Calculations of Standard Deviation and Coefficient of Variation - Assignment Example

FINANCIAL MANAGEMENT QUESTION ANALYSIS By (Student’s Name) Professor’s Name Course Name+ City Date Financial Management Question Analysis 1. Calculation Of The Annual Rate Of Return And The Average Annual Rate Of Return The annual rate of return is the return that an investment provides over a certain period of time. It is expressed as an annual percentage of the weights of time (Sanghera, 2006). It is calculated by the formula: annual rate of return = (Ending value/Beginning value) (1/number of years) -1 (Sanghera, 2006). The average annual return is used to report returns historical in nature. For example two- , three-, five- and 10- year average annual returns. It is calculate by dividing the sum of annual returns by the number of years. Year Start of x End of x Annual rate of return for x Average annual rate of return for x Start for y End of y Annual rate of return for y Average annual rate of return for y 2001 20,000 22,000 (22/20)(1/1)-1 = 10 % 10%/1 = 10% 20,000 20,000 (20 /20)(1/1)-1 = 0% 0/1= 0% 2002 22,000 21,000 (21/22) (1/2)-1 = -2.3% (10% -2.3%)/2 =3.85% 20,000 20,000 (20 /20) (1/2)-1 = -100% 100%/2= 50% 2003 21,000 24,000 (24/21) (1/3)-1 = 4.6% (10% - 2.3% + 4.6%)/3 = 4.1% 20,000 21,000 (21 / 20) ) (1/3)-1 = 1.6% (100%+1.6%)/3 = 20.8% 2004 24,000 22,000 (22/24) (1 / 4)-1 = -2.2% (10% - 2.3% + 4.6%-2.2%)/4 =2.5% 21,000 21,000 (21 /21) (1 / 4)-1 = -100% 100%+1.6% +100%)/4 = 50.4% 2005 22,000 23,000 (23 / 22)(1/5) -1 = 1% (10% - 2.3% + 4.6%-2.2% + 1%) = 2.22% 21,000 22,000 (22 / 21) 1/5) -1 = 0.9% (100%+1.6% +100%+0.9)/5 = 40.5% 2006 23,000 26,000 (26 / 23) (1 / 6) -1 = 2% (10 - 2.3 + 2.2 + 4.6 + 1-1) / 6 = 1.68% 22,000 23,000 (23 / 22) ) (1 / 6) -1 = 0.7% (100% +1.6% +100%+ 0.9 +0.7)/6 = 33.7% 2007 26,000 25,000 (25 / 26) (1/7 ) -1= -0.56% (10% - 2.3% + 4.6%-2.2% + 1% + 2%-0.56%) = 1.36% 23,000 23,000 (23 / 23) ) (1/7 ) -1= -100% (100%+1.6% +100%+0.9 +0.7 +100%)/7 = 43.31% 2008 25,000 24,000 (24/25 ) (1 /8)-1 = -0.51% (10% - 2.3%+4.6%-2.2%+1%+2%-0.56%+0.51%)/8=1.3% 23,000 24,000 (24 / 23) (1 /8)-1 = 0.53% (100%+1.6% +100%+0.9 +0.7 +100% +0.53)/8 = 38% 2009 24,000 27,000 (27 / 24)(1/9)-1=1.32% (10% - 2.3%+4.6%-2.2%+1%+2%-0.56%+0.51%+ 1.323)/9 =1.26% 24,000 25,000 (25 / 24) 1/9)-1=0.45% (100%+1.6% +100%+0.9 +0.7 +100% +0.53+0.45)/9 =33.8% 2010 27,000 30,000 (30 / 27) (1/10)-1=1.2% (10% - 2.3%+4.6%-2.2%+ 1% + 2%-0.56%+0.51% + 1.323+1.26%1.2)/10=1.26% 25,000 25,000 (25 / 25) =(1/10)-1=-100% (100%+1.6% +100%+0.9 +0.7 +100% +0.53+0.45 +100)/10 = 40.4% Question 2) Calculations of Standard Deviation and Coefficient of Variation Standard deviation is a measure of dispersion from the mean of a set of data. There is higher deviation if there are more data that is spread apart. It measures the volatility of an investment. The higher the deviation the higher the investment volatility (Sanghera, 2006).It is calculated by findinding the square root of the variance ∑(x-x1)2 where x1 is the mean, X1 is determined as follows; For asset X; (10 + 2.3 + 4.6 + 2.2 + 1 + 2 + 0.56 + 0.51 + 1.32 + 1.2) = 21.69 / 10 = 2.6 For asset Y; (0 + 100 + 1.6 + 100 + 0.9 + 0.7 + 100 + 0.53 + 0.45 + 100) = 404.18 /1 0 = 40.4 The mean percentage variation is the coefficient of variation. The coefficient of variation is calculated by dividing the standard deviation by the mean. Coefficient of variation = standard deviation /mean. Asset X Year X x-x1 2001 10 10 - 2.6 = 7.4 2002 2.3 2.3 - 2.6 =-0.3 2003 4.6 4.6 - 2.6 = 2 2004 2.2 2.2 - 2.6 =-0.4 2005 1 1 - 2.6 =-1.6 2006 2 2 - 2.6 =-0.6 2007 0.56 0.56 - 2.6 =-2.04 2008 0.51 0.51 - 2.6 =-2.09 2009 1.32 1.32 - 2.6=-1.28 2010 1.2 1.2 - 2. 6=-1.4 Total 21.69 1.73 Standard deviation of asset X = 1.730.5 = 1.32 Coefficient of variation of asset X =1.32/2.6 =0.5 x 100 = 50% Year X x-x1 2001 0 0 - 40.4 =- 40.4 2002 100 100 - 40.4 = 59.6 2003 1.6 1.6 - 40.4 = - 38.8 2004 100 100 - 40.4 = 59.6 2005 0.9 0.9 - 40.4 =- 39.5 2006 0.7 0.7 - 40.4 = -39.7 2007 100 100 - 40.4 = 59.6 2008 0.53 0.53 - 40.4 = - 9.87 2009 0.45 0.45 - 40.4 =- 39.95 2010 100 100 - 40.4 = 59.6 Total 404.18 0.18 Standard deviation of asset Y =0.180.5 =0.42 Coefficient of variation of asset Y 0.45/40.4 =0.01x100=1% Question No. 3 Note that the standard deviation is a measure of market volatility; investors prefer to invest in those assets with lesser or no deviation. Asset X has a higher deviation of 50% than that of Asset Y; 0.42%. Therefore, the most preferable asset is Y. Asset Y has a preferably lower market volatility (Sanghera, 2006). Therefore, investors in asset X cannot expect with certainty the expected market return since there is a very large deviation from the market norm. On the other hand, asset Y is more stable and investors can have confidence in it as it will certainly give back an accurate expected return. On that note, Stanley should therefore invest in asset Y. Question No. 4 CAPM The capital assets pricing model is used to calculate the investment risk and the investment returns expected. It is calculated by the formula r a =rf+ ba (rm - rf), ba is the beta of security, rm is the expected market return and (rm-rf) is the equity market premium (Sanghera, 2006). The risk free rate has been given as 7%, the market return is 10%, and the Betas are 1.6 for X and 1.10 for Y. Year CAPM X CAPM Y 2001 7 +1.6 ( 10 - 7) = 11.8 7+ 1.10 (0-7) = -4.2 2002 7 + 1.6 (2.3-7) =- 0.52 7 + 1.1 (100-7) = 155.8 2003 7 +1.6 (4.6-7) = 3.16 7 + 1.1 (1.6-7) = -1.64 2004 7 + 1.6 (2.2-7) = -0.68 7 + 1.1 (100-7) = 155.8 2005 7 + 1.6 (1-7) = -2.6 7 +1.1 (0.9-7) =-2.76 2006 7 + 1.6 (2-7) = -1 7 + 1.1 (0.7-7) =-3.08 2007 7 + 1.6 (0.56-7) =- 3.3 7 + 1.1 (100-7) =155.8 2008 7 + 1.6 (0.51-7) =- 3.38 7 + 1.1 (0.53-7) =-3.35 2009 7 + 1.6 (1.32-7) =-2 7 + 1.1 (0.45-7) =-3.48 2010 7 +1.6 (1.2-7) =-2.28 7 + 1.1 (100-7) =155.8 Total 4.3 609 Question No. 5 When comparing question three and four, the indication still is that asset Y is better than Asset X; therefore, from the onset, the recommendation to Stanley is to accept asset Y over asset X. Betas; According to this model (CAPM), beta is the most relevant risk measure of an investment. It measures the relative volatility of an investment. This means that it considers an individual product and evaluates at its changes in the market as compared to analyzing the changes in the entire market. That is it is investment specific, hence giving a true picture of an investment (Sanghera, 2006). The simple CAPM theory has delivered simple results. The model has proved the market theory that the reason as to why an individual investor can earn more by investing in one asset than another on average is because one asset may be riskier. In this case, the only best asset that Stanley can invest without any fear of risk is asset Y (Sanghera, 2006). Individual asset risk Beta X is 1.60 while beta Y is 1.10, should a market rise by 10% the beta for X would be 16% and 11% for Y. Should the market fall by 10%, the beta for X would also fall by 16% and beta for Y would fall by 11%. This shows that X depicts a higher risk asset. Question No. 6 CAPM Using a Risk Free Rate Of 8% and A Market Return Of 11% Year CAPM X CAPM Y 2001 8 + 1.6 (10-11) = 6.4 8 + 1.1 (0 -11) =-109.1 2002 8 + 1.6 (2.3-11) = -5.92 8 + 1.1 (100 -11) =105.9 2003 8 + 1.6 (4.6-11) = -2.24 8 + 1.1 (1.6 -11) = -2.34 2004 8 + 1.6 (2.2-11) = -6.08 8 + 1.1 (100 -11) = 105.9 2005 8 + 1.6 (1-11 )= -8 8 + 1.1 (0.9 -11) = -3.11 2006 8 + 1.6 (2-11) = -6.4 8 + 1.1 (0.7 -11) = -3.33 2007 8 + 1.6 (0.56-11) = -8.7 8 + 1.1 (100 -11) = 105.9 2008 8 + 1.6 (0.51-11) = -6.7 8 + 1.1 (0.53 -11) = -3.5 2009 8 + 1.6 (1.32-11) = -7.5 8 + 1.1 (0.45 -11) = -3.6 2010 8 + 1.6 (1.2-11) = -7.7 8 + 1.1 (100 -11) = 106 Total -3874. 299 CAPM Using a Market Return Of 9% Year CAPM X CAPM Y 2001 7 + 1.6 ( 10 - 9) =8.6 7 + 1.10 (0-9) =-5.7 2002 7 + 1.6 (2.3-9) =-3.72 7 + 1.1 (100-9) =107.1 2003 7 + 1.6 (4.6-9) =-0.04 7 + 1.1 (1.6-9) =-1.14 2004 7 + 1. 6(2.2-9) =-3.88 7 + 1.1 (100-9) =107.1 2005 7 + 1.6 (1-9) =-5.8 7 + 1.1 (0.9-9) =-1.91 2006 7 + 1.6 (2-9) =-4.2 7 + 1.1 (0.7-9) =-2.13 2007 7 + 1.6 (0.56-9) =-6.5 7 +1.1 (100-9) =107.1 2008 7 + 1.6 (0.51-9) =-1.5 7 + 1.1 (0.53-9) =-2.3 2009 7 + 1.6 (1.32-9) =-5.28 7 + 1.1 (0.45-9) =-2.4 2010 7 + 1.6 (1.2-9) =-5.48 7 + 1.1 (100-9) =107.1 Reference List Sanghera, P. 2006. PMP in depth project management professional study guide for PMP and CAPM exams, Boston, Thomson Course Technology, Retrieved from http://www.books24x7.com/marc.asp?bookid=26184 Read More