Tim Olson
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description, tags
| description | tags | ||||
|---|---|---|---|---|---|
| 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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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.