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 |
| Rational arbitrage amplification | Ē[pt+1 | p] − p > E[pt+1 |
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.