---
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."
tags: [stocks, trend-following, moving-average, technical-analysis]
---

# Single Moving Average

**Section**: 3.11 | **Asset Class**: Stocks | **Type**: Trend-Following / Technical Analysis

## Overview
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.

## Construction / Signal
Two types of moving averages:

**Simple Moving Average (SMA)**:
```
SMA(T) = (1/T) * sum_{t=1}^{T} P(t)                      (319)
```

**Exponential Moving Average (EMA)**:
```
EMA(T, lambda) = (sum_{t=1}^{T} lambda^{t-1} P(t)) / (sum_{t=1}^{T} lambda^{t-1})
               = ((1-lambda)/(1-lambda^T)) * sum_{t=1}^{T} lambda^{t-1} P(t)   (320)
```

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)`.

**Trading signal** (P is the current price at t=0):
```
Signal = { Establish long / liquidate short position if P > MA(T)
          { Establish short / liquidate long position if P < MA(T)   (321)
```

## Entry / Exit Rules
- **Long entry**: Current price P crosses above MA(T) → establish long position.
- **Long exit**: Current price P crosses below MA(T) → liquidate long position.
- **Short entry**: Current price P crosses below MA(T) → establish short position.
- **Short exit**: Current price P crosses above MA(T) → liquidate short position.

## Key Parameters
- **MA type**: SMA or EMA
- **MA length T**: Typically 50, 100, or 200 trading days (longer = slower, fewer signals)
- **Lambda (EMA only)**: Decay factor, 0 < lambda < 1; smaller lambda = faster decay
- **Run mode**: Long-only, short-only, or both long and short

## Variations
- **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
- **Two moving averages**: See Section 3.12 (replace price P with a shorter MA)
- **Three moving averages**: See Section 3.13

## Notes
- 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.
- However, trend-following/momentum strategies (which use MAs to compute expected returns) are broadly used and empirically validated.
- Applicable on a single-stock basis with no cross-sectional interaction between stocks.
- With a large universe, near-dollar-neutral portfolios are achievable.
- The strategy can be run as long-only, short-only, or long-short.