09portfolio_practice-2013Fall - Practice problem set...

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Practice problem set Portfolio theory and international portfolio diversification Most of the problems are from the examples in the chapters of portfolio theory or international portfolio diversification. Should you have any questions, please feel free to email me at [email protected] . Bill Hu 1. Suppose that you invested $5,000 in SPDR (the index fund for SP500) and −$1,000 in FXI (You are pessimistic on the Chinese stock market so you short sell $1000 worth of FXI shares) a year ago. Suppose further the realized return over the year for SPDR and FXI is 5% and 10%, respectively. What is the portfolio return? 2. You have $10,000 to invest equally in IBM and Merck stocks. Support that the standard deviation of monthly returns for IBM and Merck is 10% and 20%, respectively. The correlation between the two returns is 0.50. What is the expected standard deviation of the monthly return for your portfolio? 3. Consider a portfolio with $2,000 invested in the risk-free asset and $4,000 each in two risky assets, Toyota and Total. If we view the investments in Toyota and Total as a risky portfolio, what are the proportions of risk-free asset and the risky portfolio? 4. According to the capital asset pricing model (CAPM), R i = R f + β i * (R m - R f ). Apparently, this is a one factor model (i.e., y = a + b*x) with market risk premium being the factor. The
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