The Measurement of the Portfolios in Form of Beta Measurements - Essay Example

Financial Report Introduction Many investors value their investments based on the marginal growth, returns, andthe risks associated with these investments. One of the best ways of determining these returns and risks is the determinations of portfolio calculations. A portfolio is any sort of investment groups of asset investment that is held by an individual or an organization. In the case of individual assets, the key to making informed investment decisions is based on the understanding of the risks and possible returns of the portfolios. The measurement of the portfolios in form of beta measurements helps an investor in manipulating the portfolio in the changing economic times and ensures that investments patterns have higher probability of performance. The purpose of this study is to analyze use the study of portfolios, by learning their measurements, purposes, and methodologies to show how portfolios are instrumental in helping investors make informed investment decisions in the market. The volatility of the stock market invites investors despite the daily, quarterly, and the annual dramatic occurrences at the stock market. The average return of a security describes the value of the volatility of the stock market. The volatility of the portfolios is measured by the daily, monthly, quarterly, and yearly standard deviations. The standard deviations also show price variations, in the sense that when the prices are pooled together, the standard deviation tends to be very small and the reverse is true when the prices are spread apart. In the events of securities, when the standard deviations are higher, there is a greater dispersion of the returns and the risks associated with the investments are high. The risks that are created through the analysis of the daily, monthly, quarterly, or yearly averages, returns, and other measures of dispersions, are based on the degree of these analyses averages. As the chances of the expected returns lowers, the riskiness of the investments increases. According to the daily, monthly, and yearly average return, standard deviation, covariance, and correlation analysis it is clear that there is a strong link between the portfolio volatility and the stock market performances. In the analysis sheet 1, the stock portfolios of EQR, PSA, QEM, SPG, and VNQ represents the stock fluctuations that depends on volatility. A sample of the sheet1 is shown below. As shown in the table below, when the average daily range in the S&P 500 Index is low (the first quartile 0 to 1%) the odds are high (about 70% monthly and 91% annually) that investors will enjoy gains of 1.5% monthly and 14.5% annually. The variances of the portfolios measure the dispersion of data points given around their mean value. In this case, the variances create the mathematical expectation of the average squared deviations from the mean. The variance, based on the averages is determined by getting the probability-weighted average of the squared deviations from the expected value. In this case, the variances determine the variability from the average or volatility. Therefore, the volatility in this case measures risks, and this statistical data is instrumental in determining the risks that an investor might take when purchasing a specific security. The variance of a portfolios return is a function of the variance of the component assets as well as the covariance between each of them. Covariance is a measure of the degree to which returns on two risky assets move in tandem. A positive covariance means that asset returns move together. A negative covariance means returns move inversely. Covariance is directly linked to correlation analysis where the difference between the two is that the latter factors in the standard deviation. Portfolio Variance = w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cov(RA, RB) Where: wA and wB are portfolio weights, σ2(RA) and σ2(RB) are variances and Cov(RA, RB) is the covariance The expected return is obtained from the weighted average of the likely profits of the assets in the portfolio, weighted by the likely profits of each asset class. The return expected is thus obtained through the formula; This formula can also be re-written as: E(R) = w1R1 + w2Rq + ...+ wnRn . For the first portfolios, the average E(R) is based on the average figures shown in the table and =(99.8*0.001391606) + (0.1*0.001049148)+ (0.1*0.001049148)=0.1390921084 =13.909% The next set of the weighted averages, W1, W2, and W3 follows the same criteria of analysis. An efficient portfolio has a risk characteristic that is approximate to the investor’s utility function. In this regard, it is a portfolio that maximizes an investor’s preference with respect to return and risk. An efficient portfolio (also called an optimal portfolio) also provides the highest expected return for a specific level of risk. In the same way, an efficient portfolio provides the lowest risk for a particular expected return, and gives the best returns achievable for a given level of risk. Basically, an efficient portfolio is one that lies on the efficient frontier. The following table shows the calculations summarizing the average return of EQR and SPG, and CAL on efficient frontier. AVG RET (EQR) AVG RET (SPG) COR (EQR,SPG) 0.001391606 0.001113482 0.654953164 SD (EQR) SD (SPG) rfr 0.009077563 0.007963853 0.0025 VER [EQR] VER [SPG] (R)S&P 500 8.24022E-05 6.3423E-05 0.000530992 Beta(EQR) Beta(SPG) 0.221133745 0.294895994 The graph below shows the graph of efficient frontier and CAL based on the available data given. Graph 1: efficient frontier As argued from the above analyses, a stock portfolio is a group of financial assets like stocks, bonds, and or cash equivalent, and their mutual that are exchange-traded. These kinds of portfolios are held by the investors directly, but traded and managed by professionals in the financial management. A two and three stock portfolios are based on the calculated Rp and the standard deviations for the portfolios. The return of a three-asset portfolio is given by Rp= wara+wbrb+wcrc Where a is the return and wa is the weight on asset A. rb is the return and wb is the weight on asset B. rc is the return and wc is the weight on asset C. wa +wb+wc= 1. Portfolio weight is the percentage composition of a particular holding in a portfolio. Portfolio weights can be calculated using different approaches; the most basic type of weight is determined by dividing the dollar value of a security by the total dollar value of the portfolio. Another approach is to divide the number of units of a given security by the total number of shares held in the portfolio. It is important to note that the portfolio weights are not necessarily applied only to specific securities, but the investors can calculate the weights of their portfolios in terms of sector, geographical region, index exposure, short and long positions, type of security (such as bonds or small cap technology companies) or any other type of category. Basically, portfolio weights are determined based on the particular investment strategy. The return on a two-asset portfolio can be obtained through the formula, rp=wara + wbrb, where Where a is the return and wa is the weight on asset A. rb is the return and wb is the weight on asset B, and wa +wb = 1 The following calculation shows the Rp and the standard deviation for the various portfolios given in the data. The average weight of the first portfolio is 0.069987679 while of the second portfolio is 0.930012321. The return on price of the overall portfolio is 0.001132951. VER and the SD are 6.1423E-05 and 0.007837283 respectively. The utility maximizing portfolio One of the economic aspects used in finance is the use of expected utility hypothesis in making a choice under uncertainty. The theoretical application, in economic sense, that is normally used in making decision under such circumstances of risk is the use of this hypothesis. According to the expected utility hypothesis, an individual will tend to choose the portfolio weights such that the expected value of the utility is maximized. [U (W1)]=E{U[(1+∑xiRi)W0]} Subject to ∑xi=1 Portfolio optimization chooses the proportions of the various assets to be held in a portfolio in such a way that the better portfolio than other portfolios be chosen from the same way. The expected value of the portfolio’s rate of return and the return’s standard deviation and variances are the key to the criteria. The utility maximizing portfolio generated by A=2, 7, and 10 is used to determine the optimal portfolio and their return and their standard deviations. For instance, the figures of utilities U;A=2, U;A=7, and U;A=10 shown in the table below were used to generate the optimal portfolio, their return, and standards. U; A=2 U; A=7 U; A=10 0.000986978 0.000670024 0.000479851 0.00098732 0.000670526 0.00048045 0.000987662 0.000671027 0.000481047 0.000988004 0.000671528 0.000481643 0.000988346 0.000672028 0.000482238 0.000988687 0.000672527 0.000482832 0.000989028 0.000673026 0.000483425 0.000989369 0.000673524 0.000484017 0.00098971 0.000674021 0.000484607 0.00099005 0.000674517 0.000485197 0.00099039 0.000675013 0.000485786 0.00099073 0.000675508 0.000486374 0.00099107 0.000676002 0.000486961 0.00099141 0.000676495 0.000487547 The above utilities were used to generate the following returns, portfolio, and standard deviations. Y 1-Y Rc SDc 0 1 0.0025 0 0.001 0.999 0.002498633 7.84E-06 0.002 0.998 0.002497266 1.57E-05 0.003 0.997 0.002495899 2.35E-05 0.004 0.996 0.002494532 3.13E-05 0.005 0.995 0.002493165 3.92E-05 0.006 0.994 0.002491798 4.7E-05 0.007 0.993 0.002490431 5.49E-05 0.008 0.992 0.002489064 6.27E-05 0.009 0.991 0.002487697 7.05E-05 0.01 0.99 0.00248633 7.84E-05 0.011 0.989 0.002484962 8.62E-05 0.012 0.988 0.002483595 9.4E-05 0.013 0.987 0.002482228 0.000102 The calculation of the portfolio’s beta gives the measure of the portfolios market risk. It is done by determining the betas of all the stocks in the market. Each beta is then multiplied by the percentage of the total portfolio that the stocks represent. Finally, all the weighted betas together summed led to the portfolio’s overall beta. In calculating the beta for portfolios in 4 and 5 using the S&P 500 indexes as the market, the following analysis represent the calculations. For instance, the summary of the first 15 stock prices shows represent the following data; Beta 0.294822232 0.294379659 0.293937085 0.29474847 0.294305896 0.293863323 0.294674708 0.294232134 0.294600945 0.294158372 0.294527183 0.29408461 0.294453421 0.294010847 Using the data available in the S&P data for the stocks, the overall betas are 0.221133745 and 0.294895994 respectively. Five techniques of portfolio performance Every year, investors reflect on the performances of their investments. A systematic evaluation makes misconceptions very clear. However, the five techniques that are critical to be adopted when evaluating portfolio performance involve firstly the use of an investment advisor. Investment advisor is best suited to provide the performance data and hence important when evaluating the portfolio performance after a specific period of time. In addition, taking the art of evaluating the portfolio by you is very cumbersome and thus requires the use of professionals like investment advisors. Time-weighted portfolio return calculation is also critical in the evaluation of the performance of the portfolio in a calendar year. By using a time-weighted return, fluctuations that have nothing to do with portfolio picks can be eliminated from the evaluation. Actually, by using a time-weighted measurement, which is the industry standard for periods longer than three months, distortions from contributions and withdrawals will be reduced or eliminated. In addition, periodic analysis of the return measurements over the various period of time, yearly, quarterly, monthly or daily is also another way of keeping an evolutionary check on the performance of a portfolio. This is the best way to determine whether or not the investment manager is performing well. The next technique is through the use of performance attribution, where the investors become critical to the transparent achievements of the returns. Finally, when these rules are applied, the investors will learn more about how their portfolios are invested and become better able to evaluate whether or not their advisors are adding value above and beyond the fees they charge. Read More