backsolve-miner-vs-metal-ratio-with-fundamentals

<essential_principles>

<principle name="ratio_decomposition"> **Core Formula for Ratio Decomposition**

The Mining Stock/Metal Price Ratio can be decomposed into four fundamental factors:

R_t ≈ K × M_t × (1-L_t) × C_t × D_t

Where:

K: Calibration constant (estimated from observed values)
M_t: Multiple factor (EV/EBITDA)
(1-L_t): Leverage factor (1 - NetDebt/EV)
C_t: Cost factor (1 - AISC/S_t)
D_t: Dilution factor (Shares_base / Shares_t)

This decomposition provides quantifiable attributable explanations for "ratio changes". </principle>

<principle name="aisc_extraction"> **AISC Extraction Priority Order**

All-In Sustaining Cost (AISC) is the core driver of mining stock valuation:

Priority	Source	Method
1	MD&A / Financial Footnotes	Keyword extraction: "AISC", "all-in sustaining"
2	Annual Report Presentation PDF	Parse tables: $/oz or $/ounce
3	Proxy Calculation	(OpCost + SustCapex + G&A - Byproduct) / Oz

When direct disclosure is unavailable, supplement with proxy calculation; record

aisc_method

to mark the source. </principle>

<principle name="backsolve_logic"> **Backsolve Logic**

Objective: Given a target ratio R* (e.g., historical peak 1.7), back-calculate the required factor conditions.

Single-factor Backsolve: Assume other factors remain unchanged, adjust only one factor

M* = M_now × (R*/R_now)         # Required multiple
(1-L*) = (1-L_now) × (R*/R_now) # Required deleveraging level
C* = C_now × (R*/R_now)         # Required cost improvement → implied AISC*
D* = D_now × (R*/R_now)         # Required dilution discount

Two-factor Combination: List feasible combinations in a grid (e.g., +20% multiple + -15% silver price). </principle>

<principle name="event_study"> **Event Study Methodology**

Identify historical events where the ratio fell into the bottom quantile, and review the status of the four factors during those events:

Did AISC rise?: Cost pressure
Did NetDebt/EV deteriorate?: Leverage pressure
Did EV/EBITDA compress?: Multiple pressure
Did shares increase?: Dilution pressure

Rank "which factor contributed the most" to identify the main driver of the bottom. </principle>

<principle name="data_priority"> **Data Source Priority Order**

Follow the "structured data first" principle:

SEC XBRL (10-K/10-Q): Directly extract fields (debt, cash, share count, CFO, Capex)
SEDAR+ (Canada): Silver mining companies are often listed in Canada
Corporate IR Annual Reports/MD&A: Supplement non-standard fields such as AISC and production volume
ETF Holdings: Official CSV or SEC N-PORT

Use Selenium to simulate human behavior during crawling to avoid being blocked. </principle>

</essential_principles>

<objective> Implement a fundamental back-calculation system for the "Mining Stock/Metal Price Ratio":

Data Integration: Crawl price data, ETF holdings, financial statements, and operational disclosures
Factor Calculation: Calculate the four core factors: AISC, leverage, multiple, and dilution
Ratio Decomposition: Establish the approximation formula R_t ≈ K × M × (1-L) × C × D
Threshold Backsolve: Given a target ratio, back-calculate the required factor combinations
Event Study: Factor-driven analysis of historical bottom events
Report Output: Structured JSON and human-readable Markdown

Target Users: Investors who want to verify the driving factors using "actual financial statements" when the SIL/silver ratio reaches extreme levels. </objective>

<quick_start>

Fastest Way: Use Default Parameters for Analysis

bash

cd skills/backsolve-miner-vs-metal-ratio-with-fundamentals
pip install pandas numpy yfinance matplotlib  # First-time use
python scripts/fundamental_analyzer.py --quick

Full Analysis (Including Financial Statement Crawling)

bash

python scripts/fundamental_analyzer.py \
  --metal-symbol SI=F \
  --miner-universe etf:SIL \
  --region-profile us_sec \
  --start-date 2015-01-01 \
  --output result.json

Generate Visualization Dashboard

bash

python scripts/visualize_factors.py --quick --output output/
# Output: output/sil_silver_factor_analysis_YYYY-MM-DD.png

The visualization dashboard includes four panels:

Ratio Time Series: Historical trend + quantile intervals (bottom/top)
Factor Radar Chart: Overview of the health status of the four factors
Factor Score Bar Chart: Scores for cost, leverage, multiple, and dilution
Scenario Heatmap: Combination analysis of multiple expansion × silver price changes

Co-rise Scenario Simulation

bash

python scripts/scenario_path_simulator.py --quick --output output/
# Output: output/scenario_path_YYYY-MM-DD.png + return_heatmap_YYYY-MM-DD.png

Core Formula: Mining stock return = (1 + silver price return) × (R₁/R₀) - 1

Custom Parameters:

bash

python scripts/scenario_path_simulator.py \
  --silver-monthly 5 \      # Silver price monthly return 5%
  --ratio-start 1.10 \      # Ratio starting point
  --ratio-end 1.20 \        # Ratio ending point
  --months 6 \              # Simulate 6 months
  --heatmap                 # Generate return heatmap simultaneously

Output Example:

json

{
  "now": {
    "metal_price": 94.4,
    "miner_price": 103.4,
    "ratio": 1.13,
    "ratio_percentile": 0.111
  },
  "thresholds": {
    "bottom_ratio": 1.20,
    "top_ratio": 1.70,
    "median_ratio": 1.51
  },
  "fundamentals_weighted": {
    "aisc_usd_per_oz": 28.0,
    "net_debt_to_ev": 0.25,
    "ev_to_ebitda": 6.4,
    "shares_yoy_change": 0.12
  },
  "factors_now": {
    "cost_factor_C": 0.7034,
    "leverage_factor_1_minus_L": 0.75,
    "multiple_M": 6.4,
    "dilution_discount_D": 0.89
  },
  "backsolve_to_top": {
    "multiple_only_need": 9.1,
    "deleverage_only_need_1_minus_L": 1.12,
    "cost_only_implied_aisc": 15.6,
    "dilution_only_need_D": 1.26
  }
}

</quick_start>

<intake> What operation do you need to perform?

Quick Analysis - Calculate current factor status using default parameters (SIL / SI=F)
Full Analysis - Crawl financial statements, calculate factors, back-calculate thresholds
Factor Decomposition - Deep dive into the calculation logic of the four factors
Threshold Backsolve - Given a target ratio, calculate the required factor combinations
Event Study - Factor-driven ranking of historical bottom events
Methodology Learning - Understand back-calculation logic and data sources
Visualization - Generate four-panel dashboard charts
Co-rise Scenario - Simulate the proportional relationship and path of simultaneous rise in silver price and mining stocks

Please select or provide analysis parameters directly. </intake>

<routing> | Response | Action | |--------------------------------|----------------------------------------------------------------| | 1, "快速", "quick", "分析" | Execute `python scripts/fundamental_analyzer.py --quick` | | 2, "完整", "full", "財報" | Read `workflows/analyze.md` and execute | | 3, "因子", "factor", "拆解" | Read `references/fundamental-factors.md` | | 4, "反推", "backsolve", "門檻" | Read `references/backsolve-math.md` and execute back-solve analysis | | 5, "事件", "event", "底部" | Read `workflows/analyze.md` and focus on event study | | 6, "學習", "方法論", "why" | Read `references/fundamental-factors.md` + `backsolve-math.md` | | 7, "視覺化", "圖", "chart" | Execute `python scripts/visualize_factors.py --quick` | | 8, "共同上漲", "情境", "路徑" | Execute `python scripts/scenario_path_simulator.py --quick` | | "比例關係", "漲幅", "要漲多少" | Execute `python scripts/scenario_path_simulator.py --quick` | | Provide parameters (e.g., ETF/metal proxy) | Read `workflows/analyze.md` and execute with the specified parameters |

After routing, read the corresponding file and execute. </routing>

<directory_structure>

backsolve-miner-vs-metal-ratio-with-fundamentals/
├── SKILL.md                           # This file (router)
├── skill.yaml                         # Frontend display metadata
├── manifest.json                      # Skill metadata
├── workflows/
│   ├── analyze.md                     # Full analysis workflow
│   └── data-fetch.md                  # Data crawling workflow
├── references/
│   ├── input-schema.md                # Complete input parameter definition
│   ├── data-sources.md                # Data source description
│   ├── fundamental-factors.md         # Calculation logic of the four factors
│   └── backsolve-math.md              # Backsolve mathematical formulas
├── templates/
│   ├── output-json.md                 # JSON output template
│   └── output-markdown.md             # Markdown report template
├── scripts/
│   ├── fundamental_analyzer.py        # Main calculation script
│   ├── visualize_factors.py           # Visualization dashboard script
│   └── scenario_path_simulator.py     # Co-rise scenario simulator
└── examples/
    └── sample-output.json             # Sample output

</directory_structure>

<reference_index>

Input Parameters: references/input-schema.md

Complete parameter definitions
Default values and recommended ranges
Description of each method option

Data Sources: references/data-sources.md

Price data (yfinance / stooq / alphavantage)
Financial statement data (SEC EDGAR / SEDAR+ / corporate IR)
ETF holdings (official CSV / N-PORT / manual URL)

Factor Calculation: references/fundamental-factors.md

AISC cost factor
Leverage factor
Multiple factor
Dilution factor

Backsolve Mathematics: references/backsolve-math.md

Single-factor backsolve formulas
Two-factor combination grid
Calibration constant estimation

</reference_index>

<workflows_index>

Workflow	Purpose	Usage Scenario
analyze.md	Full analysis	Need to crawl financial statements and calculate factors
data-fetch.md	Data crawling	Understand how to crawl ETF holdings and financial statements
</workflows_index>

<templates_index>

Template	Purpose
output-json.md	JSON output structure definition
output-markdown.md	Markdown report template
</templates_index>

<scripts_index>

Script	Command	Purpose
fundamental_analyzer.py	`--quick`	Quick analysis of SIL/SI=F
fundamental_analyzer.py	`--miner-universe etf:SILJ`	Custom mining stock ETF
fundamental_analyzer.py	`--backsolve-target 1.7`	Specify target ratio for backsolve
fundamental_analyzer.py	`--event-study --min-separation 180`	Execute event study
visualize_factors.py	`--quick --output output/`	Generate four-panel visualization dashboard
visualize_factors.py	`--input result.json`	Generate charts from JSON results
scenario_path_simulator.py	`--quick`	Co-rise scenario path simulation
scenario_path_simulator.py	`--silver-monthly 5 --months 6`	Custom silver monthly return and simulation months
scenario_path_simulator.py	`--ratio-start 1.10 --ratio-end 1.20`	Custom ratio start and end points
scenario_path_simulator.py	`--heatmap`	Generate return heatmap simultaneously
</scripts_index>

<input_schema_summary>

Core Parameters

Parameter	Type	Default Value	Description
metal_symbol	string	SI=F	Metal price ticker (SI=F for silver, GC=F for gold)
miner_universe	object	etf:SIL	Mining stock/ETF definition
region_profile	string	us_sec	Regulatory and disclosure source (us_sec / canada_sedar)
time_range.start	string	5 years ago	Analysis start date (YYYY-MM-DD)
time_range.end	string	today	Analysis end date
time_range.frequency	string	weekly	Sampling frequency (daily/weekly/monthly)

Factor Method Selection

Parameter	Type	Default Value	Description
fundamental_methods.aisc	string	hybrid	AISC extraction method
fundamental_methods.leverage	string	net_debt_to_ev	Leverage calculation method
fundamental_methods.multiple	string	ev_to_ebitda	Multiple calculation method
fundamental_methods.dilution	string	weighted_avg_shares	Dilution calculation method

Quantile Thresholds

Parameter	Type	Default Value	Description
ratio_thresholds.bottom	float	0.20	Bottom quantile threshold
ratio_thresholds.top	float	0.80	Top quantile threshold

Complete parameter definitions can be found in

references/input-schema.md

</input_schema_summary>

<output_schema_summary>

json

{
  "skill": "backsolve_miner_vs_metal_ratio_with_fundamentals",
  "inputs": {
    "metal_symbol": "SI=F",
    "miner_universe": {"type": "etf_holdings", "etf_ticker": "SIL"},
    "region_profile": "us_sec"
  },
  "now": {
    "metal_price": 94.4,
    "miner_price": 103.4,
    "ratio": 1.13,
    "ratio_percentile": 0.111
  },
  "thresholds": {
    "bottom_ratio": 1.20,
    "top_ratio": 1.70,
    "median_ratio": 1.51
  },
  "fundamentals_weighted": {
    "aisc_usd_per_oz": 28.0,
    "net_debt_to_ev": 0.25,
    "ev_to_ebitda": 6.4,
    "shares_yoy_change": 0.12
  },
  "factors_now": {
    "cost_factor_C": 0.7034,
    "leverage_factor_1_minus_L": 0.75,
    "multiple_M": 6.4,
    "dilution_discount_D": 0.89
  },
  "backsolve_to_top": {
    "multiple_only_need": 9.1,
    "deleverage_only_need_1_minus_L": 1.12,
    "cost_only_implied_aisc": 15.6,
    "dilution_only_need_D": 1.26,
    "two_factor_grid_examples": [
      {"multiple_up": 1.20, "metal_down": -0.15, "hits_top": true},
      {"deleverage": -0.10, "multiple_up": 1.15, "hits_top": true}
    ]
  },
  "event_study": {
    "bottom_events": [
      {
        "date": "2026-01-02",
        "ratio": 1.13,
        "aisc": 29.1,
        "net_debt_to_ev": 0.27,
        "ev_to_ebitda": 5.8,
        "shares_yoy": 0.14,
        "dominant_driver": "multiple_compression"
      }
    ]
  },
  "summary": "The ratio is at a historical bottom, mainly driven by multiple compression...",
  "notes": [
    "AISC was calculated using hybrid method, some values are proxy estimates for certain companies",
    "Recommended cross-validation: COT positions, ETF flows, USD/real interest rates"
  ]
}

Complete output structure can be found in

templates/output-json.md

. </output_schema_summary>

<success_criteria> When execution is successful, the following should be produced:

Current ratio and historical quantile
Four fundamental factors (AISC, leverage, multiple, dilution)
Weighted combined factor
Threshold backsolve results (single-factor + two-factor combinations)
Factor-driven ranking of historical bottom events
Results output in specified format (JSON or Markdown)
Data source and method annotations (e.g., aisc_method)
Risk warnings and follow-up research suggestions
Visualization dashboard (PNG format, filename includes date) </success_criteria>

backsolve-miner-vs-metal-ratio-with-fundamentals

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