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

In submitting this team project or assignment for grading, we confirm:

– That the work is original and due credit is given to others where appropriate.

– That all members have contributed substantially and proportionally to each group

assignment.

– That all members are familiar with the entire content of the group assignment and

able to sign on them as original work.

– Acceptance and acknowledgement that the team is collectively responsible for

assignments found to be plagiarized in any way, and every member will be subject to

sanctions under the University’s Code of Behavior on Academic Matters.

Each group member must write their full name and student number and sign below to

indicate that they have read and abide by the statements above. Please use the fill and sign

function in pdf to write your names and merge this document with your assignment.

Name: Student number:

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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.