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Problem 1 Suppose it is the start of year 2 0 0 8 . You have $ 1 0 0 , 0 0 0 to

Problem 1
Suppose it is the start of year 2008. You have $100,000 to invest and decide to invest in a combina-
tion of a riskless asset (f), a stock index fund (S) and a long-term bond fund (B), with the following
properties:
The correlation of the returns on the long-term bond fund and the stock index fund is equal to 0.3.
a) If you only consider the risky assets, what is the global minimum variance portfolio? What
is the global minimum variance portfolio if you also consider the risk-free asset?
b) The tangency portfolio is 66% in fund S and 34% in fund 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 real-
ized (percentage) portfolio return for year 2008?
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