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 18.11​% 11.73​% 5.12​% 3.76​% Standard Deviation of returns 38.22​% 19.88​% 7.21​% 3.34​% The​ 95% prediction interval of small stocks is between ______​% and _____%.

Answer 1

The 95% prediction interval of small stocks calculated as follows:

Formula to compute the range of returns at a 95% confidence level is

95% prediction interval range = Average ± (Z* X Standard deviation)

Given,

Average return fot small stocks = 18.11%

Standard deviation fot small stocks = 38.22%

A 95% prediction interval multiplier (Z*) = 1.96

Therefore,

95% prediction interval range = Average ± (Z* X Standard deviation)

95% prediction interval range = 18.11% ± ( 1.96 x 38.22%)

= 18.11% ± 74.91%

= (–56.80% , 93.02%)

95% prediction interval range of small stocks is (–56.80% , 93.02%)

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