The countries of Stabilato and Variato have the following average returns and standard deviations for their stocks, bond, and short-term government securities. What range of returns should you expect to earn 95 percent of the time for each asset class if you invested in Stabilato’s securities? From investing in Variato’s securities?

STABILATO AVERAGE STANDARD ASSET RETURN DEVIATION Stocks 8% 3%
Bonds 5% 2%
Short- term government debt 3% 1%

VARIATO AVERAGE STANDARD ASSET RETURN DEVIATION
Stocks 15% 13%
Bonds 10% 8%
Short- term government debt 6% 3%

To determine the range of returns you should expect to earn 95 percent of the time for each asset class in Stabilato and Variato, we need to use the concept of confidence intervals.

A confidence interval represents the range of values within which we can be confident that the true value (in this case, the return) lies. A 95 percent confidence interval means that we expect the true return to fall within this range 95 percent of the time.

For Stabilato:

1. Stocks:
The average return is 8% with a standard deviation of 3%. To calculate the 95% confidence interval, we can use the formula:
95% Confidence Interval = Average Return ± (1.96 * Standard Deviation)

95% CI for Stocks = 8% ± (1.96 * 3%)
= 8% ± 5.88%
= (8% - 5.88%, 8% + 5.88%)
= (2.12%, 13.88%)

Therefore, for stocks in Stabilato, you can expect to earn a return within the range of 2.12% to 13.88% with 95% confidence.

2. Bonds:
Following the same calculation, the 95% confidence interval for bonds in Stabilato would be:
(5% - 2.94%, 5% + 2.94%)
(2.06%, 7.94%)

3. Short-term government debt:
The 95% confidence interval for short-term government debt in Stabilato would be:
(3% - 1.96%, 3% + 1.96%)
(1.04%, 4.96%)

For Variato:

1. Stocks:
Using the same formula, the 95% confidence interval for stocks in Variato is:
(15% - 1.96 * 13%, 15% + 1.96 * 13%)
(-10.56%, 40.56%)

2. Bonds:
The 95% confidence interval for bonds in Variato is:
(10% - 1.96 * 8%, 10% + 1.96 * 8%)
(-4.68%, 24.68%)

3. Short-term government debt:
The 95% confidence interval for short-term government debt in Variato is:
(6% - 1.96 * 3%, 6% + 1.96 * 3%)
(-0.88%, 12.88%)

Therefore, for stocks, bonds, and short-term government debt in Stabilato and Variato, the respective ranges of returns you should expect to earn 95% of the time are as follows:

Stabilato:
- Stocks: 2.12% to 13.88%
- Bonds: 2.06% to 7.94%
- Short-term government debt: 1.04% to 4.96%

Variato:
- Stocks: -10.56% to 40.56%
- Bonds: -4.68% to 24.68%
- Short-term government debt: -0.88% to 12.88%

for normal curve calculations I use:

http://davidmlane.com/hyperstat/z_table.html