Problem: Suppose it is the start of year 2008. You have $100,000 to invest and decide to invest in a combination of a riskless asset (f), a stock index fund (S), and a long-term bond fund (B) with the following properties:
(a) What is the mean variance efficient portfolio (i.e. mix) of the risky assets S and B?
(b) What dollar amounts should be invested in each of the three asset classes f, S, and B if you would like to achieve (for the year 2008) an expected return of 8% with the lowest possible standard deviation? What is the standard deviation of the (percentage) return on this portfolio?
(c) For the year 2008, the realized return on f was 0.03 (3%), the realized return on B was 0.10 (10%) and the realized return on S was -0.40 (-40%). At the end of 2008, what are your dollar holdings of f, of B, and of S and how much money do you have in total? What is your realized (percentage) portfolio return for year 2008?
(d) Suppose you do not make any changes to your portfolio in the sense that you do not buy or sell any f, B or S. Assume that the numbers in the table at the start of this question apply to both 2008 and 2009.
(d-i) What will your expected return be for the coming year (i.e. year 2009)?
(d-ii) Will you still be holding an efficient portfolio for the coming year (2009) (i.e. does the portfolio have the lowest possible standard deviation for its expected return)?
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E(r)
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s
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Riskless asset (f)
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0.03 (3%)
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0
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Stock index fund (S)
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0.12
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0.19
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Long-term bond fund (B)
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0.055
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0.10
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Correlation of the returns on the long-term bond fund and the stock index fund: 0.3
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