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These elements are necessary:
1. The PDF file (results, graphics and comments)
2. The EXCEL sheet containing the data and calculations
3. The GRETL program. inp file used
Exercice 1
Download the history of 3 ETFs of your choice and the benchmark from
the Yahoo Finance site corresponding.
You will use weekly quotes, over the longest common period.
You can choose from the ETFs in the following table, but this list is not
exhaustive.
List of smart beta ETFs (and corresponding benchmarks)
Strategy Europe (in euro) USA (in dollar)
Multi-factor SMRT.PA Amundi VTV Vanguard
Momentum CEU.PA Amundi PDP Invesco
Dividend CD9.PA Amundi IDV Ishare International
Value CV9.PA Amundi IVE Ishare International
Size CEM.PA Amundi SIZE Ishare International
Minimum Volatility MVAE.PA Lyxor LGLV State street global Advisory
Equal weight S6EW.L Ossian RSP Invesco
Rafi REU.PA Lyxor PRF Invesco
Growth CG9.PA Amundi IWF Ishare International
Benchmark SX5E (Eurostoxx 50) GSPC (SP500)
a. Present in a few lines the characteristics of the selected ETFs
b. Graphically represent the evolution of the value of your ETFs and the
corresponding benchmark, by normalizing the initial value to 100
euros (or $ in the US case).
c. Calculate descriptive yield statistics. Comment on the results.
Exercise 2
a. Give the interpretation of the estimated alpha and beta.
b. Analyze the breakdown of portfolio risk between market risk and nondiversifiable
risk
c. Calculate the Treynor ratio, the information ratios (IR1 and IR2), the
modified Jensen alpha.
e. Check the “illiquidity” hypothesis (model with delays) and calculate
the appropriate beta
f. Estimate Jensen's equation for your portfolio based on a simple
GARCH (1,1) model.
Exercise 3
a. Estimate the equations:
- of Treynor and of Mazuy
- of Henriksson and of Merton from your portfolio.
b. Estimate the variable beta model using:
- the Kalman filter
- the GARCH-multivariate model (MGARCH)
Exercise 4
Calculate:
- Sharpe ratio
- Sharpe ratio corrected for autocorrelation (to order 1)
- the adjusted Sharpe ratio (Pézier and White, 2008)
- Roy's ratio, giving you a minimum return of 3% annually.
- the Sharpe-VaR ratio (the value at risk will be calculated by the method
of your choice)
- Sortino ratio

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