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What is the covariance between large company stocks and

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Reference no: EM13382453

What is the covariance between large company stocks and risk-free Treasury Bills? Another measure of how they move together is the correlation. The closer the number is to 1 (100%), the greater the two variables track each other.









Finance Concepts:








Covariance is a statistical calculation that tells us how closely two variables move together.


Covarince(x,y) = cov(x,y) = 1/n((∑(Xi - Xbar)(Yi - Ybar))




Where n is the number of returns, Xi and Yi are individual returns and Xbar and Ybar are the average of the X and Y returns respectively.











Time Series Table of Historical Total Returns:















Year   Large Co Stocks   Treasury Bills   Consumer Price Index


1990   -0.0313   0.0785   0.0610


1991   0.3053   0.0571   0.0306


1992   0.0762   0.0357   0.0289


1993   0.1007   0.0308   0.0275


1994   0.0127   0.0415   0.0268


1995   0.3780   0.0564   0.0253


1996   0.2274   0.0512   0.0332


1997   0.3343   0.0522   0.0170


1998   0.2813   0.0506   0.0161


1999   0.2103   0.0485   0.0269





















Steps:








1. To calculate the covariance between Large Comapany Stocks and Treasury Bills for the 1990-1999 period, we need to find the average returns.












Calulate:









Average Return Large Stocks  















Average Return T-Bills  
























Use the average function:  =average(E21:E30) for large stks for example


The average return on T-Bills was 5.03% for the years 1990-1999.












2. The next step is to find the difference between the individual returns and the average returns


for each year. Subtract the average return from the actual return for each year for both  


the large company stocks and the T-Bills.  















In F53 enter:  = D53-$G$37. In G53 enter =E53-$G$39. Copy.



In I53 we want to multiply the differences.  Enter: =F53*G53.  Copy.












Year Large Co Stocks Treasury Bills Large          minus average T-Bills minus average   Diff Large Times Diff T-bill


1990 -0.0313 0.0785        


1991 0.3053 0.0574        


1992 0.0762 0.0357        


1993 0.1017 0.0308        


1994 0.0127 0.0415        


1995 0.3780 0.0564        


1996 0.2274 0.0512        


1997 0.3343 0.0522        


1998 0.2813 0.0506        


1999 0.2103 0.0485        





















3.   The formula:








Covarince(x,y) = cov(x,y) = 1/n((∑(Xi - Xbar)(Yi - Ybar))


 We have found (Xi - Xbar)(Yi - Ybar) in column I.














  Next, sum the column of the multiplication:     Enter  =sum(I53:I62)   =>    












  Then, we divide by the number of years (observations), which is 10.






  Enter =J69/9  =>
 












The result is that the covariance between large stock and T-Bills (risk-free rate) is 0.0001074


For practical purposes, the covariance is zero. Note that for historical returns we divide by n (not n-1). 











4.   We can find the correlation between large stocks and T-Bills.  



  The Formula:    Correlation coefficient  = cov(x,y) / (sx*sy)



  where sx and sy are the standard deviations of the Large stocks (x) and T-Bills (y).


  Correlation is the tendency of two variables to move together, and the correlation coefficient


  measures this tendency. Standard Deviation is the square root of the variance.












 A. Covarance of large stocks and T-Bills  =>     from J72












 B.  We need to find the standard deviations by using the formula:  =stdevp(range)


standard deviations of Large Co stock ==>
 



standard deviations of T-Bills    ===>
 













C. Multiply the two standard deviations=>                   =H86*H87






















Correlation between large stocks and T-Bills is ==>  




   =H83 / H89   (Cov / (stdevStk  *  stdevT-B))













What meaning does this have?  We know that the closer the correlation is to 100% (or 1), the


more the two variables track each other.  In this case we see that the correlation


between large stock returns and Treasury returns is only 5.76%, which is very, very slight.
    This has portfolio diversification and risk reduction implications.    
Test Your Skills:








The returns for the large stocks and the CPI have been copied to the table below.

We can find their covariance and correlation using Excel formulas..












To find their covariance enter:  =Covar(D109:D118, E109:E118) ==>  











To find their correlation enter:  =(Covar(D109:D118,E109:E118))/(stdevp(D109:D118)*(stdevp(E109:E118)))






















Year Large Co Stocks Consumer Price Index
==>  



1990 -0.0313 0.0610






1991 0.3053 0.0306






1992 0.0762 0.0289






1993 0.1017 0.0275






1994 0.0127 0.0268






1995 0.3780 0.0253






1996 0.2274 0.0332






1997 0.3343 0.0170






1998 0.2813 0.0161






1999 0.2103 0.0269




Reference no: EM13382453

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