapshot structure: 

order_book = {
  'bids': [(101.1, 200), (101.0, 300)],
  'asks': [(101.2, 150), (101.3, 100)]
}
mid = (order_book['bids'][0][0] + order_book['asks'][0][0]) / 2

2. Return Calculations

import pandas as pd
prices = pd.Series([100, 101, 99, 102])
returns_simple = prices.pct_change()
returns_log = (prices/ prices.shift(1)).apply(lambda x: pd.NA if pd.isna(x) else __import__('math').log(x))
Log returns additive across time slices.

3. Risk & Volatility

import numpy as np
vol_daily = returns_simple.std()
vol_annual = vol_daily * np.sqrt(252)
Value at Risk (historical): quantile of loss distribution. 
VaR_95 = returns_simple.quantile(0.05)
Expected Shortfall: average of worst tail fraction.

4. Portfolio Math

import numpy as np
weights = np.array([0.4, 0.6])
mu = np.array([0.10, 0.15])         # expected annual returns
cov = np.array([[0.04, 0.01],[0.01,0.09]])
port_return = weights @ mu
port_var = weights @ cov @ weights
port_vol = port_var**0.5
Sharpe = (R_p - R_f) / vol.

5. Correlation & Diversification

Diversification lowers unsystematic risk; correlation breakdown in crises (regimes). Use shrinkage estimators for covariance stability (Ledoit-Wolf).

6. Factor Models

Factor Interpretation
Market (MKT) Broad market exposure
Size (SMB) Small minus big
Value (HML) High book-to-market minus low
Momentum Past winners continue short-term
Quality/Low Vol Defensive characteristics

Regression for factor exposure: 

import statsmodels.api as sm
Y = asset_returns
X = sm.add_constant(factors_df[['MKT','SMB','HML']])
model = sm.OLS(Y, X).fit()
betas = model.params

7. Backtesting Principles

Principle Rationale
No Look-Ahead Avoid future info in features
Realistic Costs Include spread, slippage, fees
Execution Modeling Partial fills, latency
Out-of-Sample Segments Forward walk vs single test
Robust Metrics Sharpe, max drawdown, turnover

8. Performance Metrics

Metric Description
Sharpe Excess return / volatility
Sortino Downside risk-adjusted return
Max Drawdown Largest drop from peak
Win Rate % profitable trades
Hit Ratio Accuracy of signal classification
Turnover Trade volume relative to capital

9. Options Basics

Term Meaning
Call / Put Right to buy / sell underlying
Strike Exercise price
Premium Price paid for option
Greeks Sensitivities: Delta, Gamma, Vega, Theta, Rho

Black-Scholes call price: 

from math import log, sqrt, exp
from mpmath import quad, pi, e
# Use scipy.stats.norm.cdf in practice
Implied volatility solved by root-finding on price difference.

10. Greeks Intuition

Greek Sensitivity
Delta Price to underlying
Gamma Delta to underlying
Vega Price to volatility
Theta Price to time decay
Rho Price to interest rate

Hedging adjusts portfolio Greeks toward target (e.g., delta-neutral).

11. Execution & Slippage Modeling

Simulate fill probability vs distance from top-of-book; incorporate queue position, partial fills. 

def slip(mid, spread, aggressiveness=0.5):
    return mid + spread * aggressiveness

12. Data Engineering Considerations

Aspect Concern
Latency Efficient ingestion (async, batching)
Normalization Consistent field naming & types
Survivorship Bias Include delisted symbols
Corporate Actions Adjust splits/dividends
Timezones Normalize to UTC

13. Regimes & Robustness

Detect structural breaks (e.g., Chow test, rolling metrics). Regime-aware strategies adapt leverage or model selection.

14. Machine Learning in Finance Caveats

Label scarcity, non-stationarity, regime shifts, overfitting via heavy hyperparam search, data snooping. Emphasize cross-validation with purging/embargo (see Lopez de Prado).

15. Risk Management Essentials

Position sizing (Kelly fraction bounds), stop-loss vs volatility targeting, exposure limits, scenario & stress testing.

16. Interview Q & A (Quant Finance)

  1. Simple vs log returns difference? Log returns additive over time, approximate simple returns for small changes.
  2. Why adjust for look-ahead bias? Prevent inflated performance using unavailable future info.
  3. Purpose of volatility scaling? Normalize strategy risk, enabling comparability across periods.
  4. Explain diversification failure. Correlations increase during crises; tail dependence undermines naive diversification.
  5. What is overfitting in backtests? Excessive tuning to historical noise; signals not robust out-of-sample.
  6. Meaning of negative skew? Frequent small gains, rare large losses (risk of blow-up).
  7. Role of transaction costs? Erode alpha; high turnover strategies sensitive; must be modeled early.
  8. Gamma risk significance? High gamma increases delta variability; requires active re-hedging.
  9. Difference between VaR and Expected Shortfall? VaR is quantile threshold; ES averages tail losses beyond VaR (coherent risk measure).
  10. Why use purged k-fold CV (finance)? Avoid leakage from overlapping samples / label overlap across folds.
  11. Uses of factor models? Attribution, risk decomposition, portfolio construction constraints.
  12. Max drawdown importance? Captures tail path risk, investor psychology; complements Sharpe.
  13. Slippage modeling challenge? Dependent on order book dynamics, volume profile, market impact; hard to generalize.
  14. Regime detection usage? Adjust strategy parameters, switch models, manage leverage.
  15. Why prefer median to mean in some metrics? Robust to outliers, especially in skewed PnL distributions.

Last updated: Sep 2025