Question

Consider the following table for the total annual returns for a given period of time.

Series	Average return		Standard Deviation
Large-company stocks	10.8	%	21.1	%
Small-company stocks	16.4		33.0
Long-term corporate bonds	6.2		8.4
Long-term government bonds	6.1		9.4
Intermediate-term government bonds	5.6		5.7
U.S. Treasury bills	3.8		3.1
Inflation	3.1		4.2

Requirement 1:

What range of returns would you expect to see 95 percent of the time for large-company stocks? (Negative amount should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Expected range of returns

% to   %

Requirement 2:

What about 99 percent of the time? (Negative amount should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Expected range of returns

% to   %

Answer 1

Part 1

For 95% probability, range would fall within +-2 SD.

Range = Average return – 2 SD   to average return + 2 SD

            = 10.80% - 2 x 21.10%   to 10.80% + 2 x 21.10%  

            = -31.40% to 53%

Part 2

For 99% probability, range would fall within +-3 SD.

Range = Average return – 3 SD   to average return + 3 SD

            = 10.80% - 3 x 21.10%   to 10.80% + 3x 21.10%  

            = -52.50% to 74.10%