Question

18. There are four scenarios with probabilities 0.05, 0.25, 0.4 and 0.3. A stock fund has returns -37, -11, 14, 30 respectively, while a bond fund has returns -9, 15, 8, -5 respectively. The correlation between the two funds is (a) -0.49 (b) 0.49 (c) 0.89 (d) -0.89

Answer 1

Calculation of expected return:

Probability	Return of A	Expected return of A Probability*return of A	Return of bond	Expected return of bond Probability*return of Bond
0.05	-37	-1.85	-9	-0.45
0.25	-11	-2.75	15	3.75
0.4	14	5.6	8	3.2
0.3	30	9	-5	-1.5
	Expected return	10		5

Calculation of covariance of stock and bond:

Probability (1)	Return of A (2)	Return of A-Expected return of A (3)	Return of bond (4)	Return of bond -Expected return of bond (5)	Covariance of stock and bond (6) (1*3*5)
0.05	-37	-37-10 = -47	-9	-9-5 = -14	32.9
0.25	-11	-11-10 = -21	15	15-5 =10	-52.5
0.4	14	14-10 = 4	8	8-5 =3	4.8
0.3	30	30-10 = 20	-5	-5-5 = -10	-60
				Covariance of stock and bond	-74.8

Calculation of standard deviation of stock and bond:

Standard deviation of stock:

Probability (1)	Return of A- Expected return of A (2)	Square of Return of A- Expected return of A (3)	Variance of Stock (4) (1*3)
0.05	-47	-47*-47 = 2209	110.45
0.25	-21	-21*-21 =441	110.25
0.4	4	4*4 =16	6.4
0.3	20	20*20 =400	120
		Variance of Stock	347.1

* Return of A- Expected return of A, For calculation see covariance table

Standard deviation of stock = square root of Variance

= square root of 347.1 = 18.63

Standard deviation of Bond:

Probability (1)	Return of bond- Expected return of bond (2)	Sqaure of return of bond - expected return of bond (3)	Variance of bond (4) (1*3)
0.05	-14	-14*-14=196	9.8
0.25	10	10*10=100	25
0.4	3	3*3 =9	3.6
0.3	-10	-10*-10=100	30
		Variance of Bond	68.4

* for calculation of return of bond- expected return of bond, see the covariance table

Standard deviation of bond = square root of Variance

= square root of 68.4 = 8.27

Correlation between two funds = covariance of bond and stock/ standard deviation of bond*standard deviation of stock

= -74.8/8.27*18.63

=-74.8/154.0701

= -0.485

Approxiamately -0.49

Correct Answer : A (-0.49)