Question

Expected Return: Discrete Distribution

A stock's return has the following distribution:

Demand for the Company's Products	Probability of This Demand Occurring			Rate of Return if This   Demand Occurs (%)
Weak		0.1		-25%
Below average		0.2		-8
Average		0.4		6
Above average		0.2		30
Strong		0.1		60
		1.0

Calculate the stock's expected return. Round your answer to two decimal places.
10.3 %

Calculate the standard deviation. Round your answer to two decimal places.

???? %

I was able to answer the first question but not the second. Could you help please?

Answer 1

Compute the expected return using MS-Excel as follows:

The result of the above table is as follows:

Hence, the expected return is 10.30%.

Compute the Variance using the equation as shown below:

Standard deviation =[ (-25% - 10.30%)2 + (-8% - 10.30%)2 + (6% - 10.30%)2  + (30% - 10.30%)2 + (60% - 10.30%)2 ] / Number of observation - 1

= [ (-25% - 10.30%)2 + (-8% - 10.30%)2 + (6% - 10.30%)2  + (30% - 10.30%)2 + (60% - 10.30%)2 ] / 5 - 1

= 51.54

Hence, the variance is 51.54.

Standard deviation is the square root of Variance.

Compute the standard deviation using the equation as shown below:

Standard deviation = Variance0.5

= 51.540.5

= 7.18

Hence, the standard deviation is 7.18.