Question

    

1. A stock records the following returns over the last 6 months.

1. What are the arithmetic returns for the stocks?
2. What are the geometric returns for the stocks?
3. What are the variances for the stocks?
4. What are the standard deviations for the stocks?
5. Compute the coefficient of variation of stocks.
6. Which stock would you choose? Why?

YEAR	Returns of the Stock 1                  R	Variances        σ2	YEAR	Returns of the Stock 2                  R	Variances        σ2
1	6.31%		1	12.25%
2	5.98%		2	12.98%
3	5.74%		3	12.86%
4	5.12%		4	9.76%
5	4.76%		5	-3.21%
6	4.01%		6	4.01%
7	-2.57%		7	4.21%
8	3.50%		8	5.98%
SUM			SUM
AVERAGE			AVERAGE

Answer 1

	Arithmetic Mean Return =SUM of(Return))/(number of data)
	Variance of Return =Sum of( (Deviation ^2))/(Number of sample data-1)
	Deviation =Return -Mean Return
	Standard Deviation of Return =Square Root of Variance of Return
	ANALYSIS OF STOCK 1
		R1	D1=R1-4.11	E1=D1^2
	Year	Return(%)	Deviation(%)	Deviation Squared(%%)	Return	1+Return
	1	6.31	2.20	4.84	0.0631	1.0631
	2	5.98	1.87	3.50	0.0598	1.0598
	3	5.74	1.63	2.66	0.0574	1.0574
	4	5.12	1.01	1.02	0.0512	1.0512
	5	4.76	0.65	0.42	0.0476	1.0476
	6	4.01	-0.10	0.01	0.0401	1.0401
	7	-2.57	-6.68	44.62	-0.0257	0.9743
	8	3.50	-0.61	0.37	0.035	1.035
	SUM	32.85	SUM E1	57.44
	Average/Mean=SUM/8=32.85/8	4.11	%
	Variance=SUME1/(8-1)	8.21	%%
	Standard Deviation of return	2.86	%	(Square Root(8.21)
	Coefficient of Variation =Standard Deviation/Mean
	Coefficient of Variation	0.70	(2.86/4.11)
P	Product of (1+Return)s	1.376025	(1.0631*1.0598*1.0574*1.0512*1.0476*1.0401&0.9743*1.035)
	Geometric Average Return =(P^(1/8))-1
	Geometric Average Return =	0.0407066
	Geometric Average Return =	4.07%
	ANALYSIS OF STOCK 2
		R2	D2=R2-7.36	E2=D2^2
	Year	Return(%)	Deviation(%)	Deviation Squared(%%)	Return	1+Return
	1	12.25	4.89	23.91	0.1225	1.1225
	2	12.98	5.62	31.58	0.1298	1.1298
	3	12.86	5.50	30.25	0.1286	1.1286
	4	9.76	2.40	5.76	0.0976	1.0976
	5	-3.21	-10.57	111.72	-0.0321	0.9679
	6	4.01	-3.35	11.22	0.0401	1.0401
	7	4.21	-3.15	9.92	0.0421	1.0421
	8	5.98	-1.38	1.90	0.0598	1.0598
	SUM	58.84	SUM E1	226.28
	Average/Mean=SUM/8=58.84/8	7.36	%
	Variance=SUME2/(8-1)	32.33	%%
	Standard Deviation of return	5.69	%	(Square Root(32.33)
	Coefficient of Variation =Standard Deviation/Mean
	Coefficient of Variation	0.77	(5.69/7.36)
P	Product of (1+Return)s	1.7466704	(1.1255*1.1298*1.1286*1.0976*0.9679*1.0401*1.0421*1.0598)
	Geometric Average Return =(P^(1/8))-1
	Geometric Average Return =	0.0722014
	Geometric Average Return =	7.22%
	Stock 1 should be chosen
	It has lower Coefficient of Variation
	This means it has lower Risk to Return Ratio