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日期:2020-01-29 08:53

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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