Question

IncorrectQuestion 4

0 / 1 pts

Use the following information:

	Probability	w1	w2	w3
state1	0.3333333	15.00%	8.00%	3.00%
state2	0.3333333	9.00%	5.00%	8.00%
state3	0.3333333	12.00%	7.00%	4.00%
% wealth invested		33.3333%	33.3333%	33.3333%

What is the correlation coefficient involving the first two assets?:

  

between 75% and 80%

  

less than 75%

  

greater than 90%

  

between 85% and 90%

Answer 1

Select - (b) Less than 75%

X	Y	P	X*P	Y*P	Dx	Dy	P*DxDy	P*Dx2	P*Dy2
15	8	0.333333	5	2.666666	3	-1.66667	-1.66667	3	0.925926
9	5	0.333333	3	1.666667	-3	-3.66667	3.666667	3	4.481482
12	7	0.333333	4	2.333333	0	-2.66667	0	0	2.370371
			12	6.666666		Total =	2	6	7.777779
							SD =	2.44949	2.788867
							r	0.29277

Let ........... X and Y represents the returns of w1 and w2 respectively .......... P = Probability

Sum ( X*P) = 12 is the expected return on X and Sum (Y*P ) = 6.6666666 is the expected return on Y

Dx = X - expected return .......... i.e deduct 12, from each item of X

Dy = Y - expected retun of Y ....... i.e deduct 6.6666666 from each item of Y

Total of P*Dx2 ..... will given the variance = 6

Standard deviation ( X ) = Square root ( varaiance ) = Square root ( 6 ) = 2.44949

Standard deviation (Y) = Squre root (7.777779) = 2.788867

Finally ................. r = Correlation coeffficent = Sum ( P*Dx*Dy) / SD(X) * SD(Y)

= 2 / ( 2.44949 * 2.788867 )

= 0.2928 ............ OR .............29.28%

This is less than 75%