Fall 2019

1. (4 pts) Use the information in the table to complete the questions.

1. What is the expected return of a portfolio with 25% of wealth invested in the US, and 75% invested in the UK?

• What is the standard deviation of return of a portfolio with 25% of wealth invested in the US, and 75% invested in the UK?

• What is the covariance of return between the US and the UK?

• Can an investor obtain diversification gains by investing in both the US and the UK?  Why or why not?  Be sure to provide quantitative justification for your answer.

• (6 pts) A contention expressed commonly by academics (and practitioners) is that international portfolio diversification pushes out the efficient frontier, or, in other words, enables an investor to maintain the same level of expected return with a lower level of risk  (or, alternatively, the same level of risk with a higher expected return).      

Your assignment is to take historical monthly returns (the investable market index – IMI) for the stock markets in the U.S., Europe, and Asia/Pacific and examine the risk vs. return possibilities that can be obtained by combining these markets into 20 different portfolios (where the portfolios differ in the weight allocated to each foreign market).  Your results should include both the expected return and standard deviation for each of the 20 portfolios, as well as a graph (in expected return vs. standard deviation space) that contains the 20 points (Note: this is time series data.  For your probabilities, assume each observation has a 1/60^th probability of occurring).  (The variance of return for a 3 asset portfolio consisting of stocks a, b, and c can be calculated as:  W_a²σ_a² + W_b²σ_b² + W_c²σ_c² + 2W_aW_bσ_a,b + 2W_aW_cσ_a,c + 2W_bW_cσ_b,c)

As part of this assignment, answer the following question:  Do you think, over the 60 month time period, that international diversification was a worthwhile endeavor?  Why, or why not? 

The file containing the data is:  MSCI DATA.

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