Significance of Absolute Returns to Relative Performance - Essay Example

Finance Assessment of the of the SECTION A QUESTION PART SIGNIFICANCE OF ABSOLUTE RETURNS TO RELATIVE PERFORMANCE The term absolute return is linked to the utilization of assets by the company over a specific period of time. The absolute return measures the appreciation or depreciation in the stocks and the returns which are achieved over a specific period of time (McLaney, 2009). Relative return is the concept in which the performance of one stock is compared to that of another. In this concept one stocks performance is benchmarked by the performance of another stock. The returns which will be generated are compared relatively to other stocks of similar nature operating in the markets (Gitman, 2003). The major difference between both the absolute and relative return is that absolute return is concerned about the returns which are generated from one particular asset or stock, whereas in relative return the stock is compared or benchmarked with the measures of other stocks. The most debated concept of Security Analysis and Portfolio Management is about the understanding whether a portfolio has been properly analyzed for the returns which the investors will get or understanding the relative performance of that particular stock in the markets (Deloitte, 2010). The investors need to redefine the definition of risk, how it is measured and how to deal with it and for this reason; investors create a portfolio of different stocks and securities. Alpha and Beta are the tools used by the investors to assess their portfolios and measure whether or not their investments are generating the expected returns considering the risk they are taking. Assessing a portfolio in terms of both Alpha and Beta, the investor will have more control over the portfolio and he will maximize the returns by minimizing risk (Koba, 2012). The measurement of an investment on risk adjusted basis is called Alpha. Investors seek to minimize risk and increase returns (Loth, 2007). The stock prices are subject to volatility. The price risk associated to a portfolio determines the return expected by the investor. The additional return which an investor gets on a portfolio apart from the benchmark set is called Alpha. A negative Alpha of a portfolio shows underperformance (Faulkenberry, n.d.). Beta is a tool which is used to measure the volatility of risk associated to a portfolio as compared to the performance of the market. Regression analysis is used to calculate Beta. In other terms Beta is the propensity of investment return to respond to the market volatility. The lower the value of Beta, lesser will be the volatility of the stock with respect to the market. Both Alpha and Beta are popular tools used for the measurement of volatility. Alpha compares the asset returns on the investment to the risk adjusted expected returns whereas Beta is the movement of the asset along with the benchmark that has been set by the market. Alpha is very important for assessing the growth and the returns that are associated to the portfolio. It depends on the structure of the portfolio, the investor and the market which is being analyzed that which factor either the Beta or the Alpha will be critically significant for the investor (Seeking Alpha, 2011). With the varying school of thoughts the perceptions of the importance of Alpha or Beta vary. Alpha and Beta alone do not possess the potential to assess the risk instantly and adjust the portfolio for the returns. Alpha alone is not sufficient to assess the skills which are derived from the leverage of the portfolio. It is not suitable for a risk averse investor and may end up being a misleading performance measure for the investors. The value of Alpha itself is not sufficient for the assessment of the stock but it can be used if a benchmark of the portfolio is set. Beta does not possess this benefit. The direction of the market cannot be assessed by the benchmark Beta set for the portfolio. The use of Alpha and the speculations made by using it are very consistent. The cyclical variations in the speculations are less (Deloitte, 2010). The debate continues because although Alpha has drawbacks associated with it but still it is efficient in measuring the risk as compared to other tools which are being used. The priority of the investor today is to maximize the return with the minimum risk taken. Beta fails to identify the risk associated to the portfolio. It analyzes the market performance for the long run (Deloitte, 2010). The investor of today is more risk averse. His appetite for risk has decreased. For this purpose the investors are only interested to invest if the returns which are offered to them are more and the risk associated with it is also less. For this purpose the investors consider the measurement of Alpha more to that of Beta. The investors are more concerned to the returns which they will get by investing rather than the performance of the market. In investment management the rate of return which different investors expect vary. The portfolios of all the investors are tailored specifically as per their need. The investment managers and the investors both aim at maximizing the returns that is associated to the portfolio. Alpha is popular because it assesses the returns which the portfolio can generate. The investors and their priorities with their investments are different. Some are risk Averse and some are risk takers. If the investment of the investors are made in accordance to the market performance than the risk will increase and the rate of return which the investor requires may not be provided (Deloitte, 2010). Alpha tool is preferred by the investment managers because the returns which the investors require vary (Deloitte, 2010). The investment managers debate that all the tools are significantly important for the measurement of risk and returns. To specifically calculate the returns of the portfolio Alpha is used and to speculate the market performance Beta is used. The significance of both the methods is equally important with the varying needs of the investors. It would be wrong to say that one tool is better than the other tool. Both the methods are historical methods for the calculation of the volatility and are now the major components of the Modern Portfolio Theory (MPT) (Commentary, 2006). The conclusion suggested for this debate in the light of the discussion above is that the significance of all the tools is relatively important and all possess pros and cons. The widely used tool by the investment managers today is Alpha. This is because the investors have become more return conscious. Beta is still widely used but to assess the market performance as a whole. This shows that the importance of overall returns which the investor gets from his portfolio and to adjust the portfolio with the changing market risk is the significant priority of the investors. PART # 2 OVER THE LONG RUN, LOW BETA PORTFOLIOS PROVIDE BETTER RISK ADJUSTED RETURNS THAN HIGH BETA PORTFOLIOS Risk adjusted returns is the term used to estimate the amount of risk which is connected to the generated return. The application of the concept is widely used while assessing investment funds, portfolios and to individual securities. The most commonly used methods for the calculation of the risk is the Alpha method, Beta method, R-square, Standard Deviation and Sharp Ratio. All the methods that have been mentioned have their own significance in calculating the risk. For the calculation and the comparison of the investment plan these tools are used to compare the results. The portfolio with the most stable performance result is accepted (Frazzini, and Pedersen, 2013). The risk level of all the investors is different. The return which the investor expects varies from investor to investor. The factors like risk taking ability, resources available to the investor to sustain the financial pressure, the ability to hold a position and sustain till the market grows back etc (Swedroe, 2012). The position which the investor holds can be adjusted by speculating the market volatility. This strategy is helpful in avoiding the big losses and to focus on the gains. The calculation however can never be accurate because there are no specific rules to do so. These methods are built to assess the feasibility or the attractiveness of the stocks at that particular point in time (Hanlon, 2012). The priorities of the investors are different. The mutual funds investors are looking for stocks with higher volatility. For this purpose they are constantly looking for higher Beta. The more volatile the market, the more are the chances to make higher gains. The thought of the individual and the institutional investors are different. Individuals look for less risk and higher returns whereas the institutions are in search for higher risk and higher returns. The Beta has impact on the results which are derived by other tools. The higher the Beta the lower will be the result of Alpha and other tools that have been used. In an analysis it was estimated using the Fama and French model that the low Beta in the long run and a high Beta rate in the short run showed that the returns which were achieved were significantly high. It is observed that the investors who have the holding to sustain in the market for a long period bet on the stocks which have higher Beta. In the real world specially when dealing with individual investors the limits of the funding and investment are low (BlackRock, 2013). When the Beta of a portfolio is analyzed it is noted that a higher Beta will have a lower Alpha and Sharpe. In the same way when the Beta of a portfolio is low, the difference between the risk calculated from Alpha and other tools is lower. This minimizes the risk of the portfolio as a whole. The low Beta portfolios provide better risk adjusted returns. This is because of the fluctuation and the volatility in the markets. The markets which are more volatile show a high Beta for the portfolios. The speculation of the risk is difficult in a more volatile market. At the same time the markets which have low volatility, the risk can be easily calculated. The new markets prefer the significant use of Beta. High Beta stocks give higher results. When the prices in the stocks change the returns which the stocks with higher Beta give are higher. In theory this is true but in reality the return that is associated to such high risk which the investor is taking is higher. The speculation of the stocks in theory and in reality is different. With the use of CAPM the investors use the leveraging of the assets. In the practical world the investors are incapable and reluctant towards using the leverage. This practice of the investors lowers increases the prices of the high Beta stocks in the short term and minimizes the risk in the long term (Buttonwood, 2012). THREE FACTOR MODEL – FAMA AND FRENCH The three factors model of Fama and French is based on multiple factors to compute and explain market mechanism of equilibrium prices of the stocks. The objective of this model is to explain that whether investing in one security will minimize risk or either investing in many portfolios at the same time will reduce risk (Arnold, 2008). Comparing the volatility of the stocks and by comparing certain other factors will help in assessing the variable factors of the portfolio to calculate the overall risk associated to the portfolio (Arnold, 2008). Where, Rpt = Average monthly return on portfolio p Rft = Risk free rate observed at the end of each month βp = COV (R,R)/VAR (R) Rmt = Expected Market Return SMB = Small Minus Big (proxy for company size) HML = High Minus Low (proxy for BE/ME) Sp = the sensitivity of Rpt to a change in size premium SMB hp = the sensitivity of Rpt to a change in value premium HML αpt & εpt = these represent the intercept of the regression and the error term respectively. Fama and French (1993) worked on various methodologies to propose techniques to limit the risk associated to portfolios. Before the proposition of this model CAPM was used. To limit the model to compare the stocks as individuals rather than that to the whole market has been propose by Fama and French. They proposed that two categories of stocks perform in the markets, the small cap stocks and the stocks with high book value to price ratio (Pike, and Neale, 2009). The three factor model is based on the philosophy that high risks yield higher returns. The opportunity to earn is higher if the stock is underpriced by the markets but have the potential to grow in them. A smart investor will aim at forecasting the future after speculating the past trends. The three factor model is similarly used for this purpose. It assesses the trends and constructs the portfolios on the basis of risk. The three factors of Fama and French model are the size of the firms, book to market value of the stock and excess returns to the markets if any. These models only help in assessing the returns for the future with the use of past trends. The three factor model compares the economic, fundamental and statistical factors for this purpose. This debate can be concluded on the note that the portfolios which have higher Beta are riskier as compared to those which have lower returns. This is because of the Beta mis-specifying risk. In reality there are certain factors which are missed in the theory. The factors like formation of the leverages by the investors. The risk associated to the higher Beta stocks is more than that of lower Beta stocks. SECTION B QUESTION # 2 a. “It is always better to have a portfolio with more convexity than one with less convexity.” Disagree It is preferable to have a portfolio with less convexity rather than having a portfolio which has more convexity. This statement compliments on the stocks which are included in the portfolios. The stocks included in the portfolios must be different to reduce the effect of convexity. The wider the array of stocks in the portfolio the higher will be the return. It has been observed that if the yield curve shows a parallel shift even then the two portfolios will not depict the same performance. This is because if two portfolios are studied it can be observed that they do not possess the same amount of dollar convexity. The other factor is that it is preferable that the portfolio has less convexity when all the other factors are held constant. The markets usually charge for convexity of the portfolios by offering either higher prices or by offering the investors with lower yields. The change in the yield affects directly the convexity of the portfolio. E.g. with the change in the market yield, with less than 100 basis points the portfolio which has lesser convexity will provide better amount of the net returns. So it can be concluded that the “It is not preferable to have portfolios with more convexity. Those portfolios which have less convexity are less preferable.” b. “A bullet portfolio will always outperform a barbell portfolio with the same dollar duration if the yield curve steepens.” Disagree This statement is not appropriate for the measurement of the portfolios, if the measurement of yield steepens. When the two portfolios the bullet portfolio and the barbell portfolio are compared with each other the level at which the yield curve steepens is measured. In some situation the bullet portfolio outperforms the barbell portfolio and in the other cases the barbell outperforms the bullet portfolio. This can be illustrated by an example in which the two portfolios and their movements are shown. When the measures like yield are speculated, it can be seen from the convexity of the portfolio that in which direction is the performance of the stock going. The portfolios which are based on expectations about the shifting of yield curve are crucial for the estimation of the total return. The use of the portfolio may vary with the varying situation. In a steep environment the implementation of a bullet portfolio will be better. The main differentiation factor between the two portfolios is the steepness of the curve. The managers are responsible to see to it that the strategy which is being implemented is fit for the measurement of the steepness of the curve and whether the use will be finer or not. It can be concluded that the statement is wrong. The use of the portfolio style will vary with the steepening of the curve. QUESTION # 3 MACAULAY DURATION FORMULA The formula for calculating the Macaulay Duration is as follows: n = number of cash flows t = time to maturity C = cash flow i = required yield M = maturity (par) value P = bond price MODIFIED DURATION FORMULA The formula for calculating the Modified Duration is as follows: a. Macaulay duration = 3.53 Years Payments t*C (1+i)^t (t*C)/(1+i)^t 1 90 1.090 82.57 2 180 1.188 151.50 3 270 1.295 208.49 4 360 1.412 255.03 (n*M)/(1+i)^n 4000 2833.70 Numerator 3531.29 Macaulay duration 3.53 C (1+i)^-n 1-(1+i)^-n 1-(1+i)^-n/i M/(1+i)^n 90 0.70842521 0.291575 3.23972 708.4252 291.5748 Denominator 1000 Modified duration = 3.24 Years Macaulay duration YTM 1+(YTM/No. of periods per year) 3.53 0.09 1.09 Modified Duration 3.24 B M=4 C=90 A (1+i)^n 1/(1+i)^n 1-1/(1+i)^n (i^2)(1+i)^1+M M*M+1 D 2C 180 246913.6 1.411582 0.708425 0.291575 0.012463 0 20 1.6771 0 i^3 0.000729 2CM 720 C 57771.68 Convexity A*B-C+D 14.22 Annual Convexity 14.22 b. Macaulay duration = 4 Years For Macaulay duration of a zero-coupon bond, the duration equals to the bonds maturity and hence no calculation is required. Macaulay duration YTM 1+(YTM/No. of periods per year) 4.00 0.09 1.09 Modified Duration 3.67 Modified duration = 3.67 Years M=4 C=90 A (1+i)^n 1/(1+i)^n 1-1/(1+i)^n (i^2)(1+i)^1+M M*M+1 D 2C 180 246913.6 1.411582 0.708425 0.291575 0.012463 0 20 1.6771 0 i^3 0.000729 2CM 720 C 57771.68 Convexity A*B-C+D 14.22 Annual Convexity 14.22 c. Payments t*C (1+i)^t (t*C)/(1+i)^t 1 90 1.090 82.57 2 180 1.188 151.50 3 270 1.295 208.49 4 360 1.412 255.03 5 450 1.539 292.47 (n*M)/(1+i)^n 5000 3249.66 Numerator 4239.72 Macaulay duration 4.24 C (1+i)^-n 1-(1+i)^-n 1-(1+i)^-n/i M/(1+i)^n 90 0.64993139 0.350069 3.889651 649.9314 350.0686 Denominator 1000 Macaulay duration = 4.24 Years Macaulay duration YTM 1+(YTM/No. of periods per year) 4.24 0.09 1.09 Modified Duration 3.89 Modified duration = 3.89 Years M=5 C=90 A (1+i)^n 1/(1+i)^n 1-1/(1+i)^n (i^2)(1+i)^1+M M*M+1 D 2C 180 246913.6 1.538624 0.649931 0.350069 0.013585 0 30 1.828039 0 i^3 0.000729 2CM 900 C 66251.93 Convexity A*B-C+D 20.18 Annual Convexity 20.18 d. Payments t*C (1+i)^t (t*C)/(1+i)^t 1 35 1.035 33.82 2 70 1.071 65.35 3 105 1.109 94.70 4 140 1.148 122.00 5 175 1.188 147.35 6 210 1.229 170.84 7 245 1.272 192.57 8 280 1.317 212.64 9 315 1.363 231.13 10 350 1.411 248.12 11 385 1.460 263.70 12 420 1.511 277.95 13 455 1.564 290.93 14 490 1.619 302.71 15 525 1.675 313.37 16 560 1.734 322.96 17 595 1.795 331.54 18 630 1.857 339.17 19 665 1.923 345.90 20 700 1.990 351.80 (n*M)/(1+i)^n 20000 10051.32 Numerator 14709.84 C (1+i)^-n 1-(1+i)^-n 1-(1+i)^-n/i M/(1+i)^n 35 0.50256588 0.497434 14.2124 502.5659 497.4341 Denominator 1000 Macaulay duration = 14.71 Years Macaulay duration YTM 1+(YTM/No. of periods per year) 14.71 0.035 1.0175 Modified Duration 14.46 Modified duration = 14.46 Years M=20 C=35 A (1+i)^n 1/(1+i)^n 1-1/(1+i)^n (i^2)(1+i)^1+M M*M+1 D 2C 70 1632653 1.989789 0.502566 0.497434 0.002523 0 420 2.131512 0 i^3 0.000042875 2CM 1400 C 554938.2 Convexity A*B-C+D 257.20 Annual Convexity 64.29978922 e. Payments t*C (1+i)^t (t*C)/(1+i)^t 1 35 1.035 33.82 2 70 1.071 65.35 3 105 1.109 94.70 4 140 1.148 122.00 5 175 1.188 147.35 6 210 1.229 170.84 (n*M)/(1+i)^n 6000 4881.00 Numerator 5515.05 C (1+i)^-n 1-(1+i)^-n 1-(1+i)^-n/i M/(1+i)^n 35 0.81350064 0.186499 5.328553 813.5006 186.4994 Denominator 1000 Macaulay duration = 5.52 Years Macaulay duration YTM 1+(YTM/No. of periods per year) 5.52 0.035 1.0175 Modified Duration 5.43 Modified duration = 5.43 Years B M=6 C=35 A (1+i)^n 1/(1+i)^n 1-1/(1+i)^n (i^2)(1+i)^1+M M*M+1 D 2C 70 1632653 1.229255 0.813501 0.186499 0.001559 0 42 1.316809 0 i^3 0.000042875 2CM 420 C 269482.6 Convexity A*B-C+D 35.01 Annual Convexity 8.752 f. Macaulay duration = 3 Years For Macaulay duration of a zero-coupon bond, the duration equals to the bonds maturity and hence no calculation is required. Macaulay duration YTM 1+(YTM/No. of periods per year) 3.00 0.07 1.07 Modified Duration 2.80 Modified duration = 2.80 Years B M=3 C=70 A (1+i)^n 1/(1+i)^n 1-1/(1+i)^n (i^2)(1+i)^1+M M*M+1 D 2C 140 408163.3 1.225043 0.816298 0.183702 0.006423 0 12 1.402552 0 i^3 0.000343 2CM 420 C 65391.02 Convexity A*B-C+D 9.59 Annual Convexity 9.59 Question 4: Part A: The lower the coupon rate, the higher the price sensitivity to changes in the interest rate. Therefore considering all things constant, two bonds will be selected on the basis of lower interest rate, Bond D and Bond E with 7% coupon rate. However the duration of these bonds are different therefore bonds that have more time to maturity, are more sensitive to the changes in the interest rate. Therefore Bond D has 10 years to maturity and therefore it will have the greatest price sensitivity to the changes in interest rate. Part B: If there is a change in the interest rate then it will influence the price of the bond. If interest rate is decreased by 1% then it will impact the bond prices and the bond prices will move up considering there is no change in the coupon rate. Part C: The higher the convexity of the bond, the higher would be the capital gain from the bond. Therefore the higher convexity has been found for the bond D and therefore it will have the greatest non-symmetrical capital gain. On the other hand, the greatest capital loss would be of bond E as it has the lowest convexity. Part D: If yields are expected to decrease in near future then it is better to invest in bonds that have low convexity. So I would invest in Bond E. Part E: If yields are expected to increase in near future then it is better to invest in bonds that have high convexity. So I would invest in Bond D. Part F: Bonds that have higher maturity are more price sensitive to interest rate. On the other hand, bonds that have less time to maturity would be less price sensitive to interest rate. Part G: Bonds that have higher coupon rate are less price sensitive to interest rate changes and on the other hand, bonds that have lower coupon rates would be more sensitive to changes in the interest rate. References Arnold, G. (2008). Corporate Financial Management, 4th Edition. Harlow: FT Prentice Hall. BlackRock. (2013). Understanding Common Portfolio Statistics. Available from https://www2.blackrock.com/webcore/litService/search/getDocument.seam?contentId=51477&Source=TWITTER&Venue=PUB_IND [Accessed 3 July 2013] Buttonwood. (2012). Beta blockers. The Economist. Available from http://www.economist.com/blogs/buttonwood/2012/09/inefficient-markets [Accessed 3 July 2013] Commentary. (2006). Alpha Beta Investment Management Strategies. Available from http://www.ryanalm.com/portals/5/newsletters/Commentary_2006_05.pdf [Accessed 3 July 2013] Deloitte. (2010). Alpha or Beta. 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