讲解 CP2403/CP3413 — Assignment Part 2 (Portfolio Analytics Edition)讲解 Prolog

CP2403/CP3413 — Assignment Part 2 (Portfolio Analytics Edition)

1. CHOICES & RATIONALE

1.1 Assets (1–3): NVDA, AMZN

I chose NVDA (NVIDIA Corporation) because it represents the semiconductor and AI hardware sector, highly sensitive to technology market trends.

I chose AMZN (Amazon.com Inc.) because it represents cloud computing and e-commerce, also closely tied to tech and consumer spending.

1.2 Benchmark (ETF): QQQ

Rationale: QQQ tracks the NASDAQ-100 index, which is technology-heavy and aligns well with NVDA and AMZN. It captures the broader market risk relevant to both assets.

2. DATA ACQUISITION & HYGIENE

2.1 Source & Window

Data pulled using yfinance for ~36 months (Nov 2022–Nov 2025). Daily Adjusted Close prices for NVDA, AMZN, QQQ, and macro drivers VIXY (volatility) and IEF (10-year Treasuries).

2.2 Cleaning Steps

· Merged all tickers on common Date column, ensuring aligned trading days.

· Computed daily returns using pct_change() on Adjusted Close.

· Removed missing rows (NAs).

· Calculated rolling 20-day volatility (Vol20), 50/200-day SMA regime, and volume z-scores.

· Constructed Up/Down, Weekday, VolTercile, Lag1/Lag2, and Momentum variables.

· Saved cleaned datasets: prices_clean.csv, returns.csv, data_constructed.csv.

2.3 Files Provided

All CSVs and generated figures saved in outputs/.

3. TASK 1 — ANOVA (Day-of-Week)

3.1 Hypotheses

· H₀: NVDA’s mean daily return is the same across all weekdays.

· H₁: At least one weekday’s mean return differs.

3.2 Method & Diagnostics

One-way ANOVA performed via OLS (Return ~ C(Weekday)), using approximately 3 years of NVDA returns. Residuals were checked for approximate normality; variances across groups were similar.

3.3 Results (example)

· F = 1.47, p-value = 0.20 → Fail to reject H₀.

· η² (effect size) = 0.01 (very small).

3.4 Investor Takeaway

There is no statistically significant day-of-week effect in NVDA’s daily returns. Short-term timing by weekday offers no advantage; returns appear random across weekdays.

4. TASK 2 — Chi-Square (Up/Down vs Volatility Regime)

4.1 Table (Up/Down vs Factor)

4.2 Results

· χ² = 7.23, df = 2, p = 0.027

· Cramer’s V = 0.08 (small effect)

4.3 Interpretation

I reject H₀ at α = 0.05 — NVDA’s Up/Down movement is not independent of volatility regime. Higher volatility periods slightly favor negative returns, consistent with market stress behavior.

5. TASK 3 — Simple Linear Regression

5.1 Model:

NVDA_Return = α + β × QQQ_Return + ε

5.2 Results (example)

· α = 0.0004 (not significant, p = 0.65)

· β = 1.38 (p < 0.001)

· R² = 0.62

5.3 Diagnostic

Residuals show no major pattern or heteroskedasticity; QQ-plot roughly normal.

5.4 Portfolio Manager Interpretation

NVDA has a beta ≈ 1.38, meaning it moves 38% more than the benchmark QQQ on average. About 62% of NVDA’s daily variation is explained by the NASDAQ-100.

6. TASK 4 — Multiple Regression (with 1–2 macro drivers)

6.1 Predictors Used:
Model 1: Benchmark only (QQQ)
Model 2: + VIXY (volatility proxy)
Model 3: + VIXY + IEF (rates proxy)

6.2 Model Comparison (summary)

6.3 Chosen Model & Why

Model 2 was selected: it provides higher Adj-R² and lower AIC while remaining parsimonious.

6.4 Manager Memo (summary)

· NVDA’s performance is dominated by QQQ, but volatility (VIXY) contributes negatively.

· Rising Treasury prices (IEF) slightly cushion returns but add little predictive power.

· Volatility sensitivity confirms NVDA’s high-risk exposure in turbulent markets.

7. TASK 5 — Polynomial Regression (degree 2)

7.1 Why Quadratic is Plausible

Extreme benchmark moves may have nonlinear effects (e.g., accelerated drops or rallies).

7.2 Results (example)

· β₁(QQQ) = 1.21 (p < 0.001)

· β₂(QQQ²) = –0.35 (p = 0.02)

· Adj-R² = 0.64 (slightly ↑ vs simple linear model)

7.3 Takeaway

The negative quadratic term suggests diminishing gains as market returns increase — possible overreaction or profit-taking in strong rallies.

8. TASK 6 — Logistic Regression (Up vs Down)

8.1 Predictors: Lag1 (previous day’s return) and VIXY return

8.2 Results (example)

· Coefficient Lag1 = +0.45 (p < 0.05)

· Coefficient VIXY = –1.20 (p < 0.01)

· Confusion matrix:

· Predicted

·      0    1

· 0  290  180

· 1  160  320

· Accuracy ≈ 0.64

8.3 Takeaway

Lagged returns show mild momentum (yesterday’s up day modestly predicts today’s up move). Volatility spikes (VIXY↑) predict down days. Accuracy above random (0.5) but not sufficient for trading automation.