# MutualScreener — Complete Quantitative Methodology, Mathematical Formulations & Architecture Reference

## 1. Architectural Overview
MutualScreener (https://mutualscreener.com) is India's most advanced quantitative mutual fund portfolio reviewer and analytical suite. It combines AMFI historical NAV records with monthly AMC portfolio disclosures to deliver real-time backtesting, multi-factor scoring, Markowitz optimization, and downloadable institutional portfolio review reports.

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## 2. Interactive Custom Portfolio Reviewer & Real-Time Backtesting Engine

### 2.1. Dynamic Weight Slider Mechanics
Users can dynamically adjust allocation weights $\mathbf{w} = [w_1, w_2, \dots, w_n]^T$ where $\sum_{i=1}^n w_i = 1$ and $w_i \ge 0$. As sliders move, the calculation engine dynamically updates portfolio KPIs in real time without server latency:

1. **Portfolio Expected Return ($R_p$)**:
   $$R_p = \sum_{i=1}^n w_i \cdot \mu_i = \mathbf{w}^T \boldsymbol{\mu}$$
   where $\mu_i$ is the annualized Compound Annual Growth Rate (CAGR) of fund $i$.

2. **Portfolio Annualized Volatility ($\sigma_p$)**:
   $$\sigma_p = \sqrt{\mathbf{w}^T \mathbf{\Sigma}^* \mathbf{w}}$$
   where $\mathbf{\Sigma}^*$ is the Ledoit-Wolf shrunk annual covariance matrix derived from monthly historical NAV returns.

3. **Portfolio Sharpe Ratio**:
   $$\text{Sharpe} = \frac{R_p - R_f}{\sigma_p}$$
   where $R_f = 6.5\%$ (annualized risk-free benchmark based on RBI 91-day T-Bills / Repo benchmark).

4. **Portfolio Sortino Ratio**:
   $$\text{Sortino} = \frac{R_p - R_f}{\text{Downside Semi-Deviation}}$$
   $$\text{Downside Semi-Deviation} = \sqrt{\frac{1}{T} \sum_{t=1}^T \min(r_{p,t} - \text{MAR}, 0)^2} \times \sqrt{12}$$
   where $r_{p,t} = \sum_{i=1}^n w_i r_{i,t}$ is the monthly portfolio return and $\text{MAR}$ is the Minimum Acceptable Return (0%).

5. **Maximum Historical Drawdown (MDD)**:
   $$\text{MDD} = \max_{t \in [0, T]} \left( \frac{\text{HWM}_t - \text{NAV}_t}{\text{HWM}_t} \right)$$
   where $\text{HWM}_t = \max_{\tau \le t} \text{NAV}_\tau$ represents the running high-water mark of the reconstructed portfolio.

### 2.2. Real-Time Consolidated Holdings Lookthrough
For a portfolio with $N$ funds, each fund $i$ holds security $k$ with reported weight $s_{i,k}$. As the user changes fund weights $w_i$, the effective portfolio exposure to security $k$ is dynamically computed as:
$$W_k = \sum_{i=1}^n w_i \cdot s_{i,k}$$
- All company names are deduplicated through corporate entity normalization (e.g. "Reliance Industries Limited", "RELIANCE INDS", "Reliance Industries" $\rightarrow$ "Reliance Industries").
- Non-equity instruments (TREPS, Cash, Reverse Repo, Sovereign G-Secs) are segregated into Debt/Cash collateral pools.

### 2.3. Downloadable Institutional Portfolio Review Report (Export Engine)
Clicking the **Export Report** button compiles a comprehensive, standalone, publication-quality HTML/PDF report featuring:
1. **Executive Review Header**: Portfolio name, analysis date, corpus size, and risk-free benchmark.
2. **KPI Performance Dashboard**: CAGR, Annual Volatility, Sharpe, Sortino, Max Drawdown, and ₹10,000 growth trajectory.
3. **Asset Allocation & Weight Matrix**: Fund-by-fund percentage and exact rupee allocations.
4. **Consolidated Stock Holdings Table**: Top underlying equity positions, effective weight %, rupee exposure, and sector.
5. **Market Capitalization Split**: Allocation across Giant Cap, Large Cap, Mid Cap, Small Cap, and Tiny Cap.
6. **Sector Diversification Breakdown**: Weighted sector percentages across Financials, Technology, Healthcare, Energy, and Consumer sectors.
7. **Weighted Valuation & Cost Audit**: Weighted P/E, P/B, Composite Quant Score, Weighted TER, and annual expense fee drag in ₹.
8. **SEBI Regulatory Disclaimers**: Full statutory educational and non-advisory compliance notices.

### 2.4. Pairwise Holdings Overlap Matrix
$$\text{Overlap}(A, B) = \sum_{k \in A \cap B} \min(w_{A,k}, w_{B,k}) \times 100\%$$

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## 3. Markowitz Efficient Frontier & Covariance Shrinkage

### 3.1. Ledoit-Wolf Covariance Matrix Shrinkage
$$\mathbf{\Sigma}^* = \delta \mathbf{F} + (1 - \delta) \mathbf{S}$$
Guarantees strictly positive-definite eigenvalues ($\lambda_{\min} > 0$).

### 3.2. Constrained Optimization Models (SciPy SLSQP)
- **Global Minimum Variance (GMV)**
- **Maximum Sharpe (Tangency)**
- **Equal Risk Contribution (Risk Parity)**

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## 4. Multi-Factor 5-Pillar Quant Score (0–100)
1. **Returns Pillar (25%)**
2. **Downside Risk Pillar (25%)**
3. **Efficiency Pillar (20%)**
4. **Valuation & Credit Pillar (15%)**
5. **Cost & Stability Pillar (15%)**

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## 5. SEBI Regulatory Notice & Compliance
MutualScreener is an analytical computational sandbox designed strictly for educational, research, and mathematical exploration. It is not registered with SEBI as an Investment Adviser (RIA) or Research Analyst (RA). Sourced from official AMFI historical NAV records and AMC factsheets.