Question

The S&P 500 and Nohr Corp had the following returns over the past five years

Year        S&P 500               Nohr

1. .12                     .23
2. .01                     -.05
3. .18                     .20
4. .09                     .12
5. .10                     .20

a. What was the mean AND standard deviation of returns (population version) for Nohr for the 5 years?

b. What was the beta of Nohr relative to the S&P 500?

                 

c. What was the geometric mean return for Nohr for the 5 years?

Answer 1

(a):

	Nohr
	0.23
	-0.05
	0.2
	0.12
	0.2
Mean	0.1400
Standard deviation	0.1018

Thus mean = 14.00% and standard deviation = 10.18%

Formula:

	Nohr
	0.23
	-0.05
	0.2
	0.12
	0.2
Mean	=AVERAGE(D25:D29)
Standard deviation	=STDEVP(D25:D29)

(b):

	S&P 500	Nohr
	0.12	0.23
	0.01	-0.05
	0.19	0.2
	0.09	0.12
	0.1	0.2
Variance of Nohr		0.01036
Covariance of Nohr and S&P 500	0.0049
Beta = covariance/variance	0.47

Formula:

	S&P 500	=D24
	0.12	=D25
	0.01	=D26
	0.19	=D27
	0.09	=D28
	0.1	=D29
Variance of Nohr		=VAR.P(D36:D40)
Covariance of Nohr and S&P 500	=COVARIANCE.P(D36:D40,C36:C40)
Beta = covariance/variance	=C43/D42

(c) Geometric mean = [(1+0.23)*(1-0.05)*(1+0.2)*(1+0.12)*(1+.20)]^(1/5) – 1

= 13.51%