technical trends: can they be used to earn abnormal profits?
DESCRIPTION
Technical Trends: Can they be used to earn abnormal profits?. Ryan Weikert. Last Time. MACD E(profit) ≈ ½ (mu)(S 0 ) SD ≈ 2/3 (sigma)(S 0 ) RSI – Quick Trigger E(profit) ≈ 0 CCI – Quick Trigger E(profit) ≈ 0. - PowerPoint PPT PresentationTRANSCRIPT
Technical Trends: Can they be used to earn abnormal profits?
Ryan Weikert
Last Time
• MACD– E(profit) ≈ ½ (mu)(S0)
– SD ≈ 2/3 (sigma)(S0)
• RSI – Quick Trigger– E(profit) ≈ 0
• CCI – Quick Trigger– E(profit) ≈ 0
Technical Indicators applied to random walks generated using Geometric Brownian Motion will not yield abnormal returns
New Studies
• More realistic distribution• Lévy Processes• Autoregressive Models (AR & ARMA)
• Correlation between price movements and technical indicators
Historical Returns
Xbar=0.000327663s=0.009664387
Daily Return
Stable Distribution
• rstable(alpha,beta,gamma,mu)• Alpha=parameter• Beta=skewness• Gamma=scale• Mu=shift
Change Model
• Old Model– Walk[j]=walk[j-1]*(1+mu*dt+rnorm(nruns,0,s*sqrt(dt))
• New Model– walk[j]=walk[j=1]*(1+rstable(1.9,0,s*sqrt(dt)/2,mu*dt))
MACD with new Model
• Standard deviation of closing prices increases ever so slightly while mean remained constant
• Expected profit and standard deviation generated by MACD signals remain unchanged
• Slight improvement
Lévy Processes: Definition
• Starts at some origin at time t=0• Independent Increments• Stationary Increments• Right continuous with left limits
• Geometric Brownian Motion is a Lévy Process
Lévy Processes
• Randomize mu• Randomize sigma• Sigma mean reversion
Autoregressive Models
• Use previous outputs to predict the next output
• Output=Constant+Parameters+randomness(white noise)
• AutoRegressive Conditional Heteroskedasticity (ARCH) Models – variance is a function of previous period’s variance
AR Results
• E(profit) = 13.85 stderr=.0035• MACD E(profit)=6.46 stderr=.00234
• Same as before
Correlation between MACD signals and subsequent price changes
0 10 20 30 40 50
-0.1
0-0
.05
0.00
0.05
S&P Index Average Return N Days After MACD Signal
N
Per
cent
Ret
urn
0 10 20 30 40 50
-0.4
-0.2
0.0
0.2
Apple Average Return N Days After MACD Signal
N
Per
cent
Ret
urn
0 10 20 30 40 50
-0.2
0.0
0.2
0.4
0.6
0.8
US Steel Average Return N Days After MACD Signal
N
Per
cent
Ret
urn
0 10 20 30 40 50
-0.5
0.0
0.5
1.0
Google Average Return N Days After MACD Signal
N
Per
cent
Ret
urn
0 10 20 30 40 50
0.0
0.2
0.4
0.6
0.8
1.0
Windstream Average Return N Days After MACD Signal
N
Per
cent
Ret
urn
0 10 20 30 40 50
-0.3
-0.2
-0.1
0.0
0.1
0.2
Santander Average Return N Days After MACD Signal
N
Per
cent
Ret
urn
0 10 20 30 40 50
-1.0
-0.5
0.0
0.5
Dolby Average Return N Days After MACD Signal
N
Per
cent
Ret
urn
1 6 12 19 26 33 40 47 54 61 68 75 82 89 96
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
-2-1
01
2
For 1 Year Period
Beginning N Years
ago
Days after Signal
S&P 500 Returns after MACD signal
Results for S&P 500
• Long Position– E(profit) = 111.78– Stderr=2.212
• MACD Trading– E(profit)=0.28– Stderr=1.897
Can Technical Trends be used to generate abnormal returns?
• Efficient Markets• Independent increments
– Lévy Processes– Various Distributions
• In reality, day to day prices are not correlated• Indicators are lagging• Returns following a MACD signal are not
correlated to the signal
No Abnormal Returns