Tim Olson
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58 lines
3.0 KiB
Markdown
58 lines
3.0 KiB
Markdown
---
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description: "Generates long/short signals for a stock when its current price crosses above or below a single moving average, used as a trend-following entry and exit rule."
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tags: [stocks, trend-following, moving-average, technical-analysis]
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---
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# Single Moving Average
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**Section**: 3.11 | **Asset Class**: Stocks | **Type**: Trend-Following / Technical Analysis
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## Overview
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This strategy generates buy and sell signals based on whether the current stock price is above or below a single moving average (MA). If the price is above the MA, the stock is in an uptrend and a long position is established; if below, a downtrend is indicated and a short position is established. It can be applied on a single-stock basis or across a universe of stocks simultaneously.
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## Construction / Signal
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Two types of moving averages:
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**Simple Moving Average (SMA)**:
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```
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SMA(T) = (1/T) * sum_{t=1}^{T} P(t) (319)
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```
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**Exponential Moving Average (EMA)**:
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```
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EMA(T, lambda) = (sum_{t=1}^{T} lambda^{t-1} P(t)) / (sum_{t=1}^{T} lambda^{t-1})
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= ((1-lambda)/(1-lambda^T)) * sum_{t=1}^{T} lambda^{t-1} P(t) (320)
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```
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where `t=1` is the most recent day, `T` is the MA length (in trading days), and `lambda < 1` suppresses past contributions. For T >> 1: `EMA(T, lambda) ≈ (1-lambda) P(1) + lambda EMA(T-1, lambda)`.
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**Trading signal** (P is the current price at t=0):
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```
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Signal = { Establish long / liquidate short position if P > MA(T)
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{ Establish short / liquidate long position if P < MA(T) (321)
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```
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## Entry / Exit Rules
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- **Long entry**: Current price P crosses above MA(T) → establish long position.
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- **Long exit**: Current price P crosses below MA(T) → liquidate long position.
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- **Short entry**: Current price P crosses below MA(T) → establish short position.
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- **Short exit**: Current price P crosses above MA(T) → liquidate short position.
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## Key Parameters
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- **MA type**: SMA or EMA
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- **MA length T**: Typically 50, 100, or 200 trading days (longer = slower, fewer signals)
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- **Lambda (EMA only)**: Decay factor, 0 < lambda < 1; smaller lambda = faster decay
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- **Run mode**: Long-only, short-only, or both long and short
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## Variations
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- **Multi-stock application**: Apply to a large universe of stocks on a single-stock basis; with many stocks, (near-)dollar-neutral portfolios can be constructed
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- **Two moving averages**: See Section 3.12 (replace price P with a shorter MA)
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- **Three moving averages**: See Section 3.13
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## Notes
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- Single-stock technical analysis strategies are considered "unscientific" by many academics, as there is no fundamental reason why a price crossing a moving average should have forecasting power.
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- However, trend-following/momentum strategies (which use MAs to compute expected returns) are broadly used and empirically validated.
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- Applicable on a single-stock basis with no cross-sectional interaction between stocks.
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- With a large universe, near-dollar-neutral portfolios are achievable.
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- The strategy can be run as long-only, short-only, or long-short.
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