Financial Risk Manager Part 1

Get started today

Ultimate access to all questions.

Deep dive into the quiz with AI chat providers.

We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.

A log-linear trend model is approximated on the interest rate (in %) movement in a certain market given as:

\ln I_t = -0.001567 + 0.000134t + \hat{e}_t

for the last 20 years. The standard deviation of the residual is 0.0342. Assuming that the residuals are white noise, what is the 95% confidence interval for interest rate movement 3 years from now.

Other

Community

NNikitesh

Last updated: February 2, 2026 at 10:22

[0.9517, 0.6257]

[-0.6917, 0.8259]

[-0.0645, 0.0695]

[0.7917, -0.6917]

Explanation:

The 95% confidence interval is given by:

E_T(Y_{T+h}) \pm 1.96\sigma

We need:

E_T(I_3) \pm 1.96\sigma

First, calculate the expected value:

E_T(Y_{T+h}) = \sigma_0 + \sigma_1(T + h)

= -0.001567 + 0.000134 \times 3 = 0.0025

Then calculate the confidence interval:

E_T(I_3) \pm 1.96\sigma = 0.0025 \pm 1.96 \times 0.0342

= 0.0025 \pm 0.067032

= [-0.064532, 0.069532] \approx [-0.0645, 0.0695]

Therefore, the 95% confidence interval for interest rate movement 3 years from now is [-0.0645, 0.0695].

Powered ByGPT-5.2

Comments

Loading comments...