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Datasets:
? UK US bond stock.xlsx
? hedging.xlsx
? monthly stocks.xlsx
available on CANVAS
Exercise 1 In the file hedging.xlsx there are data on cash and future
oil price contracts. The data are expressed in daily returns. Suppose that
the conditional mean of each series can be modelled as a univariate AR(1)
process. Using a CCC-GARCH(1,1) model, evaluate optimal hedging ratios
for the following risk aversion parameter values:
λ = ∞
λ = 10
λ = 4
Compare the results with the ones you would obtain by using a diagonal
BEKK model and a DCC model. Compare also with the results obtained by
assuming a constant conditional variance covariance matrix.
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October 8 2022
Exercise 2 The file indices.xlsx, Sheet2 contains excess returns on
many stock indexes (the series with names starting with ’ms) and bond in dexes
1. Estimate the efficient frontier using all the assets included in the dataset.
2. Verify the hypothesis that the stock indexes for US, UK, JP and DE
(Germany) are sufficient to generate the efficient frontier.
3. Verify the hypothesist that a balanced stock-bond portfolio is efficient.
Exercise 3 The file monthly stocks.xlsx contain data on returns for 18
US companies and some other useful series. Choose a subset of 12 of the 18
asset returns contained in the file and use them to estimate a static CAPM
model. Test the validity of the CAPM model equation by equation. Com ment the results. Test the validity of the CAPM model by using the multi variate model. Construct all the possible tests and comment the results.
Exercise 4 Choose a subset of 5 from the asset returns contained in the file
and use them to estimate a static CAPM model in its version due to Black.
Test the validity of this version of the CAPM model by using the multivariate
model. Construct all the possible tests and comment the results.
Exercise 5 Prove that the estimation strategy of Black’s CAPM model
described at the end of TN08 and in TN10 is appropriate (verify the validity
of the formulae used in the recursive estimation strategy).
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