Financial engineering assignment: CTA Fund

Résumé du document

From the prices of the seven futures markets, we explore various ways of engineering the performance measurement and market and operational risk management for the Commodity Trading Advisor or the CTA fund. We assume a portfolio account size of $200 000. From trading limits, the portfolio is equally weighted with margins ($82.5K). The margin to equity is therefore equal to 41.25%. We forecast positions, either long (+1) or short (-1), for each day and for the other instruments by applying a 30-day moving average. If the price is superior to the moving average, we buy and if not we sell. We assume no trading costs, no reinvestment of profits and a risk free rate of 3%. We present more details of these transactions in this document.

Extraits

[...] The F = / - equal to and 1.31 is more than the critical value Fc = 2.30 for CTA and WCM but less than HFS. Hence, we can reject the null and we are confident that the volatility of CS is different from CTA and WCM but we fail to reject the null for HFS. In the same way, the null is H0: ( and the alternative is H1: [...]

[...] Even if CS has high return, it has also high drawdown risk. We can rank the funds with this risk-adjusted performance: CS, WCM, HFS and CTA . Assignment 5 We recommend the minimum funding level of the fund over a yearly horizon with a probability of a margin call at risk by using two methods: the Monte Carlo simulation and the global Cornish-Fisher approach Monte Carlo method We simulate 10,000 iterations assuming a Gaussian distribution of returns. The estimates are for the mean $190,000 and the standard deviation $50,000 and so the VaR is $190,000. [...]

[...] The t = / SE - respectively equal to for CS CTA WCM 8.99 and HFS 10.05 - is in all cases largely more than the rejection point t = 2.701 so we can reject the null hypothesis. Thus, we are confident that the mean is different from zero. In the same way, we test that the mean is superior to for every fund with the same level of significance. The null is H0: ( ( and the alternative is H1: ( > 3%. [...]

[...] The Z statistic is Z = / with ( = 1/n equal to and 4.20 is more than the critical value z = As a result, we reject the null and conclude that the risk-adjusted performance is not equal and that CS over performs CTA, WCM and HFS. Assignment 4 We can simulate various performance metrics for each instrument and fund, particularly the Sortino, Omega and Calmar Ratios. Indeed, the Sharpe Ratio measure the risk thanks to the volatility and assumes a normal distribution of returns. [...]

[...] The null H0 is: ( and the alternative H1 is: ( (2. The degrees of freedom are the same and the t - and 3.96 is more than the critical value t1%,df equal to and So we can reject the null and we are confident that the performance of the CS is more than the returns of the other funds. If we consider that the returns are dependent, we perform a paired comparison test. The null is H0: = 0 and the alternative is H1: ( 0. [...]