Analysis of Technical Trends

Ryan Weikert

Asset Valuation

• Pricing, Buying, and Selling of Assets• Methods of Appraisal• What stocks, when?• Fundamental Analysis• Technical Analysis

Fundamental Analysis

• Quality• Sector/Industry• Financial Statements• Peer and Historical Comparisons• Earnings• Management• Fair Value

Technical Analysis

• Study trends and the state of the market• Behavioral Indicators• Anticipate price movements

Examples

• Support/Resistance Levels• Moving Averages and Momentum• Overbought and Oversold Signals• Buy and Sell

Is it possible to earn greater profits using pure technical analytics?

Process

• Generate Random Walks• Geometric Brownian Motion• Apply certain technical indicators to these

random walks• Generate buy and sell signals• Record asset price at the time of those signals• Calculate profit

Moving Average Convergence Divergence (MACD)

• Signals upward and downward momentum• Exponential Moving Average (EMA)

• Xi=(Pi - Xi-1)*[2/(# of periods + 1)]+Xi-1

• MACD=12 day EMA – 26 day EMA• Signal Line=9 day EMA MACD• MACD Histogram = MACD – Signal Line• Buy if MACD Histogram > 0 (upward momentum)• Sell if MACD Histogram < 0 (downward momentum)

Apple MACD Chart

MACD Results

• E(profit) ≈ ½ (mu)(S0)

• SD ≈ 2/3 (sigma)(S0)

• If mu = .08, S0 = 100, sigma=.3– E(profit)=3.95– SD = 22.15

• ½ expected profit of a long position• Only slightly less risk

• Inferior

DistributionHistogram of profvec

profvec

Frequency

-50 0 50 100 150

0500

1000

1500

2000

2500

3000

3500

Relative Strength Index (RSI)

• Overbought and Oversold signals• RSI = 100 – 100/(1+Relative Strength)• Relative Strength = Average Gain/Average Loss• Agi = [Agi-1 * 13 + current gain] / 14

• 0<RSI<100• Oversold if RSI <30 Buy• Overbought if RSI >70 Sell

BBVA RSI Chart

RSI Results – Perfect Timing

S0 100 100 100 100mu 0.08 0.04 -0.02 0.08sigma 0.3 0.3 0.3 0.1mean 29.08 29.17 28.63 9.28sd 21.37 20.97 20.64 7.42lb 28.66 28.66 28.23 9.13ub 29.50 29.50 29.04 9.43

E(profit) ≈ sigma* S0

DistributionHistogram of profit

profit

Frequency

-50 0 50 100 150

0500

1000

1500

RSI Results – Quick Trigger

E(profit) ≈ 0

S0 100 100 100 100mu 0.08 0.02 -0.02 0.08sigma 0.3 0.3 0.3 0.1mean -1.32 -0.02 0.23 -2.68sd 25.69 23.68 22.46 9.836lb -1.83 -0.48 -0.20 -2.87ub -0.82 0.44 0.67 -2.49

Distribution

Histogram of profit

profit

Frequency

-200 -150 -100 -50 0 50

01000

2000

3000

4000

Overall RSI Results

• Further technical analysis would be required• Impossible to receive returns of Perfect

Investor– If it were possible, technical indicators wouldn’t be

needed• Expected profit won’t be as high• Closer to 0

Commodity Channel Index (CCI)

• Overbought and Oversold signals• CCI = (Typical Price – 20 day SMA of TP) (.015 * Mean Deviation)TP = (High + Low + Close)/3

Overbought if CCI > 100 SellOversold if CCI < -100 Buy

Apple CCI Chart

Results

• Similar to RSI

• Perfect Timing– E(profit) ≈ 2*sigma*S0

– SD ≈ 2/3 * sigma• Quick Trigger– E(profit) ≈ 0– SD ≈ 2/3 * sigma

Histogram of profit

profit

Frequency

-150 -100 -50 0 50 100

01000

2000

3000

Histogram of profit

profit

Frequency

0 50 100 150 200 250

01000

2000

3000

4000

CCI Conclusion

• Still impossible to attain perfect timing• Expected profit likely to be closer to 0

Conclusion

• Technical analysis• Geometric Brownian Motion• Not useful

Upcoming

• What must be true for these indicators to yield a statistically significant profit?

• Other Distributions– How are real world returns distributed?– How do they vary in different situations?

• Other Processes– Autoregressive process– Lévy Process

• Applied to actual graphs

Questions?