Financial Risk Manager Part 1

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⁑Yt=βˆ’0.1567+0.00134t+e^t\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?

TTanishq

Explanation:

Explanation

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

  1. Expected value of ln(Y_T): ET[ln⁑YT]=βˆ’0.1567+0.00134Γ—2023=2.554\mathrm{E}_T[\ln Y_T] = -0.1567 + 0.00134 \times 2023 = 2.554

  2. Variance adjustment: Οƒ22=0.034222=0.0006\frac{\sigma^2}{2} = \frac{0.0342^2}{2} = 0.0006

  3. Expected value of Y_T: E[Y2023]=exp⁑(2.554+0.0006)=12.866\mathrm{E}[Y_{2023}] = \exp(2.554 + 0.0006) = 12.866

  4. Error bounds multiplier: exp⁑(Β±1.96Γ—0.0342)=[0.935,1.069]\exp(\pm 1.96 \times 0.0342) = [0.935, 1.069]

  5. 95% Confidence Interval: 95%CI2023=[0.935Γ—12.866,1.069Γ—12.866]=[12.030,13.754]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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