Question

The mean change in the value of a portfolio of trading assets has been estimated to be 0 with a standard deviation of 20 percent. Yield changes are assumed to be normally distributed. What is the maximum yield change expected if a 90%, 95%, and 99% confidence (one-tailed) limit is used?

Answer 1

The maximum yield change for a portfolio with a standard deviation of 20 percent is 32.9% for a 90% confidence level, 39.2% for a 95% confidence level, and 46.52% for a 99% confidence level, calculated by multiplying the z-score for each confidence level by the standard deviation.

Step-by-step explanation:

The question is asking for the maximum yield change that is expected from a portfolio with the mean change estimated at 0 and a standard deviation of 20 percent, using normalized distribution (z-scores) for different confidence levels. To determine these yield changes for confidence levels of 90%, 95%, and 99%, one would use the corresponding z-score for each confidence level and multiply it by the standard deviation.

For a 90% confidence level (one-tailed), the z-score is approximately 1.645. Thus, the maximum yield change is 1.645 x 20%, which equals 32.9%.

For a 95% confidence level (one-tailed), the z-score is approximately 1.960. Hence, the maximum yield change is 1.960 x 20%, equating to 39.2%.

For a 99% confidence level (one-tailed), the z-score is about 2.326. Therefore, the maximum yield change is 2.326 x 20%, resulting in 46.52%.

These calculations provide investors with a range of possible outcomes based on the confidence level they choose, which can help with making informed decisions about their portfolio.