Question

You are interested in two investment, Fidelity Capital and Income (FAGIX) , and Fidelity Low Price Stock Fund (FLPKX). The followings are their 12 month returns in 2017 that I have recorded from finance.yahoo.com :

Month	FAGIX	FLPKX
1/1/17	1.96%	2.16%
2/1/17	-0.30%	0.94%
3/1/17	1.14%	1.53%
4/1/17	0.91%	1.11%
5/1/17	-1.28%	0.64%
6/1/17	3%	2.01%
7/1/17	0.22%	0.18%
8/1/17	1.01%	-4.87%
9/1/17	1.28%	9.90%
10/1/17	-0.08%	2.92%
11/1/17	0.29%	0.42%
12/1/17	2.17%	5.90%

1. What are the average returns of the two funds?

2. What are the return volatilities of the two funds?

3. Compute the covariance and correlation between returns of the two funds.

4. Plot the returns of FLPSX against the returns of FAGIX (using Excel) . Do you see a relationship

between the two? From Fin6301, why do you think there is or is not a relation?

5. Compute the regression line: RFLPKX = α + β * RFAGIX , using the formulas in Lecture Note 1, and

plot the line on the same graph in (d). What do you observe?

6. Using regression analysis in Excel, find the linear relationship between the returns of the two

funds, i.e. regressing returns of FLPKX on returns of FAGIX.

Answer 1

Answer
	Month	FAGIX (A)	A - 0.86 - Column C	Square	FLPKX (B)	B - 1.90 - Column D	Square	C * D
	1/1/2017	1.96%	1.10	1.21	2.16%	25.67%	0.07	0.28
	2/1/2017	-0.30%	(1.16)	1.35	0.94%	-96.33%	0.93	1.12
	3/1/2017	1.14%	0.28	0.08	1.53%	-37.33%	0.14	(0.10)
	4/1/2017	0.91%	0.05	0.00	1.11%	-79.33%	0.63	(0.04)
	5/1/2017	-1.28%	(2.14)	4.58	0.64%	-126.33%	1.60	2.70
	6/1/2017	3%	2.14	4.58	2.01%	10.67%	0.01	0.23
	7/1/2017	0.22%	(0.64)	0.41	0.18%	-172.33%	2.97	1.10
	8/1/2017	1.01%	0.15	0.02	-4.87%	-677.33%	45.88	(1.02)
	9/1/2017	1.28%	0.42	0.18	9.90%	799.67%	63.95	3.36
	10/1/2017	-0.08%	(0.94)	0.88	2.92%	101.67%	1.03	(0.96)
	11/1/2017	0.29%	(0.57)	0.32	0.42%	-148.33%	2.20	0.85
	12/1/2017	2.17%	1.31	1.72	5.90%	399.67%	15.97	5.24
	Average Return	0.86%	0.00%	15.33	1.90%	0.00%	135.37	12.76
A)	Average Return =		Total Return / No of period
	Average return of A		0.86%
	Average return of B		1.90%
B)	Volatility of A		(Total of Squares/n-1)^1/2
			1.18
	Volatiity of B		(Total of Squares/n-1)^1/2
			3.51
C)	Covariacne = Total (X -Mean of X) (Y - Mean of Y) / n-1
			12.76 / 12-1
			1.16
C)	Correlation		Covariance / (S.D of A * S.D of B)
			1.16 / (1.18*3.51)
			0.28
D)	There is positive relation between Fidelity capital and stock fund as they have the positive correlation of 0.26

Thanks & regards,

Devendra Agarwal