Question

Calculate the​ 95% prediction intervals for the four different investments included in the following table. Small Stocks ​S&P 500 Corporate Bonds ​T-Bills Average Return 18.37​% 11.84​% 6.47​% 3.46​% Standard Deviation of returns 38.79​% 20.01​% 6.98​% 3.14​% A.The​ 95% prediction interval of small stocks is between ?​% and ?​%. (Round to two decimal places and put the lower number​ first.) B. The​ 95% prediction interval of the​ S&P500 is between ?​% and ?%.(Round to two decimal places and put the lower number​ first.) C. The​ 95% prediction interval of corporate bonds is between ?​% and ?%. (Round to two decimal places and put the lower number​ first.) D. The​ 95% prediction interval of​ T-bills is between ?% and ?% (Round to two decimal places and put the lower number​ first.)

Answer 1

Given :

Investments	Average Returns	Standard Deviation
Small Stocks	18.37%	38.79%
S&P 500	11.84%	20.01%
Corporate Bonds	06.47%	06.98%
T- Bills	03.46%	03.14%

Solution :

At 95% prediction interval, the expected range of returns will be calculated by the formula as,

Lower Bound = Mean - [Z value] * [Standard Deviation] , here Z value = 2

Upper Bound = Mean + [Z value] * [Standard Deviation] , here Z value =2

At 95% prediction interval, Z value = 2

A) The 95% prediction interval of Small stock is -59.21% and 95.95%

Lower bound = 18.37 - [ 2* 38.79] = 18.37 - 77.58 = -59.21

Upper Bound = 18.37 + [ 2* 38.79] = 18.37+ 77.58 =  95.95

B) The 95% prediction interval S&P 500 is -28.18% and 51.86%

Lower bound = 11.84 - [ 2* 20.01] = 11.84 - 40.02 = -28.18

Upper Bound = 11.84 + [ 2* 20.01] = 11.84 + 40.02 = 51.86

C) The 95% prediction interval of Corporate Bonds is -07.49% and 20.43%

Lower bound = 06.47 - [ 2* 06.98] = 06.47 - 13.96 = -07.49

Upper Bound = 06.47 + [ 2* 06.98] = 06.47+13.96 = 20.43

D) The 95% prediction interval of T-Bills is -02.82% and 09.74%

Lower bound = 03.46 - [ 2* 03.14] = 03.46 - 06.28  = -02.82

Upper Bound = 03.46 +[ 2* 03.14] = 03.46 + 06.28 = 09.74

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