1. Role a sample plays in making statistical inferences about the population
The sample plays an essential role in the process of making statistical inferences about the population. Ordinarily, the entire population is usually too large to be fully studied. The limitations that limit study of an entire population include costs, time and convenience in the application of the study modes. A sample from the entire population is selected. It is assumed that the sample would be representative of the entire population and contains minimum bias towards any aspect of the population. The sample, therefore, forms the basis on which the population characteristics are inferred. The researchers assume that the characteristics displayed by the sample are proportional to the entire population. The sample, hence, plays a critical role in the inferences made about the population.
Samples must represent the population and should be with minimal bias. In satisfaction of that requirement, selection of the sample must be carried out using an acceptable methodology. The methodology should be inclusive so as to incorporate all the characteristics in the population. The typical method employed is the random sampling. The researchers assume that the characteristics are evenly spread, and the random selection of a sample would incorporate all these characteristics. As such, the inferences made from the sample would be representative of the entire population.
2. Purpose of measures of variability and commonly used measures
The variability essentially refers to spread in a set of data. Variability suffices for purposes of illustrating the spread of the data in the set. As such, it would indicate the degree of difference which is presented in the form of the spread. Variability would reflect the distributions in a set of data. Distribution is essential when doing comparisons within the same set of data. Say for instance, when one wants to know the distribution of risk associated with different investments in a portfolio, he would be advised to apply variables of the rates of return.
The commonly used variables include the following: variance, the range, standard deviation and inter quartile range. The range in a set of data shows the spread from the lowest figure to the highest figure. It, therefore, shows the variation between the two extremes. It suffices for the purpose of analyzing the differences in the data in relation to one extreme to the other. The inter quartile range essentially gives the value or the figure in the middle of the set of data. It suffices for purposes of noting the middle point from either extreme value or figure. Variance illustrates the spread of an individual figure or data from the middle point. In this case, the middle point is the mean of the set of data. Variance, as such, shows the deviation of one value from the mean in the set of data. The standard deviation is the square root of the variance. It suffices for data in a normal distribution. The standard deviation of data in a normal distribution can be used to compute the proportion of data within a given range.
3. Drawbacks and benefits of Markowitz method compared to the single index model
The Markowitz model helps in the selection of an optimum portfolio of investments through the use of the variances and covariance of the securities involved. However, the single index model employs the use of the security’s betas. The Markowitz model facilitates the flexible modeling of the asset covariance. However, its limitations lie in the estimated covariance which may introduce inaccuracies in the computation. However, the single index model aids in the separation of the macro factors from the security analysis. However, the Markowitz model is preferable for its practical ability. The former requires a substantial amount of input which may not be practical in the limitation of time. In addition, it merely reduces the problem to the Markowitz model. The ease of application of the Markowitz, therefore, leads to the preference of use. Further, the Markowitz model usually produces results that are significantly superior to the results from the single index model. This makes the investors employing the risk return approach decision basis on selecting their portfolio of investments prefer the Markowitz as it ensures higher returns for lesser risks.
4. Assumptions of CAPM, its usefulness and criticism
The capital asset pricing method is an investment selection decision method that essentially employs the concept of risks and returns to obtain the best investment portfolio. It, however, has an idealistic approach and makes the following assumptions: that the investors do have control on the price of the securities and would take them as the market indicates. The access to borrowing and lending is free to all investors; no transaction costs are incurred and that the borrowing is at the risk free rate. The investors have homogenous expectations in the market and would act rationally in the optimization of wealth. CAPM is useful in the prediction of the returns of an investment or security in relation to its systematic and market risks. It essentially contemplates the effects of risks on the returns of an investment. Investors could employ it for the calculation of the returns of investments in a portfolio and use the results in decision making functions. CAPM has been adversely criticized for its approach in which it only contemplates the non diversifiable risks in the determination of the returns. This is through the use of the beta.
References
Devore, J. L. (2011). Probability and Statistics for Engineering and the Sciences. New York: Cengage Learning.
Kürschner, M. (2008). Limitations of the Capital Asset Pricing Model (CAPM):Criticism and New Developments. New York: GRIN Verlag.
LeBlanc, D. C. (2006). Statistics:Concepts and Applications for Science. New York: Jones & Bartlett Learning.
Strong, R. A. (2008). Portfolio Construction, Management, and Protection:With Stock-trak Coupon. New York: Cengage Learning.
