Covariance between large company stock and risk-free bills

Reference no: EM13216642

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: EM13216642

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