notion of risk and return

notion of risk and return

Instructions/Descriptions

notion of risk and return

PAPER REQUIREMENTS

INTERNATIONAL PORTFOLIO INVESTMENT DUE: December 9, 2019

Length: Three page executive summary plus graphs and data from spreadsheet in an Appendix.

Paper focus: Analyze the feasibility of international portfolio diversification. Would you diversify internationally? Examine the lowest risk portfolio and the notion of risk and return. Calculate the Sharpe performance measure for each market examined.

GRADING CRITERIA

The papers will be graded on a number of criteria. Among these are:

1. Content: complete set of references are important.
2. Logical progression: see Writing Guide.
3. Presentation of the tables, figures, and data. They should be presented in a professional manner. See Writing Guide!
4. Writing style and whether the writing guidelines were met.

DIRECTIONS

Your paper should have an introduction, literature review, body and results, and conclusion. You should take your paper and instructions to the Writing Center before you submit your paper.

Introduction

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Your introduction should include the following:

1. Importance of international diversification to a domestic portfolio.
2. Potential impact of risk and return to a domestic portfolio.
3. Explain what you will do in the rest of the paper.

Literature Review:

Use the library’s sources to summarize academic research into international diversification. Benefits and costs of international diversification should be addressed.

Body and Results:

The following should be addressed:

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1. What data sources did you use?
2. Discuss the correlations between your stock market, the U.S. stock market, and the exchange rate.
3. Discuss the Sharpe index and for your country and the U.S. market.
4. Discuss the graph for your efficient frontier. Details are shown below.
5. How do your result compare with your literature review?

Graph Construction:

Create a graph between the standard deviation (risk) and return of an international portfolio consisting of the U.S. (S&P 500) and your country’s index adjusted for the exchange rate (U.S. dollar returns).

Use the following equations:

Equation 1: rp = arUS + (1-a)rEAFE

where r = average rate of return on equity over the period;

p = portfolio;

a = weight (0, 0.1, 0.2, 0.3, …, 1) These weights change in ten percent increments, so there are eleven combinations to compute for the risk and return that can be graphed.

Equation 2: sp = [a2s2US + (1-a)2s2EAFE + 2a(1-a)sUSsEAFEsUS,EAFE]½

s2 = variance

s = standard deviation;

sUS,EAFE = correlation between the two markets.

The variance is a measure of dispersion expressed in squared deviations. It is the average squared deviation from the mean, or on average how far away are observations from the mean.

The standard deviation also describes dispersion and is the square root of the variance. An important difference is that it is measured in the same units as the data.

The portfolio standard deviation is the standard deviation of the U.S. market, the standard deviation of the EAFE, and how the two are related.

Correlation measures how strongly two variables are related. The correlation coefficient can range in value from 1 to -1. If the correlation coefficient is high, then the benefits to international diversification are low. As long as the correlation between the two markets is not perfect, then there are benefits from international diversification.

Data:

The data you created is a daily index. You will need to create a daily rate of return by the following:

(It+1 – It)/It * 100

For example:

If your index in August 26, 2019 was 1,233.06 and 1187.54 in August 27, 2019, then the rate of return was (1,233.06-1,187.54)/1,187.4 * 100 = 3.83% for that day.

Excel Commands:

To create the first equation, you must first get the averages of all the rates of return. Use the Average command under Insert, Functions, Statistics.

You must use the graph XY scatter option to create a chart.

For example:

If the U.S. average rate of return over the period was 1.95% per day and the German rate was 0.59% per day, then the rate of return on an international portfolio with 80% U.S. stocks (a=0.8) and 20% German stocks would be:

rp = (0.8)(1.95%) + (1 – 0.8)(0.59%) = 1.68%

To create the second equation, you must get the standard deviations and correlation between series. Use the CORREL and STDEV under Insert, Functions, Statistics.

For example:

If the U.S. standard deviation was 3.96%, the German standard deviation was 3.90%, and the correlation between the U.S. and EAFE markets was 0.67, the standard deviation for an international portfolio with 80% U.S. stocks (a=0.8) and 20% German stocks would be:

)

667

.

0

)(

90

.

3

)(

96

.

3

)(

8

.

0

1

)(

8

.

0

(

2

)

90

.

3

(

)

8

.

0

1

(

)

96

.

3

(

)

8

.

0

(

2

2

2

2

–

+

–

+

=

p

s

= 3.73

note: the standard deviation of the combination of the two assets is lower than either asset alone.

APPENDIX

This should include your figure and all relevant materials not discussed in the paper. Label your graph fully. Then refer to your figure as Figure 1.

Countries:

1. Brazil
2. Chile
3. Germany
4. Italy
5. United Kingdom
6. Switzerland
7. China
8. India
9. South Korea
10. Hong Kong

notion of risk and return

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