Analyst Targets Probability

5 ก.ย.

This indicator calculates the probability of the current stock price reaching or exceeding the analyst-provided high, average, and low price targets within a one-year time horizon. It utilizes a geometric Brownian motion (GBM) model, a standard approach in financial modeling that assumes log-normal price distribution with constant volatility.

### Key Features:
- **Analyst Targets**: Automatically pulls the high, average, and low one-year price targets from TradingView's syminfo data.
- **Risk-Free Rate**: Fetched from the 1-year US Treasury yield (symbol: TVC:US01Y). Defaults to 4% if unavailable.
- **Dividend Yield**: Uses trailing twelve-month (TTM) dividends per share (DPS) from financial data, divided by current price. Defaults to 0% if unavailable.
- **Volatility**: Computed as annualized historical volatility based on 252 trading days of daily log returns. Falls back to a 20-day period if insufficient data, or defaults to 30% if still unavailable.
- **Probability Calculation**: Employs the barrier hitting probability formula under GBM:
- Drift (μ) = risk-free rate - dividend yield - (volatility² / 2)
- The formula for probability P of hitting target H from current price S₀ over time T is:
P = Φ(d₊) + (H / S₀)^p ⋅ Φ(d₋) for H > S₀ (or adjusted for H < S₀)
Where l = ln(max(H, S₀)/min(H, S₀)), ν = drift, p = -2ν / σ², d₊ = (-l + νT) / (σ√T), d₋ = (-l - νT) / (σ√T), and Φ is the standard normal CDF (approximated using a polynomial method for accuracy).
- **Output Display**: A table in the top-right corner shows each target type, its value, and the estimated probability (as a percentage). "N/A" appears if data is unavailable or calculations cannot proceed (e.g., zero volatility).

### Assumptions and Limitations:
- Assumes constant volatility and drift, no transaction costs, and continuous trading (real markets may deviate due to jumps, news events, or changing conditions).
- Probabilities are model-based estimates and not guarantees; they represent the likelihood under risk-neutral measure.
- Best suited for stocks with available analyst targets and historical data; may default to assumptions for less-liquid symbols.
- No user inputs required—fully automated using TradingView's data sources.

This script is provided under the Mozilla Public License 2.0. For educational and informational purposes only; not financial advice. Test on your charts and consider backtesting for validation.

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### Overview
This Pine Script v5 indicator, titled **Analyst Targets Probability (ATP)**, overlays on TradingView charts to assess the likelihood of a stock reaching analyst price targets (or fallback historical highs/lows) within a 1-year horizon. It assumes stock prices follow a geometric Brownian motion (GBM) model and incorporates risk-adjusted metrics like alpha, Sharpe ratio, and Sortino ratio. The script dynamically fetches external data (e.g., Treasury yields, dividends) and computes a custom beta relative to SPY. It's designed for stocks but handles non-stocks by defaulting values.

Key updates in this version include:
- **Dynamic market risk premium (MRP)**: Now derived from historical S&P 500 returns minus the risk-free rate, rather than a static 6% assumption.
- **Improved fallbacks**: Enhanced handling of missing data (e.g., volatility defaults to 30%, downside deviation to half of volatility).
- **Historical performance integration**: Adds a "Historical 1Y" row in the table and uses past returns for MRP and alpha calculations.
- **Visual signals**: New conditional labels (green/red arrows) for undervalued/overvalued signals based on stock risk premium vs. MRP, plus a dynamic red target line at 125% of current close.
- **Refined probability model**: Clamps outputs to [0,1] for robustness; uses an approximation for the normal CDF.
- **Table expansion**: Now 35 rows (though only ~8 used), with added rows for MRP, stock risk premium, and drift.

The script runs on the last bar for efficiency and supports dynamic requests for real-time data.

### Key Inputs and Parameters
- **Market Proxy**: SPY (S&P 500 ETF) for beta calculation.
- **Lookback Periods**:
- Beta: 252 days (1 trading year).
- Volatility/Downside Deviation: 252 days (fallback to 20 days).
- **Time Horizon (T)**: Fixed at 1 year.
- **Risk-Free Rate (r)**: 1-year US Treasury yield (TVC:US01Y), default 4%.
- **Dividend Yield (q)**: Trailing twelve months (TTM) dividends per share from financial data, default 0%.
- **Volatility (sig)**: Annualized historical std. dev. of log returns, default 30%.
- **Downside Deviation**: Semi-deviation of negative log returns (annualized), default sig/2.
- **Targets**:
- High/Low/Average: From `syminfo.target_price_*` (analyst consensus); falls back to 252-day highest/lowest and midpoint.

### Core Calculations
1. **Beta (β)**:
- Computed manually via covariance of log returns (stock vs. SPY) divided by market variance over 252 days.
- Defaults to 1.0 if invalid/NA.
- Formula: β = Cov(R_stock, R_market) / Var(R_market).

2. **Historical Returns and MRP**:
- Stock return: (Current price - Price 252 days ago + TTM dividends) / Past price.
- Market return: Similar for SPY, plus average S&P dividend yield (~1.2% default).
- MRP = Historical market return - Average risk-free rate (over 252 days).
- Stock risk premium = β × MRP.
- Required return = r + Stock risk premium.
- Historical alpha = Historical stock return - Required return.
- Historical Sharpe/Sortino: Excess return (historical return - r) divided by sig/downside deviation.

3. **Drift (ν)**:
- ν = r - q - (sig² / 2) (annualized GBM drift).

4. **Probability of Hitting Target (p_hit)**:
- Uses a closed-form GBM barrier hitting probability for a constant barrier.
- For target > S0 (upper barrier): p = N(d+) + (target/S0)^{2ν/σ²} × N(d-), where:
- d+ = [-ln(target/S0) + νT] / (σ√T)
- d- = [-ln(target/S0) - νT] / (σ√T)
- N(·) ≈ Normal CDF via Hart's approximation (polynomial tail expansion).
- Symmetric for lower barrier (target < S0).
- Clamped to [0, 100%]; NA if inputs invalid.

5. **Risk-Adjusted Metrics (for each target)**:
- Expected return = (Target - S0)/S0 + q.
- Alpha = Expected return - (r + β × MRP).
- Sharpe = (Expected return - r) / sig.
- Sortino = (Expected return - r) / Downside deviation.

### Outputs and Display
- **Table (Top-Right Corner)**: A 6-column table updates on the last bar:
| Target Type | Value | Prob. of Hitting (1Y) | Alpha | Sharpe | Sortino |
|-------------------|-----------|-----------------------|-----------|----------|----------|
| **High** | [Price] | [XX.X%] | [XX.X%] | [X.XX] | [X.XX] |
| **Average** | [Price] | [XX.X%] | [XX.X%] | [X.XX] | [X.XX] |
| **Low** | [Price] | [XX.X%] | [XX.X%] | [X.XX] | [X.XX] |
| **Historical 1Y**| [XX.X%] | N/A | [XX.X%] | [X.XX] | [X.XX] |
| **Market Risk Prem/Disc** | [XX.X%] | - | - | - | - |
| **Stock Risk Prem/Disc** | [X.XX%] | - | - | - | - |
| **Drift** | [X.XX%] | - | - | - | - |

- "N/A" for missing data.
- Headers in gray; values in white/black.
- If no analyst data, labels adjust (e.g., "1 Year HL[mid]" header, "Mid Point" row).

- **Visual Signals**:
- **Green Up Arrow**: If stock risk premium > MRP and MRP < 0% (potential undervaluation in bearish market).
- **Red Up Arrow**: If stock risk premium > MRP > 0% (wait, condition seems inverted—likely a bug; flags overvaluation?).
- Arrows placed at current low on the last bar.
- **Red Target Line**: Horizontal line extending right from current close × 1.25 (as a visual upside reference); updates dynamically, deleting prior instance.

### Usage Notes
- **Best For**: Stocks with analyst coverage; works on any timeframe but fetches daily data for consistency.
- **Limitations**: Relies on TradingView's `syminfo` and `request.*` functions—may lag on illiquid symbols. Probability assumes constant volatility/drift (no jumps). Visual labels have conditional logic that might need tweaking for accuracy.
- **Customization Ideas**: Adjust `T` for different horizons; add alerts on prob_high > 70%. Test on symbols like AAPL for analyst targets.

This script provides a comprehensive, probabilistic view of upside/downside potential, blending fundamental targets with quantitative risk metrics.