Chapter 2: Building Blocks – Financial Instruments & Markets

## Chapter 2: Building Blocks – Financial Instruments & Markets ### 2.1 Equities Equities, also known as shares or stocks, represent partial ownership in a corporation. They are the most liquid and widely traded asset class, forming the backbone of most retail and institutional portfolios. | Feature | Typical Convention | Example | |---|---|---| | Settlement | T+2 (trade date + 2 business days) | NYSE, NASDAQ | | Day‑count | Actual/365 | Dividend calculations | | Market hours | 9:30‑16:00 EST | US equities | | Liquidity tier | Large‑cap, Mid‑cap, Small‑cap | S&P 500, Russell 2000 | **Key drivers of equity price dynamics**: - **Fundamental factors**: earnings, revenue growth, sector performance. - **Macro‑economic data**: GDP growth, unemployment, interest rates. - **Sentiment & behavioral biases**: news flow, analyst ratings. - **Technical factors**: liquidity, bid‑ask spread. **Mathematical representation** A simple log‑return model: \[ \ln \frac{P_{t+1}}{P_t} = \mu\,\Delta t + \sigma\,\sqrt{\Delta t}\,Z, \] where \(Z \sim \mathcal{N}(0,1)\). **Practical insight** – *Data feeds*: - Tick‑level data for high‑frequency strategies. - Daily bars for long‑term modeling. - Use APIs (e.g., Bloomberg, Polygon, IEX) and store in time‑series databases (TimescaleDB, kdb+). --- ### 2.2 Bonds Bonds are fixed‑income instruments that promise periodic coupon payments and return of principal at maturity. They are categorized by issuer, credit quality, maturity, and currency. | Bond type | Typical convention | Settlement | Day‑count | Yield curve convention | |---|---|---|---|---| | Treasury | 1‑month, 3‑month, 1‑year, 5‑year, 10‑year | T+1 | 30/360 | ISMA | | Corporate | Investment‑grade, high‑yield | T+1 | Actual/Actual | Bloomberg | | Municipal | US muni, Euro‑muni | T+2 | 30/360 | US muni curve | | Repo | Overnight, 1‑week | T+0 | Actual/360 | Repo curve | **Yield calculations** ```python # Example: Zero‑coupon yield from price price = 950.0 # USD face_value = 1000.0 maturity = 3 # years yield_ = (face_value/price)**(1/maturity) - 1 print(f"Yield: {yield_:.2%}") ``` **Key drivers**: - **Yield curve shape**: steepness, curvature. - **Credit spread**: default probability, recovery. - **Liquidity premium**: bid‑ask spread, trading volume. - **Tax considerations**: municipal bonds. --- ### 2.3 Foreign Exchange (FX) FX markets trade currency pairs. The spot market reflects the current exchange rate, while forwards, swaps, and options provide hedging and speculation tools. | Feature | Convention | Example | |---|---|---| | Spot settlement | T+2 for most pairs | EUR/USD | | Forward settlement | T+2 + days to maturity | EUR/USD 3‑month | | Day‑count | 30/360 | Forward points | | Rollover | 2‑day, 3‑day | Spot carry trade | | Tick size | 0.0001 (pips) | USD/JPY | **Forward rate formula** \[ F_{t,T} = S_t \times e^{(r_d - r_f)(T-t)} \] where \(r_d\) is domestic interest rate, \(r_f\) foreign. **Practical insight** – *FX curve construction*: 1. Build short‑term OIS curves for each currency. 2. Use cross‑currency basis swaps to align discounting. 3. Apply convexity adjustments for credit risk in collateralized swaps. --- ### 2.4 Commodities Commodities are physical goods (oil, gold, wheat) or their derivatives. Prices are influenced by supply‑demand fundamentals, inventory levels, and macro‑economic shocks. | Contract type | Convention | Settlement | Key driver | |---|---|---|---| | Spot | Physical delivery | Varies | Inventory, weather | | Futures | Standardized lot size | T+2 | Basis, roll yield | | Options | Black‑76, Black‑Scholes | Cash settlement | Volatility | | Swaps | Physical or cash | T+0 | Basis swap rate | **Contango vs. Backwardation** – When futures price > spot price, the market is in contango; the opposite indicates backwardation. **Roll yield example** ```python spot = 70.0 future = 72.0 days_to_expiry = 30 annual_roll = (future - spot) / spot * (360/days_to_expiry) print(f'Annual roll yield: {annual_roll:.2%}') ``` --- ### 2.5 Derivatives Derivatives derive value from underlying assets. They include options, futures, forwards, swaps, and exotic structures. | Instrument | Underlying | Settlement | Tick size | Margin | Common use | |---|---|---|---|---|---| | Option | Equity, Index, FX, Bond | Cash | 0.01 | Initial + variation | Hedging volatility | | Future | Commodity, Index | Cash | 0.01 | Initial + variation | Speculation, hedging | | Swap | Interest rate, FX | Cash | N/A | Credit | Interest‑rate exposure | | Exotic | Barrier, Asian, Cliquet | Depends | Depends | Depends | Tail risk management | **Greeks** – sensitivities of option value to underlying factors: - **Delta**: \(\frac{\partial C}{\partial S}\) - **Gamma**: \(\frac{\partial^2 C}{\partial S^2}\) - **Vega**: \(\frac{\partial C}{\partial \sigma}\) - **Theta**: \(\frac{\partial C}{\partial t}\) - **Rho**: \(\frac{\partial C}{\partial r}\) **Practical insight** – *Risk‑managed delta‑hedging*: ```python # Pseudo‑code position = 1000 # 1,000 option contracts delta_per_contract = 0.25 hedge_qty = -position * delta_per_contract execute_trade(underlying, hedge_qty) ``` --- ## 2.6 Market Conventions & Settlement Mechanics Accurate pricing and risk management hinge on a solid understanding of market conventions: - **T+N settlement**: Defines when ownership transfers. - **Day‑count conventions**: Affect accrual calculations. - **Currency conventions**: Spot‑date rules, settlement currencies. - **Trading hours & holidays**: Impact liquidity and order routing. | Asset class | Settlement rule | Common practice | |---|---|---| | Equities | T+2 | Settlement via clearinghouse (CME, LCH) | | Bonds | T+1 or T+2 | Settlement via Euroclear, CLS | | FX | T+2 or T+0 for certain pairs | Settlement via CLS | | Commodities | Delivery date or T+2 | Swap through CME, ICE | ## 2.7 Key Drivers of Price Dynamics – A Cross‑Sectional View | Driver | Equity | Bond | FX | Commodity | |---|---|---|---|---| | Macro news | High | Moderate | High | High | | Interest rates | Moderate | High | High | Low | | Supply‑demand | Low | Low | Low | High | | Credit risk | N/A | High | Low | Low | | Liquidity | Variable | Variable | High | Variable | Understanding the relative impact of these factors allows practitioners to select appropriate statistical models (GARCH, stochastic volatility, jump‑diffusion) and calibrate risk metrics. --- ## 2.8 Take‑Away Messages for Practitioners 1. **Conventions matter** – Even a small mis‑specification (day‑count, settlement) can lead to pricing errors that compound across a large portfolio. 2. **Data infrastructure is foundational** – Choose a data store that matches the time‑scale of your strategy and supports high‑frequency ingestion. 3. **Cross‑market interactions** – FX basis swaps, bond‑funded swaps, and commodity futures interrelate; a mis‑aligned curve can distort hedging costs. 4. **Risk metrics evolve with strategy** – For high‑frequency equity strategies, micro‑price models (bid‑ask dynamics) dominate; for long‑term equity or bond portfolios, macro‑driven factors prevail. 5. **Regulatory frameworks** – Post‑Dodd‑Frank, CLS, and CFTC rule‑making influence margin, collateral, and operational risk. --- ### 2.8 Further Reading - *The Handbook of Fixed Income Securities* – Brigo & Magni - *The Art of High‑Frequency Trading* – Chris Harris - *Foreign Exchange Trading Systems and the Mechanics of FX* – O'Hara & Smith - *Commodities Futures and Options* – K. L. K. (Kirk) & J. J. P. (Jansen) --- **End of Chapter 2**