﻿ Arbitrage代写 Arbitrage Trading代写 Backtesting techniques代写

# Arbitrage代写 Arbitrage Trading代写 Backtesting techniques代写

2020-10-11 13:38 星期日 所属： 作业代写 浏览：3 ## Arbitrage Trading on Cointegration withBacktest

Arbitrage代写 The aim here is the estimation and analysis of an arbitrage relationship between two or more financial time series.

### Summary Arbitrage代写

The aim here is the estimation and analysis of an arbitrage relationship between two or  more financial time series. Identifying and backtesting a robust cointegrated relationship means exposing a factor that drives two (several) asset prices. The factor is traded by entering a long- short position given by cointegrating weights.

Through implementation you will have a hands-on experience with model-free multivariate regression with Vector Autoregression (for returns) and Error Correction (for price levels). The task is not to perform econometric forecasting. Backtesting techniques and recipes are spe-  cific to systematic strategy selected. This topic focuses on generating an optimal trading signal from mean-reversion strategy. Cointegrating factor discussed above is represented by a mean- reverting spread, for trading on which optimal bounds can be computed.Arbitrage代写

A successful project requires coding from the first principles: matrix form regression esti- mation, Engle-Granger Procedure (or Johansen  Procedure),  ADF  test  for  stationarity.  After the cointegrated (mean-reverting) relationship estimated, ready optimisation and backtesting libraries can be used.4

A project that solely runs pre-programmed statistical tests and procedures on data is insufficient.

### Signal Generation and Backtesting Arbitrage代写

• Searchfor inventive applications of cointegration beyond equity  Consider commodity futures, interest rates, and aggregated indices.
• The strategy is realised by using cointegrating coefficients ØCoint as allocations w. That creates a long-short portfolio that generates a mean-reverting spread. All project designs should include optimal trading signal generation and backtesting. Present optimisation results for entry/exit
• Does cumulative P&L behave as expected  for  a  cointegration  trade?  Is  P&L  coming  from a few or many trades, what is half-life? Maximum Drawdown and behaviour of volatility/VaR?
• Common backtest is done by computing the rolling SR and beta against S&P500 and three factors (returns from value, momentum, and small cap strategies). Use a ready software library, such as pyfolio in

4Use the environment with facilities for matrix and time series manipulation (R, Matlab) or code in Python/C++ with the use of quant libraries. VBA will be cumbersome for time series analysis.Arbitrage代写

#### Step-by-Step Instructions Arbitrage代写

A starting source for historical daily close prices of US equities and ETFs is Yahoo!Finance. Today’s environments have libraries to access Quandl, Bloomberg, Reuters and others.

#### ‘Learning’ and Cointegration in Pairs

An understanding-level design can use the ready specification tests, but matrix form regres-  sion estimation must be re-coded. The project can rely on the Engle-Granger procedure for cointegration testing among pairs but multivariate exploration is encouraged.Arbitrage代写

1. Implement concise matrix form estimation for multivariate regression and conduct model specification tests for (a) identifying optimal lag p with AIC BIC tests and (b) stability  check with eigenvectors of the autoregression system. Here, it is choice whether to code thesetests or use ready
2. Implement Engle-Granger procedure and explore several cointegrated pairs. Estimate relationships both ways to select the appropriate lead variable.  ADF test for unit root  must be coded and
3. Ensurerobust estimation: one recipe to do so is to shift time window (2-3 months shift) and apply LR testing for di↵erence in time series’ means between  As an alternative, develop  the  adaptive  estimation  of  cointegrating coefficients  YtØC0  oint et.
4. Decide on strategy trading rules (common approach is to enter on bounds, exit on ettouch- ing the mean value µe). Use optimisation to compute optimal bounds Zoptoeq. Produce appropriate plots for Drawdown, Rolling SR and backtesting against factors for the P&L. oeq, speed of mean-reversion, and half-life between trades are obtained by fitting of et to the OU

#### OPTIONAL Multivariate Cointegration

It is recommended to validate results for Johansen Procedure against existing R/Matlab libraries. Efficient implementation steps for the procedure are outlined in Jang & Osaki (2001).Arbitrage代写

New 2. Apply Maximum Likelihood Estimation (Johansen Procedure) for multivariate cointegra- tion on prices data. Test specification will involve the in-calibrated constant trend inside the cointegrating residual et—1 in the OYt error-correction equation.

There are five possible kinds of deterministic trend in et—1, however rarely utilised in practice because that leads to overfitting of cointegrated relation to particular sample. Particularly for time-dependent trend (ie, do not make your time series function of time   as an independent variable of regression).Arbitrage代写

Present analysis for Maximum Eigenvalue and Trace statistical tests, both are based on Likelihood Ratio principle, on how you decided the number of cointegrated relationships. 