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