Investment Analysis and Portfolio Management Homework
PART I - The monthly return data for the following 3 stocksare given bellow. Use them to answer the following questions. The risk-free interest rate is 3.25% p.a.
|
Month
|
Poly Real Estate
|
Kweichow Moutai
|
China Construction Bank
|
|
2012-01
|
0.05
|
-0.035644
|
0.050661
|
|
2012-02
|
0.057143
|
0.09683
|
0.023061
|
|
2012-03
|
0.017117
|
-0.036682
|
-0.010246
|
|
2012-04
|
0.10806
|
0.14013
|
-0.008282
|
|
2012-05
|
0.090328
|
0.053972
|
-0.06263
|
|
2012-06
|
0.012562
|
0.010436
|
-0.012165
|
|
2012-07
|
0.005291
|
0.046849
|
-0.054762
|
|
2012-08
|
-0.174561
|
-0.108262
|
0.012594
|
|
2012-09
|
0.143464
|
0.118493
|
-0.00995
|
|
2012-10
|
0.032528
|
0.006265
|
0.037688
|
|
2012-11
|
0.032403
|
-0.126668
|
0.009685
|
|
2012-12
|
0.185702
|
-0.03236
|
0.103118
|
1. Estimate annualized expected return and variance for each stock from historical return data.
2. Calculate the correlation coefficients between those stocks.
3. Use the results from above 2 questions, construct and calculate annualized expected returns and variances for portfolios constructed using Moutai&Poly according to following methodology:
(1) Naïve diversification (equally-weighted portfolio)
(2) Minimal variance portfolio (*for this problem, you also need to calculate the weight for each stock)
(3) Write down the mathematical expression for efficient frontier (*short sell is allowed, expressed in terms of variance and portfolio raw return (not excess return)), draw efficient frontier and locate the two portfolios above on the curve.
(4) Find the portfolio with highest sharpe ratio on the efficient frontier. Calculate expected return, variance and sharpe ratio of this portfolio.
4. Now by adding the China Construction Bank, construct and calculate annualized expected returns and variances for portfolios constructed by all 3 stocks according to following methodology:
(1) Naïve diversification (equally-weighted portfolio)
(2) Minimal variance portfolio (*for this problem, also calculate the weight for each stock)
(3) Write down the expression for efficient frontier (*short sell is allowed, expressed in terms of variance and portfolio raw return (not excess return)), draw efficient frontier on previous efficient frontier figure and locate above 3 stocks within feasible region.
(4) Compare two efficient frontiers, what can you conclude?
PART II - Please write a letter to Chairman of China Securities Regulatory Commission, to provide some suggestion in terms of the Registration System of IPO and the Examination and Approval System of IPO in China.
"The most important argument in finance is whether the financial market is efficient." Please express your opinions about this question.