Question

You observe a portfolio for five years and determine that its average return is 11.3​% and the standard deviation of its returns in 19.7​%. Would a​ 30% loss next year be outside the​ 95% confidence interval for this​ portfolio?

Answer 1

-28.1%

Step-by-step explanation:

Calculation for what would a​ 30% loss next year be outside the​ 95% confidence interval for the​ portfolio

The standard deviation of 95% confident will be 2

The first step is to find the Upper tail using this formula

Upper tail= Average return percentage +(Standard deviation of 95% confident *Standard deviation of its returns)

Let plug in the formula

Upper tail=0.113+(2*0.197)

Upper tail =0.113+0.394

Upper tail=0.507*100

Upper tail =50.7%

Second step is to find the Lower tail using this formula

Lower tail=Average return percentage -(Standard deviation of 95% confident *Standard deviation of its returns)

Let plug in the formula

Upper tail=0.113-(2*0.197)

Upper tail =0.113-0.394

Upper tail=-0.281*100

Upper tail =28.1%

Based on the above calculation the lower tail was -28.1% which means that it wouldn't in any way loss more than the 30% of it value next year outside the​ 95% confidence interval for the portfolio