Question

If returns of​ S&P 500 stocks are normally​ distributed, what range of returns would you expect to see​ 95% of the​ time? Base your answer on the information below. Small Stocks ​S&P 500 Corporate Bonds ​T-Bills Average Return 18.83​% 11.44​% 6.81​% 3.84​% Standard Deviation of returns 38.81​% 20.07​% 6.69​% 3.25​%

Answer 1

Answer: Between -28.7% and 51.58%

Explanation:

95% of the time would mean a 95% interval which would mean that it is between -2 and +2 standard deviation as it is Normally distributed.

We can therefore use the following formula to find the confidence interval,

= Average return + (2 * standard deviation) and,

= Average - return (2 * standard deviation)

= 11.44% + (2*20.07%)

= 0.5158

= 51.58%

and

= 11.44% - (2*20.07%)

= -0.287

= -28.7%

Between -28.7% and 51.58% is the range of returns expected to be seen​ 95% of the​ time.

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