Variance and Standard Deviation Paper

13. Variance and Standard Deviation (expected). Using the data from problem 13, calculate the variance and standard deviation of the three investments, stock, corporate bond, and government bond. If the estimates for both the probabilities of the economy and the returns in each state of the economy are correct, which investment would you choose considering both risk and return? Why?

ANSWER

Variance of Stock = 0.10 x (0.25 – 0.033)2 + 0.15 x (0.12 – 0.033)2 + 0.50 x (0.04 – 0.033)2 + 0.25 x (-0.12 – 0.033)2

= 0.10 x 0.0471 + 0.15 x 0.0076 + 0.50 x 0.0000 + 0.25 x 0.0234

= 0.0047 + 0.0011 + 0.0000 + 0.0059 = 0.0117 or 1.17%

Standard Deviation of Stock = (0.0117)1/2 = 0.1083 or 10.83%

Variance of Corp. Bond = 0.10 x (0.09 – 0.052)2 + 0.15 x (0.07 – 0.052)2 + 0.50 x (0.05 – 0.052)2 + 0.25 x (0.03 – 0.052)2

= 0.10 x 0.0014 + 0.15 x 0.0003 + 0.50 x 0.0000 + 0.25 x 0.0005

= 0.0001 + 0.0000 + 0.0000 + 0.0001 = 0.000316 or 0.00316%

Standard Deviation of Corp. Bond = (0.000316)1/2 = 0.017776 or 1.78%

Variance of Gov. Bond = 0.10 x (0.08 – 0.042)2 + 0.15 x (0.06 – 0.042)2 + 0.50 x (0.04 – 0.042)2 + 0.25 x (0.02 – 0.042)2

= 0.10 x 0.0014 + 0.15 x 0.0003 + 0.50 x 0.0000 + 0.25 x 0.0005

= 0.0001 + 0.0000 + 0.0000 + 0.0001 = 0.000316 or 0.0316%

Standard Deviation of Gov. Bond = (0.000316)1/2 = 0.017776 or 1.78%

The best choice is the corporate bond. First comparing the corporate bond and the stock, the corporate bond has a higher expected return and a lower variance (standard deviation). Second comparing the corporate bond and the government bond the corporate bond has a higher return and the same variance (standard deviation). This result is due to the low probabilities of “good” economic states where the stock performs