Charts, Trends & Dow Theory

Question 1 (10 marks)

(a) Body = $|Close - Open|$; upper wick = $High - \max(O,C)$; lower wick = $\min(O,C) - Low$. (6 marks — 2 per day)

• Day 1: Body $=|106-100|=6$; upper $=108-106=2$; lower $=100-98=2$; Close>Open ⇒ bullish.
• Day 2: Body $=|105-106|=1$; upper $=110-106=4$; lower $=105-104=1$; Close<Open ⇒ bearish.
• Day 3: Body $=|98-105|=7$; upper $=107-105=2$; lower $=98-96=2$... wait: lower $=\min(105,98)-96=98-96=2$; Close<Open ⇒ bearish.

(0.5 per correct value.)

(b) A long lower wick means price sold off intraday (down to 96) but buyers stepped in and pushed price back up before close — signals rejection of lower prices / potential buying support. (2 marks)

(c) Line chart plots only the Close = 106 (single point connected to neighbours). Bar chart shows the full range: high tick 108, low tick 98, left tick = open 100, right tick = close 106. (2 marks: 1 each)

Question 2 (10 marks)

(a) Alternating from High: $102(H), 96(L), 110(H), 104(L), 118(H), 112(L), 116(H), 108(L)$. (2 marks)

(b) Highs: $102 \to 110 \to 118 \to 116$. Lows: $96 \to 104 \to 112 \to 108$.

• $102\to110\to118$: higher highs ✓; $96\to104\to112$: higher lows ✓ — uptrend intact through point 6.
• Break: at the 7th point ($116$) the high fails to exceed prior high $118$ (lower high), AND the 8th point ($108$) is a lower low than prior low $112$. The uptrend structure breaks at the lower high of 116 → confirmed by lower low of 108. (5 marks: 2 for HH/HL tracking, 3 for identifying/justifying the break)

(c) (3 marks)

• Uptrend: successive HH and HL.
• Downtrend: successive LH and LL.
• Range: highs and lows oscillate roughly horizontally (no consistent HH/HL or LH/LL).

Question 3 (12 marks)

(a) Slope $m=\dfrac{112-100}{6-2}=\dfrac{12}{4}=3$. Intercept: $100=3(2)+b \Rightarrow b=94$. Support: $P=3t+94$. (4 marks)

(b) Parallel ⇒ same slope $m=3$. Through $(4,118)$: $118=3(4)+b \Rightarrow b=118-12=106$. Resistance: $P=3t+106$. (4 marks)

(c) At $t=10$: support $=3(10)+94=124$; resistance $=3(10)+106=136$. Channel width $=136-124=12$ (constant, since parallel). (4 marks)

Question 4 (10 marks)

(a) Leg 1: absolute +\10$, percentage$+100%$. Leg 2: absolute$+$20$, percentage$+100%$. (3 marks)

(b) On a log scale, vertical position $\propto \log(P)$. Distance of a move $=\log(P_2)-\log(P_1)=\log(P_2/P_1)$, which depends only on the ratio. Both legs have ratio $2$, so $\log 2$ each ⇒ equal heights. On a linear scale height $\propto (P_2-P_1)$; leg 2 = 20 vs leg 1 = 10, hence twice as tall. (4 marks)

(c) Logarithmic scale — equal percentage moves get equal visual weight, so long-term compounding growth and trend consistency are represented fairly; a linear scale would exaggerate later moves and compress early ones. (3 marks)

Question 5 (10 marks)

(a) Any four (1 each): (1) The averages discount everything. (2) The market has three trends (primary/secondary/minor). (3) Primary trends have three phases (accumulation, public participation, distribution). (4) The averages must confirm each other. (5) Volume must confirm the trend. (6) A trend is assumed in effect until a clear reversal signal.

(b) (4 marks)

• Primary: major trend, months to years — the "tide."
• Secondary: corrective moves against primary, weeks to months — the "waves."
• Minor: short-term noise, days — the "ripples."

(c) In a healthy uptrend, volume should expand on up moves (advances) and contract on pullbacks (declines), confirming buyer commitment; the opposite (rising volume on declines) warns of weakness. (2 marks)

Question 6 (8 marks)

(a) (5 marks)

def trend_direction(highs, lows):
    h1, h2 = highs[-2], highs[-1]
    l1, l2 = lows[-2], lows[-1]
    if h2 > h1 and l2 > l1:
        return "up"
    elif h2 < h1 and l2 < l1:
        return "down"
    else:
        return "range"

(3 marks logic, 2 marks correct up/down/range mapping.)

(b) Top-down: the higher timeframe defines the dominant/primary trend and key S/R; trading in its direction on the lower timeframe gives higher-probability entries. Checking it first prevents taking counter-trend trades that look valid only on a small timeframe. (3 marks)

[
  {"claim":"Day1 body=6, upper=2, lower=2, bullish","code":"O,H,L,C=100,108,98,106; body=abs(C-O); up=H-max(O,C); lo=min(O,C)-L; result=(body==6 and up==2 and lo==2 and C>O)"},
  {"claim":"Day3 body=7, lower wick=2, bearish","code":"O,H,L,C=105,107,96,98; body=abs(C-O); lo=min(O,C)-L; result=(body==7 and lo==2 and C<O)"},
  {"claim":"Support trendline P=3t+94","code":"m=(112-100)/(6-2); b=100-m*2; result=(m==3 and b==94)"},
  {"claim":"Resistance P=3t+106 and channel width 12 at t=10","code":"m=3; b=118-m*4; sup=3*10+94; res=m*10+b; result=(b==106 and sup==124 and res==136 and res-sup==12)"},
  {"claim":"Both legs are 100% moves with ratio 2","code":"from sympy import log; r1=(20-10)/10; r2=(40-20)/20; result=(r1==1 and r2==1 and log(2)==log(20)-log(10) and log(2)==log(40)-log(20))"}
]