这个作业是通过研究比较和评估绩效的不同方法来分析四支美国共同基金的收益
Investment and Portfolio Theory 2 (6012B0234Y)
Assignment 1: Performance Evaluation and
International Diversification
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IPT2 – Group Assignment 1
Assignment policies:
1. The assignment consists of two parts (two questions with multiple sub-questions). The total
number of points on all parts is 100.
2. The solution should be typed; handwritten solutions will not be accepted. All pages should be
stapled together. Use Word’s formula editor to type formulas/calculations when needed. The
grader can deduct points from the total if it is hard for him to understand your solutions.
3. Groups should be of size 5-6 people (members can be from different workgroups/tutorials).
Add all the names before handing in – no late addition of names.
4. Show at least the formulae that you use as well as some part of the solution path and don’t
just write down only the final solutions so that the grader understands how you obtained
your result. (This may also help with partial points, if applicable.)
5. We recommend working with Excel to solve questions and to verify your results. When asked
to provide an Excel chart, make sure that the grader can read the axes’ units and is able to
determine that you have not just a similar answer but indeed the right answer.
6. Provide any dollar values with two digits after the decimal (so, e.g., $1234.56). For returns
give 5 digits after the decimal, so 12.345% or 0.12345. Other values (e.g., Sharpe ratio,
Information ratio, etc.) provide 3 digits after the decimal, so for example 1.234.
7. The deadline for this assignment is Friday, 24 April, 17:00.
8. Note that this assignment is going to take a considerable amount of time – please do not start
just one week before its due. This is on purpose in order to have you practice, work with
Excel, and to work in groups. Solving this assignment should therefore be considered part of
general study time and not just time spent on an assignment.
9. This is a take-home group assignment. This means that you are not allowed to discuss the
solutions across groups, but each group should solve the assignment by itself.
10. You should hand in your assignment through Canvas. We cannot accept submissions by email.
Good luck!
Aleksandar Andonov
QUESTION 1: PERFORMANCE EVALUATION (60 points)
This question studies the different ways to compare and evaluate performance. The excel file “Part 1
– Performance Evaluation Data” reports the returns of four U.S. mutual funds. The return data is on
a monthly frequency and it covers the period from January 2000 to December 2019. You need to
evaluate the performance of these four mutual funds during the entire sample period. Please
calculate and compare the performance measures listed below for all four mutual funds. You should
report all performance measures in one table to make the comparison easier.
a) Sharpe ratio. (4p)
b) M2 measure. (4p)
c) Treynor measure. (4p)
d) T2 measure. (4p)
e) Information ratio. (4p)
f) Please discuss the results. What can you conclude from the performance measures? (5p)
You need to annualize the Sharpe ratio, M2 measure, Treynor ratio, and T2 measure. You do NOT need
to annualize the Information ratio.
Advice: If the average monthly return is 0.01, or 1%, the annualized average monthly return is 0.01
× 12 (Note that this ignores compounding. To account for compounding, you would do, 1.0112 – 1. For
this project, it is okay to ignore compounding and annualize by simply multiplying the monthly
returns by 12.) If the standard deviation of monthly stock returns is 0.045, or 4.55%, the annualized
standard deviation is 4.55% × 120.5, or 15.76%.
The excel file “Part 1 – Performance Evaluation Data” provides also data on several time-series of
returns. First, it reports the return on the market index (Mkt). Second, it reports the return on SMB
(small-minus-big) factor, HML (value-minus-growth) factor, and MOM (winners-minus-losers)
factor. Third, it presents the risk-free rate of return (RF). Using these data, please calculate the alpha
potential and the factor exposure of the four mutual funds. Use regressions for your analysis and
report all coefficients.
Advice: For every mutual fund and for the market factor please calculate excess returns. The other
factors, SMB, HML and MOM, are already expressed as differences in returns between two portfolios
so you do not need to calculate excess returns on them.
g) Alpha and beta from CAPM. (5p)
h) Alpha and beta coefficients from Fama-French three factor model. (10p)
i) Alpha and beta coefficients from Fama-French-Carhart four factor model. (10p)
j) Please discuss the results. What can you conclude from the regression estimations? (10p)
QUESTION 2: INTERNATIONAL DIVERSIFICATION (40 points)
This question asks you to demonstrate the potential benefits of international diversification to a
small U.S. based pension fund. The U.S. public pension fund currently invests only in U.S. equities and
wants to gain exposure also to foreign equities. However, the pension plan is quite small and cannot
start investing in all international market at this moment. The pension plan needs to decide whether
to diversify internationally their equity exposure by investing in European equity markets or by
investing in Far East Australasian markets. They cannot go into both regions at the same time, so they
need to choose one region. Please give a recommendation at the end of your answer.
The pension plan can gain exposure to the following five European markets in addition to its
exposure to U.S. equities: Denmark, Finland, Ireland, Switzerland, and UK. Alternatively, the pension
plan can gain exposure to the following five Far East Australasian markets in addition to its exposure
to U.S. equities: Australia, Hong Kong, Japan, New Zealand, and Singapore.
The excel file “Part 2 – International Diversification Data” reports the returns on these ten
international equity markets and the U.S. equity market. The return data is on a monthly frequency
and covers the period from January 2000 to December 2019. All returns are reported in US dollars,
so you do not need to convert them. Since, you are looking at international diversification from a
perspective of U.S. client, you can apply the U.S. risk-free rate to all countries and equity returns.
a) Compute the average monthly return and its standard deviation for each country over the
entire sample period. Note that you should annualize the average monthly returns and the
standard deviation of the monthly returns (see Q1 for the annualization example). Finally,
based on the annualized figures, you should compute the Sharpe ratio for each country. (6p)
Next, analyze whether the US-based pension fund is better off by diversifying across European
countries or across Australasian countries. U.S. equities are also one of the potential assets in both
cases, so include them in the potential set of assets. In your analysis, please identify the following four
international portfolios where the country returns are the underlying assets:
Portfolio 1: Equally weighted across all countries.
Portfolio 2: Tangency portfolio.
Portfolio 3: Tangency portfolio without short positions.
Portfolio 4: Global minimum variance portfolio.
b) Report in a table (i) the country weights in each of the international portfolios, (ii) the mean
return, (iii) standard deviation and (iv) Sharpe ratio. Report separately the statistics for the
international portfolios with U.S. plus European countries and the international portfolios
with U.S. plus Far East Australasian countries. Thus, you should have in total eight
international portfolios. (24p)
c) Compare and discuss the results. (10p)
o Which of the eight international strategies performs best? Is that surprising? Explain
why or why not.
o Are the portfolio weights reasonable? Explain. What is the impact of short sales
constraints?
o What would be your recommendation to the U.S. public pension fund? Which region
delivers better diversification opportunities? Should it diversify across European or
Far East Australasian countries? Discuss and explain.
o Are there any important limitations of the analysis that would affect the conclusions?
You can include other important comments or observations in your answer as well.