##### Data Analysis and Decision Modelling Oz Assignments

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The computation SD is commonly seen in statistic for measurement of dispersion. This is considered as a simple procedure for investment in volatility of the portfolio. The lesser is the amount of SD, lesser is the volatility. Dispersion is considered as a statistical term which describes the range of values which are related to particular variables. The financial dispersion is further used to study the effects associated with the investors and **business analysis** of the beliefs pertaining trading of securities. These are further seen to be depicted in terms of variability of returns as a result of a particular trading strategy. The risk measurement beta is considered with measures of dispersion as per the security’s return which relative to the market or benchmark. In case the dispersion is seen to be greater than the benchmark, the security is considered to be riskier in compared to benchmark. On the hand, a security is regarded as less risky in case the dispersion is seen to be less risky than benchmark.

Normal distribution is considered as the probability distribution for plotting of the values in a symmetrical manner considered with the mean of the probability. The optimization of the portfolio is seen to be based on considering the lowest possible value for the risk and highest value for returns. Therefore, the use of normal distribution aids in the process of mean for returns and standard deviation for risk. For example, in real situation the share price may go up by 1.5% on a daily basis, this means that the expected value has strong significance as per the expected value.

The expected return as per the probability distribution has been further depicted as the function which shows all possible value during the evaluation for the expected return from a portfolio. This analysis is further seen to be confined with the range of derived statistical possibility of selecting the range of discrete and continuous inputs of the share prices.

The consideration of adding the new shares is mainly identified with the dependence on diversification strategy. Covariance aids in the process of diversification and reducing the volatility in the portfolio. This is considered as the measure for determining how two assets move corresponding to each other. Positive value of the covariance suggests how the assets vary in similar manner. On the other hand, the negative value in the covariance indicates that the assets move in the opposite directions. However, covariance is identified with certain limitations which depicts the direction among the two assets. It cannot provide the specific relation between the process. This gap needs to be filled with the determination of the correlation coefficient between the assets for measuring the strength among the same. The risks which are diversifiable in nature can be reduced with the use of coefficients of correlation of the assets. This measures the degrees of correlation ranging from -1 from a perfectly negative correlation of +1 depicted with a perfectively positive correlation.

As the correlation is identified as the statistical measure of perfectly uncorrelated pair of investments the possibility of zero correlation coefficient is rarely possible in real practice. In general, even the most diversified portfolio will bear the greatest negative correlation. Even for a portfolio of uncorrelated assets there may be higher degree of risk, which is less than the positively correlated investment decisions. It needs to be understood that a positive correlation in the portfolio is identified with less risk when compared with single assets or investments which are completely positively correlated. It needs to be however determined that there is no scope of reducing the overall risk even with the combination of assets with positive correlation.

The application of the SD is applied to the investment returns which are based on the quantitative statistical measure pertaining to the variation for the specific returns as per the average of the returns. The **risk management** is generally represented by SD of the expected returns of an asset which is equal to the square of the variance. The calculation of the variances using the SD for two assets are depicted with the probability of multiplying the return for the state less the square of the expected return.

The risk weighted assets (RWA) are represented as the bank’s assets pertaining to the off-balance sheet exposures which are weighted as per the risk. This asset is useful in determining the capital requirement or CAR as per the financial situation. In practical terms this computation is depicted to be useful in terms of determining comparison of rate of return among banks. In addition to this, the off-balance sheet exposure exposures can be easily considered for the capital adequacy determinations. The different classes of assets are determined with different risk weights associated to them. Such assets are typically inferred with debentures which has higher risk associated in compare to others.

As per the given statement it has been asked what the implication of combination of two assets in case of the two assets would be was risk free during the computation of weighted risk of two assets. It needs to be discerned that if even one of the asset is risk free the net impact on the overall risk will be zero. As per the formula of RWA, the risk rate is multiplied with the expected rate of return. Therefore, even if there is decrease in the risk rates the added result for the overall risk will be zero. This is mainly due to the fact the risk of the portfolio is multiplied with the expected rate of the return for one asset and further added with the same rate to other assets. As the rates are multiplied all along the computation of RWA, even if the risk-free rate is 1, the net impact on the overall risk of the portfolio will be nil.

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