Volume, Fibonacci & Elliott Wave

Question 1

(a) Move size $= H-L = 60$. Retracement level formula (measuring down from the high): $P(r) = H - r\,(H-L) = 160 - 60r.$

Marks: formula (1), each correct level (0.8 each ≈ 4). (5)

(b) Solve $\varphi^2=\varphi+1 \Rightarrow \varphi^2-\varphi-1=0$. $\varphi = \frac{1+\sqrt5}{2} = 1.6180339\ldots$ (taking positive root). (2) From $\varphi^2=\varphi+1$ divide by $\varphi$: $\varphi = 1 + \tfrac1\varphi \Rightarrow \tfrac1\varphi = \varphi-1 = 0.6180\ldots$ — this proves $0.618=1/\varphi=\varphi-1$. (2) Also $1-\tfrac1\varphi = 1-(\varphi-1)=2-\varphi = 2-1.618=0.382$, and $\tfrac1{\varphi^2}=(\tfrac1\varphi)^2=0.618^2=0.382$, so $1-1/\varphi=1/\varphi^2=0.382$. (2) Trivially $\tfrac1\varphi\cdot\varphi=1$. (6)

(c) $C = P(0.618) = 122.92$. Leg $B-A = 60$.

• $1.272$ target: $C + 1.272\times60 = 122.92 + 76.32 = 199.24$.
• $1.618$ target: $C + 1.618\times60 = 122.92 + 97.08 = 220.00$.

Marks: $C$ (1), each target (2). (5)

(d) The $61.8\%$ level $=122.92$ lies just above the $118$–$121$ zone; the closest confluence is the $50\%$ level $130$ (outside) — so within $118$–$121$ none of the exact standard levels fall inside, but $61.8\%$ (122.92) is nearest, ~2 points above. A careful answer notes the zone slightly undercuts $61.8\%$; a reaction near $121$–$123$ combines prior S/R (118–121) with the $61.8\%$ Fib, giving confluence. (award marks for reasoning even if noting the near-miss.)

Confluence argument: independent methods (structural S/R memory + Fibonacci proportion) predicting the same price zone means more market participants place orders there, so liquidity and probability of a reaction increase — a coincidence of signals raises posterior probability. Quantitative scoring: e.g. confluence score = number of independent levels within a fixed price window, or an inverse-distance weighted sum $\sum_i w_i \exp(-d_i^2/2\sigma^2)$ where $d_i$ is distance of each level from the test price.

Marks: identify nearest level & note zone position (3); confluence rationale (3); quantitative scoring method (2). (8)

Question 2

(a) Three inviolable rules (2 each):

1. Wave 2 never retraces more than 100% of wave 1 (cannot go below wave 1 start).
2. Wave 3 is never the shortest of the three impulse waves (1,3,5).
3. Wave 4 does not overlap the price territory of wave 1 (in a standard impulse; end of 4 must not enter wave-1 range).

Guidelines: alternation (if wave 2 is sharp, wave 4 is sideways, and vice-versa); equality/extension (typically one impulse wave extends—often wave 3—and the other two tend toward equality). Breaking a rule means the labelling is structurally impossible, so the count must be redrawn. (6)

(b) Wave 1 length $= 62-50 = 12$. Wave 3 length $=1.618\times12 = 19.416$, starting from $W_2=56$: $W_3 = 56 + 19.416 = 75.416.$ Wave 4 retraces $38.2\%$ of wave 3 length: $0.382\times19.416 = 7.417$: $W_4 = 75.416 - 7.417 = 67.999 \approx 68.00.$

Rule check:

1. Wave 2 = 56 > 50 (start), retrace $= (62-56)/12=50\%<100\%$ ✓.
2. Lengths: W1=12, W3=19.416, W5 $=90-68=22$. Wave 3 (19.42) is not the shortest ✓ (shortest is W1=12).
3. Wave 4 low $=68.00 >$ wave 1 high $=62$: no overlap ✓.

All three rules satisfied → valid impulse.

Marks: $W_3$ (2), $W_4$ (2), each rule check (1.5×3 ≈ 5). (9)

(c) Healthy impulse volume: highest on wave 3 (the strongest, most participated move — driven by accumulation completing and trend recognition); wave 1 moderate, wave 5 often on lower volume / divergence (fewer buyers, distribution begins). Corrections A–B–C run on lighter volume than impulses; wave C may spike as capitulation. Accumulation shows rising volume on up-bars with narrowing spreads at lows; distribution shows rising volume on up-bars that fail to make progress (wide spread, close off highs) near tops. Distrust a wave-3 breakout if it occurs on declining or below-average volume, or a wide-range up-bar closing in its lower third with high volume (no demand / supply overwhelming) — a VSA sign of weakness signalling a false breakout.

Marks: impulse volume pattern (3), corrective (2), distrust signature (2). (7)

Question 3

(a) Pseudocode:

function fib_reaction_signal(swingLow, swingHigh, bars):
    move = swingHigh - swingLow
    dir  = sign(move)                 # +1 uptrend swing, -1 downtrend
    ratios = [0.236,0.382,0.5,0.618,0.786]
    levels = [swingHigh - r*move for r in ratios]   # works for both dirs
    tol = 0.003
    for b in bars:
        avgVol = mean(volume[b-20 .. b-1])
        for (r, L) in zip(ratios, levels):
            if abs(bars[b].close - L) <= tol * L:
                rng = bars[b].high - bars[b].low
                if rng == 0: continue
                closePos = (bars[b].close - bars[b].low) / rng
                volOK  = bars[b].volume >= 1.5 * avgVol
                bullVSA = closePos >= 2/3          # upper third
                confirmed = volOK and bullVSA
                return (L, confirmed)
    return (None, False)

Marks: levels computation (2), tolerance band detection (2), volume ≥150% avg (2), upper-third close test (2), return structure (1). (9)

(b) Complexity: for each bar the 20-bar average is $O(20)=O(1)$ amortised (or maintain a running window), and the inner loop over 5 ratios is $O(1)$, so $O(1)$ per bar, $O(n)$ overall for $n$ bars. Edge case: swing direction — using swingHigh - r*move with signed move keeps the level formula valid whether the impulse is up (swingHigh>swingLow, retracements below high) or down (swingHigh<swingLow, "retracements" above the low), so dir prevents inverted level ordering; also guard $rng=0$ (doji/no-range bar) to avoid division by zero.

Marks: complexity (2), edge-case explanation (3). (5)

[
  {"claim":"61.8% retracement of 100->160 is 122.92","code":"H=160;L=100;lvl=H-0.618*(H-L);result=abs(lvl-122.92)<1e-9"},
  {"claim":"1.618 extension target from C=122.92 is 220.00","code":"C=160-0.618*60;t=C+1.618*60;result=abs(t-220.0)<1e-9"},
  {"claim":"phi solves x^2=x+1 giving 1.618...","code":"from sympy import sqrt,Rational; phi=(1+sqrt(5))/2; result=simplify(phi**2-phi-1)==0"},
  {"claim":"1-1/phi = 1/phi^2 = 0.382","code":"from sympy import sqrt; phi=(1+sqrt(5))/2; result=simplify((1-1/phi)-(1/phi**2))==0 and abs(float(1-1/phi)-0.381966)<1e-4"},
  {"claim":"Wave3=75.416, Wave4=68.0, W3 not shortest, no overlap","code":"W2=56;len1=12;W3=W2+1.618*len1;W4=W3-0.382*(1.618*len1);W5=90;lenW3=1.618*len1;lenW5=W5-W4;ok=(W4>62) and (lenW3>len1) and not(lenW3<len1 and lenW3<lenW5);result=abs(W3-75.416)<1e-3 and abs(W4-68.0)<1e-2 and ok"}
]