Building a Portfolio
A new investor is planning to build a portfolio based on the Emerging Markets Bonds Indexes (EMBI Global). She collects data on ten indexes (Indonesia, Malaysia, Vietnam, Hungary, Poland, Russia, Argentina, Brazil, Mexico and Turkey) from December 1, 2009 to December 1, 2010. The expected returns look promising, although they show remarkable differences from one country to the next. Before performing a complete analysis of the data, she reads the following notes in order to understand how risk is measured and how it is possible to distinguish between systemic and non-systemic risk.
The Capital Asset Pricing Model
Risk can be avoided by investing in a risk-free asset. Any asset whose possibility of loss is considered to be non-existent may be considered risk free for practical purposes. A typical choice is the one-year treasury bond (T-bill), which has a yield (at the time of the data collection) of 0.25 .
According to the capital asset pricing model (CAPM), the amount by which the expected return of an investment exceeds the return of the risk-free asset is proportional to the amount by which the expected market return exceeds it. This relationship is expressed as the beta (þ) of the investment. Each particular investment has its own beta and the model assumes that the beta does not change over time. This can be expressed using the following equation:
RETURN ( t ) = Constant + β MARKET ( t ) + ERROR ( t )
The error term, i.e., the deviation from the model, accounts for the non-systemic risk. In practice, the returns of a general index, such as the Composite EMBI Global Index in this case, are used to provide a value for the expected market returns and þ is estimated as the slope coefficient in a linear regression of the past returns of the investment on those of the general index.
In order to understand how to use betas in practice, it is worthwhile to consider the following situations:
- For an investment with β = 1, when the market return varies by 1%, the return varies by 1 on average. We say on average because the investment will also be affected by its specific, non-systematic risk.
- If β = 2, for every 1% variation in the market return, the return varies by 2% on average.
- An investment with 0 < β < 1 is less affected by general economic conditions.
- If β < 0, the return (on average) goes in a direction opposite to that of the market and, therefore, also to that of most other investments. This property makes it useful for risk-reduction strategies.
(a) Produce a table of daily returns for the nine indexes.
(b) Calculate the expected (mean) return and the standard deviation of each index. Do these data support the assertion that expected returns are higher for riskier assets?
(c) Calculate the beta for each index, using the returns of the Composite EMBI Global index as expected market returns.
(d) How can we identify the indexes with less systemic risk?
Assignment submission guidelines:
1. On the due date, hand-in the report before class.The report must be two pages long (this will be enforced), printed recto/verso. We reiterate: this is an exercise in communication as well as in statistics and critical thinking. Communicate your findings clearly and concisely. The report must be self-contained and should not reference the excel file.
2. In addition, on the due date before class, you must upload your excel file in the moodle, which must include all your calculations and graphs. We will not look at this excel file under normal circumstances.
Attachment:- embi_data.rar