# Support and Resistance Levels: A Limited-Attention Theory of Technical Trading

Cite as: Gorak, R. (2026). Support and Resistance Levels: A Limited-Attention Theory of Technical Trading. Tradicted. https://www.tradicted.com/research/teeple-support-2020/
Paper: Keisuke Teeple — *Support, Resistance, and Technical Trading*
Published in: SSRN Working Paper (2020)
Original: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3667920

Key finding: A 1,000,000-period simulation with spacing ε = 100 and transaction cost τ = 2 produces a symmetric, single-peaked ergodic price density satisfying the formal support-and-resistance condition Covmod(E[pt+1|p] − p, p) < 0 (Teeple, 2020).

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Support and resistance levels are price points where a falling or rising asset price tends to stop and reverse direction. In Support, Resistance, and Technical Trading, Teeple (2020) proves traders optimally choose equally-spaced posterior means, Pi = ℓb + (i − 1)ε + ε/2. A simulation with ε = 100 and τ = 2 produces a symmetric, single-peaked price density over 1,000,000 periods. That outcome matches Donaldson and Kim's (1993) definition of support and resistance.

## What the Study Found

Theorem 1 proves that traders optimally choose equally-spaced posterior means, Pi = ℓb + (i − 1)ε + ε/2, given k cells. A 1,000,000-period simulation with ε = 100 produces a symmetric, single-peaked ergodic density of mod(p, ε), shown in Figure 4. That density satisfies Covmod(E[pt+1|p] − p, p) < 0, the formal support-and-resistance condition from Definition 1. A second simulation with ε = 10 and noise drawn from Uniform[−5, −4] and Uniform[4, 5] produces a non-hump-shaped density, violating Definition 2. Corollary 1 shows rational arbitrageurs strengthen the pattern: Ē[pt+1|p] − p exceeds E[pt+1|p] − p for p ∈ (0, ε/2).

## Methodology

Teeple's model is theoretical rather than empirical, so it uses no historical dataset. The model combines coarse Bayesian updating (Jakobsen, 2021) with an ex ante optimal partition of posterior means (Gul et al., 2017). Equilibrium properties are derived analytically and illustrated with two numerical simulations rather than from any sample of real trades. Key parameters controlled across simulations are price elasticity c, risk aversion ρ, transaction cost τ, and the distribution of noise trading ut.

## Key Statistics

| Metric | Finding | Context |
|---|---|---|
| Optimal posterior-mean spacing | Pi = ℓb + (i − 1)ε + ε/2 | Theorem 1, unique solution to the ex ante attention problem |
| Baseline simulation parameters | c = 1, ε = 100, ρ = 1, τ = 2, ut ~ Normal(0, 25) | Section 3.3, 1,000 periods plotted in Figure 3 |
| Ergodic density simulation length | 1,000,000 periods | Section 3.3, symmetric single-peaked density of mod(p, ε), Figure 4 |
| Support and resistance condition | Covmod(E[pt+1|p] − p, p) < 0 | Definition 1, verified in Theorem 2 |
| Rational arbitrage amplification | Ē[pt+1|p] − p > E[pt+1|p] − p > 0 for p ∈ (0, ε/2) | Corollary 1, Section 4.3 |

## Why This Matters

Teeple's theory offers a formal, micro-founded explanation for a price pattern that technical traders have long described informally as chart-based support and resistance. It suggests that price barriers can emerge naturally from limited attention rather than from any irrationality or asset-specific inefficiency. The same mechanism could plausibly extend to other markets with retail traders and market makers, including foreign exchange, commodities, and cryptocurrency markets. Traders using range-break strategies can read a broken level as a signal of continued momentum, since prices move further once a barrier is crossed. Identifying a level after the fact is easier than calling it while price approaches. A [trading simulator](/tools/fake-trading-simulator/) hides the outcome until you commit.

## FAQ

### What are support and resistance levels in technical trading?

Pi = ℓb + (i − 1)ε + ε/2 gives the equally-spaced posterior means traders optimally choose under limited attention (Teeple, 2020). Buying pressure builds near support and selling pressure builds near resistance, as traders treat the asset as underpriced or overpriced.

### What does the model predict about the ergodic density of prices modulo the spacing parameter ε?

1,000,000 simulated periods produce a symmetric, single-peaked density of mod(p, ε) when ε = 100 and τ = 2 (Teeple, 2020). That density satisfies Covmod(E[pt+1|p] − p, p) < 0, the formal definition from Donaldson and Kim (1993).

### Does rational arbitrage eliminate support and resistance effects in this model?

Corollary 1 shows that rational arbitrageurs strengthen, rather than eliminate, support and resistance effects in Teeple's (2020) model. Adding arbitrageurs causes Ē[pt+1|p] − p to exceed E[pt+1|p] − p for p ∈ (0, ε/2), amplifying the original coarse-Bayesian-only pattern.

### Why do stock prices often stop and reverse at round numbers?

Equally-spaced price grids, spaced ε apart, explain why prices often reverse near round numbers, according to Teeple (2020). Near each grid point, traders perceive the asset as overpriced or underpriced, generating buying or selling pressure that produces the reversal pattern.

## Source

Keisuke Teeple. (2020). Support, Resistance, and Technical Trading. SSRN Working Paper.

[Read the full paper →](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3667920)