Level 4 — ApplicationIndicators & Oscillators

Indicators & Oscillators

⏱ 60 minutes60 marksprintable — key stays hidden on paper

Level 4 (Application — novel problems, no hints) Time limit: 60 minutes Total marks: 60

Question 1 — Moving Averages & Crossovers (12 marks)

A stock closes at the following prices over 6 consecutive days:

$P = [20,\ 22,\ 21,\ 24,\ 26,\ 25]$

(a) Compute the 3-day Simple Moving Average (SMA) for days 3 through 6. (3)

(b) Compute the 3-day Exponential Moving Average (EMA). Use smoothing factor $\alpha = \frac{2}{N+1}$ , and seed the EMA on day 3 with the day-3 SMA value. Report EMA for days 4, 5 and 6. (5)

(c) On day 5 the EMA lies above the SMA; on day 3 it was equal. Explain why the EMA reacts faster than the SMA to the rising prices, referencing your numbers. (2)

(d) State what a golden cross and a death cross are, and why traders use longer MA pairs (e.g. 50/200) rather than 3-day averages for these signals. (2)

Question 2 — RSI & Divergence (12 marks)

Over 5 days a stock's day-to-day price changes are:

$\Delta = [+2,\ -1,\ +3,\ -1,\ +2]$

(a) Using the simple average method over these 5 changes (average gain, average loss), compute the RSI. Show $RS$ and $RSI = 100 - \frac{100}{1+RS}$ . (5)

(b) State the standard overbought and oversold thresholds and classify your RSI result. (2)

(c) Define bearish RSI divergence and describe, in your own words, the price/RSI pattern that would signal it. (3)

(d) A trader sees RSI = 45 and calls it "oversold, time to buy." Critique this statement. (2)

Question 3 — MACD & Bollinger Bands (14 marks)

(a) Given a 12-period EMA = 51.2 and a 26-period EMA = 49.8, compute the MACD line. (2)

(b) The MACD signal line (9-period EMA of MACD) equals 1.1. Compute the MACD histogram value and state whether momentum is bullish or bearish and whether it is strengthening or weakening if the previous histogram was 0.8. (4)

(c) A 20-period SMA = 100 with standard deviation $\sigma = 2.5$ . Compute the upper and lower Bollinger Bands at $\pm 2\sigma$ , and the bandwidth $= \frac{\text{Upper}-\text{Lower}}{\text{Middle}}$ . (4)

(d) Explain what a Bollinger squeeze signals and one way MACD could be used to confirm the eventual breakout direction. (4)

Question 4 — Stochastic, ATR & VWAP (12 marks)

For a session, over the last 14 periods the highest high = 58, lowest low = 50, and the current close = 56.

(a) Compute %K of the stochastic oscillator. Classify overbought/oversold using standard 80/20 thresholds. (4)

(b) Three consecutive True Ranges are 1.2, 1.6, 1.0. Compute a simple 3-period ATR and state what a rising ATR tells a trader. (3)

Trade	Price	Volume
1	10	100
2	11	300
3	12	100

(d) Explain one practical use of VWAP for an institutional trader. (2)

Question 5 — OBV, ADX, Ichimoku & Indicator Overload (10 marks)

(a) Given close prices $[30, 31, 30, 32]$ with volumes $[500, 400, 600, 300]$ , compute the running On-Balance Volume (OBV), starting OBV = 0. (4)

(b) An ADX reading is 15 and then rises to 32 over two weeks. Interpret both readings in terms of trend strength (state the conventional ADX < 20 / > 25 thresholds). (2)

(c) In the Ichimoku system, price trades above the cloud (Kumo) and the cloud is green (Senkou A > Senkou B). State the overall directional bias this implies. (2)

(d) Explain the problem of indicator overload and give one concrete rule to avoid it. (2)

Answer keyMark scheme & solutions

Question 1 (12)

(a) 3-day SMA — average of trailing 3 closes.

Day 3: $(20+22+21)/3 = 21.00$
Day 4: $(22+21+24)/3 = 22.33$
Day 5: $(21+24+26)/3 = 23.67$
Day 6: $(24+26+25)/3 = 25.00$ (3 marks: ½ each correct, round to full 3)

(b) EMA, $\alpha = 2/(3+1) = 0.5$ . Seed day 3 EMA = 21.00. $EMA_t = \alpha P_t + (1-\alpha)EMA_{t-1}$

Day 4: $0.5(24) + 0.5(21) = 22.50$
Day 5: $0.5(26) + 0.5(22.5) = 24.25$
Day 6: $0.5(25) + 0.5(24.25) = 24.625$ (5 marks: α correct 1, each EMA value 1, plus seeding logic 1)

(c) On day 5 EMA = 24.25 > SMA = 23.67. The EMA weights the most recent (rising) price 26 more heavily via $\alpha=0.5$ , whereas the SMA weights all 3 days equally, so the EMA climbs faster in an uptrend. (2)

(d) Golden cross = short MA crosses above long MA (bullish); death cross = short crosses below long (bearish). Long pairs (50/200) smooth out noise so signals are more reliable and less prone to whipsaws than 3-day averages. (2)

Question 2 (12)

(a) Gains: +2, +3, +2 → sum 7. Losses: 1, 1 → sum 2. Average gain = $7/5 = 1.4$ ; average loss = $2/5 = 0.4$ . $RS = 1.4/0.4 = 3.5$ . $RSI = 100 - \frac{100}{1+3.5} = 100 - 22.22 = 77.78$ . (5 marks: avg gain 1, avg loss 1, RS 1, RSI formula+value 2)

(b) Overbought > 70, oversold < 30. RSI ≈ 77.8 → overbought. (2)

(c) Bearish divergence: price makes a higher high while RSI makes a lower high. Momentum weakens even as price rises, warning of a potential reversal down. (3: definition 2, description 1)

(d) Wrong: RSI 45 is neutral (mid-range), not oversold (<30). The trader has misapplied the threshold; 45 gives no buy signal. (2)

Question 3 (14)

(a) MACD = 12-EMA − 26-EMA = $51.2 - 49.8 = 1.4$ . (2)

(b) Histogram = MACD − Signal = $1.4 - 1.1 = 0.3$ . Positive → bullish momentum. Previous histogram 0.8 > 0.3, so bullish momentum is weakening (histogram shrinking). (4: value 2, bullish 1, weakening 1)

(c) Upper = $100 + 2(2.5) = 105$ ; Lower = $100 - 2(2.5) = 95$ . Bandwidth = $(105-95)/100 = 10/100 = 0.10$ (10%). (4)

(d) A squeeze = bands contract (low volatility/bandwidth), signalling a period of consolidation that often precedes a large breakout. MACD can confirm direction: a bullish MACD crossover at breakout points up; a bearish crossover points down. (4: squeeze meaning 2, MACD confirmation 2)

Question 4 (12)

(a) $\%K = \frac{Close - Low}{High - Low}\times100 = \frac{56-50}{58-50}\times100 = \frac{6}{8}\times100 = 75\%$ . 75 < 80 → not overbought (neutral-to-high, approaching overbought). (4: formula 2, value 1, classification 1)

(b) ATR = $(1.2+1.6+1.0)/3 = 3.8/3 = 1.267$ . A rising ATR means increasing volatility (larger price ranges). (3)

(c) VWAP = $\frac{\sum P\cdot V}{\sum V} = \frac{10(100)+11(300)+12(100)}{100+300+100} = \frac{1000+3300+1200}{500} = \frac{5500}{500} = 11.0$ . (3)

(d) Institutions use VWAP as an execution benchmark — buying below VWAP / selling above VWAP means beating the average price and minimising market impact. (2)

Question 5 (10)

(a) OBV starts 0.

Day 1→2: 31 > 30 → +400 → OBV = 400
Day 2→3: 30 < 31 → −600 → OBV = −200
Day 3→4: 32 > 30 → +300 → OBV = 100

Final OBV = 100. (4: each step 1, direction logic)

(b) ADX 15 (< 20) → weak/no trend (ranging market). ADX 32 (> 25) → strong trend developing; trend-following strategies now favoured. (2)

(c) Price above cloud + green cloud → bullish directional bias. (2)

(d) Indicator overload = using too many indicators that give redundant/conflicting signals, causing analysis paralysis and false confidence (many are correlated). Rule: use a small set covering different dimensions (e.g. one trend + one momentum + one volume) rather than several of the same type. (2)

[
  {"claim":"Q1 day6 SMA = 25", "code":"result = ((24+26+25)/3)==25.0"},
  {"claim":"Q1 day6 EMA = 24.625", "code":"e3=21.0; e4=0.5*24+0.5*e3; e5=0.5*26+0.5*e4; e6=0.5*25+0.5*e5; result = abs(e6-24.625)<1e-9"},
  {"claim":"Q2 RSI = 77.78", "code":"rs=(7/5)/(2/5); rsi=100-100/(1+rs); result = abs(rsi-77.7777777778)<1e-6"},
  {"claim":"Q3 bandwidth = 0.10", "code":"u=100+2*2.5; l=100-2*2.5; bw=(u-l)/100; result = abs(bw-0.10)<1e-9"},
  {"claim":"Q4 %K = 75 and VWAP = 11", "code":"k=(56-50)/(58-50)*100; v=(10*100+11*300+12*100)/(100+300+100); result = (k==75.0) and (v==11.0)"},
  {"claim":"Q5 OBV final = 100", "code":"o=0; o+=400; o-=600; o+=300; result = o==100"}
]