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Alternative investments and optimal portfolios

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  • Alternative investments and optimal portfolios

    Hi everybody
    I wonder if anyone could help me out in solving the case. I've not attached the data and teh excel sheet that is mentioned in teh problems cuz i just need the help in how to approach and solve these and then i will myself solve the cases


    Open the file alternatives.xls. This file contains the returns on a Hedge Fund index (HFR), an emerging markets index (Morgan Stanley Emerging Markets MSEM), a bond index (Salomon Brothers World Government Bonds SBWGU), and the market, Fama-French, and Carhart factors. The latter for are already excess returns.

    Question 1.
    Some people in the industry claim that hedge funds cannot be explained well by traditional style factors. This would make them an ideal investment category for large institutional investors.
    Compute the correlation of the HFR index with the other asset categories and comment on your findings.
    Also perform a so-called style regression, where you regress the HFR excess returns on a constant term and the excess returns on all of the other available investment factors. Interpret the result.
    Is the claim of industry people warranted?
    [Tip: convert the non-excess returns into excess returns first.]

    Question 2.
    A crucial issue when discussing covariances and correlations (or regression parameters) is whether these are stable over time. If they are stable, you can use them for assessing future return and risk. If they are not stable, then this cannot be done.
    You now have to check the stability of your regression estimates above. To do this, you need to compute your regression coefficients for every month starting from Dec 1998, using the past 60 months of data. (So Jan 1994-Dec 1998, then Feb 1994-Jan 1999, …)
    Make a graph with the resulting coefficients, indicating which coefficients are significant, and which are not.
    Tip 1: work extensively with the ''''' functions (so ctrl-shift-enter) LINEST and INDEX in excel. Also for question 3. See also Note that LINEST(Y,X,TRUE,TRUE) gives an ''''' back with top line the coefficients (regressor 1,2,…,constant term), and second line the standard errors of the coefficients. So INDEX(LINEST(Y,X,TRUE,TRUE),1,1) gives the coefficient of the first regressor, while INDEX(LINEST(Y,X,TRUE,TRUE),2,3) gives the standard error of the 3rd regressor.
    Tip 2: for the graph, you can plot the coefficients as a line plot with two curves. The first curve contains the coefficients and is depicted with a line (no marks). The second curve contains the coefficients if they are significant, and #N/A otherwise (and is plotted with marks only, no lines). You can use IF statements for this. Work at a 5% two-sided testing level. In this way you get the plot for the value of the coefficients, and with symbols on top if the coefficient is significant for that estimation window.

    Question 3.
    Also make a graph of the rolling R2. Interpret your graphs from question 2 and 3 and comment on your findings. [R2 is also an output of LINEST; find out yourself which element.]

    [Note that you can use the methodology in Question 2 for excel also to easily generate beta’s in a Fama-McBeth type methodology (see chapter 8 of CN).]

    Question 4.
    Carry out an MV optimization using Rf (set at 0.15%), SBWGU, SMB, HML, UMD, and Rm only. You are NOT allowed to take short positions in any of these categories [which is, acknowledged, a bit artificial in this context].
    Show that the composition of the risky part of your portfolio remains identical for different values for the minimum required expected return. Use the three different values for the minimum required expected return of 0.2%, 0.4%, and 0.6%.
    Tip: use the Solver from Excel. You should find it under Tools. If it is not there, switch it on by clicking Tools  Add Ins  Check Solver  OK. Now you should find it under the Tools menu.
    Tip 2: a covariance matrix is easily computed using the data analysis Add-In or using the function COVAR in combination with the functions INDEX, ROW, and COLUMN.

    Question 5.
    Now include the alternatives MSEM and HFR to recompute question 4 (again using the expected returns from question 4 as the lower bound on expected return). Interpret the results and give a brief advice on: (i) diversification benefits of alternative investments; (ii) advised asset allocations; (iii) further analyses required before your advice should really be implemented.