Question

Consider a sample with 10 observations of 2, 3, 10, 13, 12, 5, –1, 10, 2, and 12. Use z-scores to determine if there are any outliers in the data; assume a bell-shaped distribution. (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)

	The z-score for the smallest observation The z-score for the largest observation There are in the data.

Consider the following data for two investments, A and B:

Investment A: x¯x¯ = 7 and s = 4

Investment B: x¯x¯ = 8 and s = 6

Given a risk-free rate of 1.90%, calculate the Sharpe ratio for each investment. (Round your answers to 2 decimal places.)

Sharpe Ratio
Investment A
Investment B

Answer 1

For the given observations mean and standard deviation are calculated

2, 3, 10, 13, 12, 5, –1, 10, 2, 12

Mean:

Standard deviation:

x
2	-4.8	23.04
3	-3.8	14.44
10	3.2	10.24
13	6.2	38.44
12	5.2	27.04
5	-1.8	3.24
-1	-7.8	60.84
10	3.2	10.24
2	-4.8	23.04
12	5.2	27.04

Z-score is calculated as below

The lowest value of x is -1. Hence, the z-score for the smallest observation is given as

The highest value of x is 13. Hence, the z-score for the largest observation is given as

Since, the z-score of the smallest and largest observation are with in the range of 1.95 (limit for 95%) we can say that there are no outliers.

Final Answer:

The z-score for the smallest observation -1.52

The z-score for the largest observation 1.21

There are no outliers in the data.

2.

Hence, for the given = 7 and s = 4, the sharpe's ratio for investment A with risk free rate of 1.90% is given as

For the given = 8 and s = 6, the sharpe's ratio for investment B with risk free rate of 1.90% is given as

Final answers:

	Sharpe Ratio
Investment A	1.28
Investment B	1.02