Financial Risk Manager Part 1

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A log trend model is approximated on the interest rate (in %) movement in a certain market based on data from 2000 until 2020. The estimated model is given as:

\ln Y_t = -0.1567 + 0.00134t + \hat{e}_t

The standard deviation of the residual is 0.0342. Assuming that the residuals are normally distributed, what is the 95% confidence interval for interest rate movement for year 2023?

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TTanishq

[12.030, 13.754]

[12.018, 13.739]

[-0.0584, 0.0756]

[11.994, 13.713]

Explanation:

Explanation

For a log-linear model with normally distributed residuals, the 95% confidence interval for the forecast is calculated using:

Expected value of ln(Y_T): $\mathrm{E}_T[\ln Y_T] = -0.1567 + 0.00134 \times 2023 = 2.554$
Variance adjustment: $\frac{\sigma^2}{2} = \frac{0.0342^2}{2} = 0.0006$
Expected value of Y_T: $\mathrm{E}[Y_{2023}] = \exp(2.554 + 0.0006) = 12.866$
Error bounds multiplier: $\exp(\pm 1.96 \times 0.0342) = [0.935, 1.069]$
95% Confidence Interval: $95\%\text{CI}_{2023} = [0.935 \times 12.866, 1.069 \times 12.866] = [12.030, 13.754]$

This approach accounts for the log-normal distribution properties and provides the correct confidence interval for the interest rate forecast.

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