Question

Assume that the standard deviation of daily returns for Marcus, Inc. stock in a recent period is 1.5 percent. Furthermore, a 95 percent confidence interval is desired for the maximum loss. Daily returns are normally distributed, and the expected daily return is 0.05 percent. What is the lower boundary of the maximum expected loss

Answer 1

= - 2.43%

Explanation:

From the information given:

Since the variable (daily returns) is normally distributed, Then, using empirical rule at 95% confidence interval level, we have:

`( \mu - 1.96 \sigma \ , \ \mu + 1.96 \sigma)`

where;

The expected mean daily return
`\mu = 0.05 \%`

The standard deviation
`\sigma = 1.5\%`

Given that the 95% confidence interval is expected to be a maximum loss, then the probability is left-tailed which is 1.65
`\sigma` away from the average.

Thus the distribution of the lower boundary can be computed as:

=
`(0.05 - 1.65 * 1.5)\%`

=
`(0.05 - 2.475)\%`

=
`( - 2.425)\%`

= - 2.43%