# Essays on Estimation and Decomposition of Downside Risk for Portfolios With Non-normal Returns Assignment

The paper 'Estimation and Decomposition of Downside Risk for Portfolios With Non-normal Returns' is a great example of a Macro and Microeconomics Assignment. ConclusionThe price/earnings (P/E) ratio of the firm and the stock’ s CAPM beta coefficient of the firm  do not have significant effects on the returns of the security since their t-ratios do not fall within the rejection region. However, the size of the firm measured in terms of sales revenue and the market to book ratio of the firm  have significant effects on the returns of the security since their t-ratios fall within the rejection region.

Therefore, the size of the firm  measured in terms of sales revenue and the market to book ratio of the firm are major determinants of the returns of the security. Based on these results, the variables that should be deleted from the regression are the price/earnings (P/E) ratio of the firm and the stock’ s CAPM beta coefficient of the firm since their effects on the returns of the security are not significant. Increase in betaIf the beta of the stock increased from 1 to 1.2, the stock’ s return is not expected to decrease.

This is because this variable does not have a significant effect on the returns of the security hence will not influence a change. The sign on beta is not as expected. This is because stock’ s return is always in direct relationship with the risk. As it is, it will mean that stock’ s return will increase when risk reduces which is not common in an ordinary market situation. Question 2The econometric model is a simple regression model. This is because it analyses the relationship between the two variables only.

The dependent variable in this model is (RJ-rf) which is the risk premium on security j. the independent variable in the model is (rm-rf) which is the risk premium on the market portfolio. MOBIL’ s betaThe beta of MOBIL is 0.714695. The stock of MOBIL is defensive. This is because its beta is less than 1 (0.714695< 1). This implies that the systematic risk of the stock of MOBIL is less than the overall market. Intercept parameter α jThe assertion that the intercept parameter α j in the model should be zero is correct.

This is because it is a constant hence does not influence a change when the explanatory variable changes. In addition, the figure is very small as to cause a significant difference in risk premium if it is incorporated. The intercept parameter α j is estimated at 0.004241.Estimation under the assumption that aj = 0The estimate of the beta of the stock does not change much. The estimated MOBIL’ s beta under this assumption is 0.721124 which is very close to 0.714695. This is an insignificant change. Question 3Variances and covarianceMOBIL stock variance = 0.006449Market variance = 0.004672Risk free rate variance = 0.000005The covariance of MOBIL stock and market = 0.003306δ 2MOBIL stock δ 2 = 0.006449Market δ 2 = 0.004672Risk free rate δ 2 = 0.000005hypothesisHo: β 1 = 1HA: β 1 < 1Test statisticRejection regionTherefore, since the test statistic falls within the rejection region, you should reject the null hypothesis and accept the alternative hypothesis.

Hence at the 5% level of significance, the beta value of MOBIL is less than.

Works cited

Boudt, Peterson. Estimation and decomposition of downside risk for portfolios with non-normal returns. The Journal of Risk, 11: 79-103. 2008. Print.

Brigham, Houston. Fundamentals of Financial Management. New York: Cengage Learning, 2009. Print.