1. Compute the correlation and covariance between the return on company #12 and
ID: 2769516 • Letter: 1
Question
1. Compute the correlation and covariance between the return on company #12 and the return on the equally-weighted portfolio.
2. Compute the beta of Company #12 using the information you have collected.
3. Now using the beta you created for Company #12, compute the required rate of return using the Capital Asset Pricing Model (CAPM), assuming that the average market return is the return of your equally-weighted portfolio and the risk-free rate of return is 2.5%.
4. If you were told that analysts estimate Company #12 will have a 5% rate of return next year, would you buy the stock? Why or why not?
Comp. #1 Comp. #2 Comp. #3 Comp. #4 Comp. #5 Comp. #6 Comp. #7 Comp. #8 Comp. #9 Comp. #10 Comp. #11 Comp. #12 Return Return Return Return Return Return Return Return Return Return Return Return Return 2012 3.60% -10.04% -1.38% 5.25% -3.50% 0.14% 5.33% -2.55% 14.18% 14.76% -3.35% 0.10% 1.88% 2011 54.44% 23.22% 0.55% 15.35% 0.22% 22.32% 23.55% 23.00% 36.36% 42.15% 9.90% -0.10% 20.91% 2010 -29.30% -18.92% -44.54% -22.24% -17.66% 11.87% -1.93% -5.68% -39.86% 6.04% 5.36% -9.57% -13.87% 2009 -37.57% -11.88% -6.00% -13.93% -16.09% 6.23% -15.42% -55.35% -5.78% 9.63% 13.75% 33.93% -8.21% 2008 -11.00% -11.64% -9.39% -4.00% -2.80% 12.18% 3.33% -3.33% 4.18% -4.76% -7.85% -5.33% -3.37% 2007 7.11% 13.59% 0.52% 26.35% -6.06% 23.92% 22.90% 4.23% -46.36% 59.17% 6.02% -37.79% 6.13% 2006 20.91% 18.92% -44.54% 2.24% -17.66% 11.87% 1.93% -5.68% 39.86% 6.04% 5.36% 9.57% 4.07% 2005 16.02% 11.88% -6.00% -13.93% 16.09% 6.23% 15.42% 55.35% -5.78% -9.63% 13.75% 33.93% 11.11% 2004 55.35% 23.14% 43.33% 23.33% 0.33% -1.08% -1.44% 38.53% 35.44% 9.40% -15.05% 49.56% 21.74% 2003 -11.56% 23.00% -38.30% -3.53% 5.07% -6.58% -5.12% -13.43% -12.18% -24.68% -7.69% -37.39% -11.03% 2002 11.52% 39.67% -28.46% -20.72% -6.22% -8.25% 22.70% -2.60% -32.87% -13.16% -34.55% -20.56% -7.79% 2001 -0.23% -1.48% -51.99% 7.35% 16.54% 1.83% 32.25% 47.38% 11.10% 2.96% -51.00% -14.48% 0.02% 2000 3.10% 13.56% -7.33% -11.03% 17.69% 44.92% 0.93% -3.72% -9.20% -4.87% 298.67% 6.04% 29.06% 1999 -3.43% -7.16% 47.74% 2.39% 4.27% 31.57% 19.44% -3.90% 12.12% 53.37% -19.46% 62.66% 16.63% 1998 31.48% 45.52% 53.49% 29.15% 58.33% 67.99% 25.12% 0.44% 26.83% 50.67% 40.62% 6.72% 36.36% Average Return 7.36% 10.09% -6.15% 1.47% 3.24% 15.01% 9.93% 4.85% 1.87% 13.14% 16.97% 5.15% 6.91% Standard deviation 26.24% 19.60% 33.39% 16.57% 19.11% 20.62% 13.93% 27.19% 27.31% 26.06% 80.91% 29.33% 15.29%Explanation / Answer
Covariance
The covariance is the measure of how two assets relate (move) together. If the covariance of the two assets is positive, the assets move in the same direction. For example, if two assets have a covariance of 0.50, then the assets move in the same direction. If however the two assets have a negative covariance, the assets move in opposite directions. If the covariance of the two assets is zero, they have no relationship.
Covariance(a,b)=sum of (Ra-Average Ra) (Rb-Average Rb)/Number of periods
Covariance=2693.2136/15=1.79
Correlation
The correlation coefficient is the relative measure of the relationship between two assets. It is between +1 and -1, with a +1 indicating that the two assets move completely together and a -1 indicating that the two assets move in opposite directions from each other.
Correlation (a,b)= Covariance(a,b)/(Standard deviation of a )(Standard deviation of b)
In the above question, we need to calculate the covariance between portfolio return and company 12 as well as the correlation coefficient between portfolio return and company return 12.
Correlation coefficient=Covariance of comp 12 and portfolio/(Standard deviation comp12 * Standard deviation portfolio )
Correlation coefficient =1.79/(29.33*15.29)Correlation coefficient=0.4
Beta=Covariance (comp 12 return, portfolio return)/Variance of portfolio return
Variance of portfolio return=Square of standard deviation of portfolio return
Standard deviation of portfolio=15.29
Variance of portfolio=233.7841
Beta=0.00765
Required return=Risk free return+ Beta(Market return-Risk free rate)
Required return=2.5 + 0.00765(6.91-2.5)=2.533%
If the rate of return is estimated to be 5% next year,a buy recommendation will be given.
As the required return on comp12 is 2.533%, a rate of 5% means that the stock is performing good and hence offers a profitable investment.
Year Return company 12 Return on portfolio Deviation comp 12=R-Average return Deviation portfolio=Return-Average return Deviation com 12 * Deviation portfolio 2012 0.10% 1.88 -5.05% -5.03 25.4015 2011 -0.10% 20.91 -5.25% 14 -73.5 2010 -9.57% -13.87 -14.72% -20.78 305.8816 2009 33.93% -8.21 28.78% -15.12 -435.1536 2008 -5.33% -3.37 -5.33% -10.28 54.7924 2007 -37.79% 6.13 -42.94% -0.78 33.4932 2006 9.57% 4.07 4.42% -2.84 -12.5528 2005 33.93% 11.11 28.78% 4.2 120.876 2004 49.56% 21.74 44.41% 14.83 658.6003 2003 -37.39% -11.03 -42.54% -17.94 763.1676 2002 -20.56% -7.79 -25.71% -14.7 377.937 2001 -14.48% 0.02 -19.63% -6.89 135.2507 2000 6.04% 29.06 6.04% 22.15 133.786 1999 62.66% 16.63 57.51% 9.72 558.9972 1998 6.72% 36.36 1.57% 29.45 46.2365 Average return 5.15% 6.91 Total 2693.2136 Covariance=2693.2136/15 Covariance 1.79 Correlation coefficient=Covariance of comp 12 and portfolio/(Standard deviation comp12 * Standard deviation portfolio ) Correlation coefficient =1.79/(29.33*15.29) Correlation coefficient 0.4Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.