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Purpose of the Assignment The purpose of this assignment is to review and to adopt the statistical concepts (mean, standard deviation, regression coefficient, confidence limits, etc. ) which we have learned in the first two classes, and to develop our further understanding of how those concepts can be used in business management. 2. Calculation Assumptions Expected return : the mean of daily returns daily return(t) = (price(t) – price(t-l)) / price (t-1)
Here, I define expected return as “the mean of daily returns”, not “the mean of daily excessive return”. Thus, “risk-free-rate” is not used in calculation processes. Risk : the standard deviation of daily returns Beta : the slope coefficient in a liner regression (X: the daily return of the IMBIBE; Y: the daily return of country indexes) 3. Calculation Result 10 country indexes sorted by Expected return, Risk, and Beta: (see Appendix for scatter diagrams) 95% confidence limits of Beta, R, and R square of 10 country indexes: 4.
Interpretation of Results Risk vs.. Expected Return According to the results, we can see that while some country indexes have economic rationality, high risk high return (Argentina, Indonesia) low risk low return (Poland), others take a unique move, high risk low return (Hungary), low risk high return (Vietnam). The IMBIBE, which combines all these characteristics, seems well built. While the IMBIBE secures middle return, its risk remains at the lowest level.
Comparing an investment efficiency of each country index with that of the IMBIBE by taking the ratio of expected sis and return (see right table), only Vietnam exceeds the IMBIBE. Seta, R, and RE According to the results, we can see that all country indexes have positive Beta and R. Therefore, the return of each country index does not respond in an opposite direction to that of the IMBIBE. In Beta, we can get an initial idea of market variance. While 6 country indexes (Russia, Turkey, Indonesia, Hungary, Mexico, Brazil) are at the relatively same level of IMBIBE (В±1), Argentina index is 3. Times higher, and other 3 country indexes have 0. 2-0. Times lower value. When evaluating Beta, we also needs to consider its reliability by checking its confidence limits. For instance, while the confidence limits of Russia are at the 10% movement of its mean, those of Malaysia are at the 80% of its mean. This would bring us an idea that in case of Malaysia, other factors aside from market variance may give more impact to the index. RE statistic helps us scrutinize this part. While RE square of Russia is 0. 70, that of Malaysia is only 0. 07.
Therefore, we can consider Malaysia index does not much reflect the variation of the general market condition, but contains more non-systemic risk which are unique to this country. In such a case, Beta will not provide the right picture. Based on the above interpretations, we can conclude that for a new investor, using Composite index which reflects a general market conditions as a benchmark helps them light up characters of investment candidates it is important to keep in mind that making an investment decision solely by Beta is dangerous and checking its confidence limits, R, and RE are necessary.