Question

Explain why the following annual results for two stocks would be very unlikely to occur.

	Mean	Standard Deviation
Stock A	4.4%	5.1%
Stock B	7.2%	3.6%

If these were predicted figures for the coming year and you were asked to predict a more appropriate standard deviation for Stock A based on an assumption of constant risk-return ratio, what figure would you predict?

Answer 1

In general, mean (expected return) and standard deviation (risk) shares a direct relationship that is if risk increases, expected return or mean will also increase and vice versa. In the given problem, for Stock A SD is 5.1% and Mean is 4.40% whereas for Stock B Mean is 7.20% and SD is 3.6%. As the SD or risk has decreased from 5.10% to 3.6% mean should also decrease but it is increasing which is very unlikely.

Constant risk return ratio using stock B= Risk/ Return

                                                                           = 3.60% /7.20%

                                                                           = 0.50

Standard Deviation for Stock A = Constant risk return ratio x Mean

                                                            = 0.50 x 4.40%

                                                            = 2.20%

                                            

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