1. www.themegallery.com LOGO Time Series technical analysis via new fast estimation methods Yan Jungang A0075380E Huang Zhaokun A0075386U Bai Ning A0075461E Yan Jungang A0075380E Huang Zhaokun A0075386U Bai Ning A0075461E

2. Contents Introduction Technical analysis Trading strategies Presentation

3.  Fundamental Approach based on a wide range of data regarded as fundamental economic variables that determine exchange rates Forecast foreign exchange rates

4. Steps of fundamental approach 1. starts with a model 2. collects data to estimate the forecasting equation 3. generation of forecasts 4. evaluation of the forecast Fundamental Approach

5. Trading Signal 1. significant difference between the expected foreign exchange rate and the actual rate 2. a mispricing or a heightened risk premium 3. a buy or sell signal is generated Fundamental Approach

6.  Technical Approach does not rely on a fundamental analysis of the underlying economic determinants of exchange rates or asset prices, but only on extrapolations of past price trends Forecast foreign exchange rates

7. Steps of technical approach 1. recognize the type of trend the market is 2. a level of support 3. form trend lines Technical Approach

8. Models 1. Autocorrelations 2. MA model 3. GARCH model Technical Approach

9.  in-sample: works within the sample at hand  out-of-sample works outside the sample Two kinds of forecasts:

10.  where is the trendline which satisfies the above linear equation  is the mismatch between the real data and the trendline Linear difference equations

11. Thus we only assume that Linear difference equations

12. From equation (4) that also satisfies (5) and (6). Hence, the finite linear combinations of i.i.d. zero-mean process, do satisfy almost surely such a weak assumption.  Our analysis  Does not make any difference between non- stationary and stationary time series Linear difference equations

13. Consider again Equation (1). The Z-transform X of x satisfies where Rational generating functions

14. We introduce the Wronskian matrix Parameter identifiability

15. The unknown linearly identificable parameters can be solved by the matrix linear equation Parameter identifiability

16. Methodology  Data Analysis  Model Setup  Example: US Dollar/Euros Exchange Rate

17. Sample data: US Dollar – € uros Time interval: 1999-01-04 to 2011-03-11 The data can be downloaded from here: http://www.ecb.int/stats/exchange/eurofxref/html/index.en.html Data Analysis

18.  volatility clusters  volatility evolves over time in a continuous manner  volatility varies within some fixed range  leverage effect

19. Data Analysis Stylized-facts of financial return series The {r t 2 } is highly correlated The changes in { r t } tend to be clustered. { r t } is heavy tailed stylized-facts of financial return series

20. Data Analysis: Clustered daily returns of exchange rate daily exchange rate

21. Data Analysis: Data Analysis: Correlation {X t } {X t 2 } The log returns are independent The square of log returns are highly correlated. H0: H1: for some.

22. Data Analysis Data Analysis : Heavy tail Density function of exchange rate Normal-QQ plot

23. Model Setup  GARCH Model

24. Model Setup  Forecast of GARCH Model.

25. Example: US Dollar/Euros Exchange Rate EstimateStd. Errort-valuePr( >|t| ) μ7.365e-054.584e-051.6070.1081 α0α03.136e-081.334e-082.3500.0188 α1α13.147e-024.240e-037.4211.16e-13 β1β19.651e-014.583e-03210.588<2e-16. Estimate of Std. Errors are based on Hessian. Significance at 1, 5, 10 percent are indicated by (***), (**), (*).

26. Example: US Dollar/Euros Exchange Rate Residuals Tests The Ljung-Box Test are performed for standardized residuals and squared standardized residuals respectively

27. Trading strategy Simulate data (ACF) ACF of historical return ACF of simulated return Green:| r t | Red: r t ^2 Blue: r t

28. Trading strategy  Take the 10-day historical volatility (HV) reading.  Take the 50-day historical volatility (HV) reading. If (VAR(10) < 0.5*VAR(50)) Display(“a big move is likely near !”)

29. Trading strategy Using historical data to test: If(VAR(+n)>VAR(-10)) The strategy is efficient VAR(-10):volatility between trading signal and10 days before the trading signal VAR(+n):volatility between trading signal and n days after the trading signal

30. Trading strategy n VAR(+n) > VAR(-10) 10.4194 20.5161 30.6419 40.7161 50.7548 60.7871 70.8161 80.8419 90.8484 100.8581

31. Trading strategy Make an assumption: when we face the trading signal :  exchange our US dollar to Euro dollar at current time t.  exchange Euro dollar back to US dollar n days after. By using the historical 3024 days’ exchange rate data, the program gave us 310 trading signals.

32. Trading strategy nProbability of making profit 10.4645 2 30.4484 40.4677 50.4806 6 70.5065 80.4968 90.5161 100.4935 110.5129 120.5290 130.5484 140.5290 150.5355

33. Trading strategy Property of GARCH: Large shocks tend to be followed by another large shock; Small shocks tend to be followed by another small shock. Trading signal Market will volatile in next days

34. Trading strategy Problems we faced by now Know some significance moves are about to take place. Not sure what the direction will turn out to be. using STRADDLE or STRANGLESTRADDLESTRANGLE

35. Trading strategy Straddle: purchase the same number of call and put options at the same strike price with the same expiration date. Strangle: purchase the same number of call and put options at different strike prices with the same expiration date.

36. Trading strategy Steps of trading: Straddle :  Buy an ATM (At-The-Money) Put  Buy an ATM Call Strangle:  Buy an OTM (Out-The-Money) Put  Buy an OTM Call

37. Trading strategy Risk and Reward :  The maximum risk of a Straddle/ Strangle is equal to the amount that you paid for the two option contracts. If the stock moves nowhere, and volatility drops to nothing, you lose.  The reward is that same as for calls and puts - unlimited.

38. Trading strategy Tricks to buy the straddle/ strangle  Buy options while volatility is relatively slow  Sell as volatility increase either just before a news report or soon after.

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