Calculating the Variance and Standard Deviation Suppose the Supertech Company and the Hyperdrive Company have experienced the following returns in the last four years:

Question

Calculating the Variance and Standard Deviation

Suppose the Supertech Company and the Hyperdrive Company have experienced the following returns in the last four years:

Year	Supertech Return	Hyperdrive Return
2008	-.20	.05
2009	.50	.09
2010	.30	-.12
2011	.10	.20

What are the average returns? The variances? The standard deviations? Which investment was more volatile?

Accepted Answer

To calculate the average returns, we add up the returns and divide by 4. The results are:

Supertech average return [latex]=\overline{R}={.70}/{4}=.175[/latex]

Hyperdrive average return [latex]=\overline{R}={.22}/ {4}= .055 [/latex]

To calculate the variance for Supertech, we can summarize the relevant calculations as follows:

	(1)	(2)	(3)	(4)
Year	Actual Return	Average Return	Deviation (1) - (2)	Squared Deviation
2008	-.20	.175	-.375	.140625
2009	.50	.175	.325	.105625
2010	.30	.175	.125	.015625
2011	.10	.175	-.075	.005625
Totals	[latex]\underline{\underline{.70} }[/latex]		[latex]\underline{\underline{.000} }[/latex]	[latex]\underline{\underline{.267500} }[/latex]

Because there are four years of returns, we calculate the variance by dividing .2675 by (4 - 1) = 3:

	Supertech	Hyperdrive
Variance (σ²)	.2675/3 = .0892	.0529/3 = .0176
Standard deviation (σ)	[latex]\sqrt{.0892}=.2987[/latex]	[latex]\sqrt{.0176}=.1327[/latex]

For practice, verify that you get the same answer as we do for Hyperdrive. Notice that the standard deviation for Supertech, 29.87 percent, is a little more than twice Hyperdrive’s 13.27 percent; Supertech is thus the more volatile investment.

Question 12.2: Calculating the Variance and Standard Deviation Suppose the ...

Related Answered Questions

Calculating the Geometric Average Return Calculate the geometric average return for S&P 500 large-cap stocks for the first five years in Table 12.1, 1926–1930. ...

Verified Answer:

Recent Return History Use Table 12.1 to calculate the average return over the years 1996 through 2000 for large-company stocks, long-term government bonds, and Treasury bills. ...

Verified Answer:

More Recent Return History Calculate the standard deviation for each security type using information from Problem 12.1. Which of the investments was the most volatile over this period? ...

Verified Answer:

More Geometric Averages Take a look back at Figure 12.4 . There, we showed the value of a $1 investment after 85 years. Use the value for the large-company stock investment to check the geometric average in Table 12.4. ...

Verified Answer:

Verified Answer:

Calculating Returns Suppose you bought some stock at the beginning of the year for $25 per share. At the end of the year, the price is $35 per share. During the year, you got a $2 dividend per share. This is the situation illustrated in Figure 12.3. What is the dividend yield? The capital gains ...

Verified Answer: