Financial Risk Manager Part 1

Financial Risk Manager Part 1

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An organization estimates that the effect of increasing the number of qualified Financial Risk Managers hired by 1 will improve the stock's annual return by 2.8% with a standard error of 0.52%. Construct a 90% 2-sided confidence interval for the size of the slope coefficient, assuming the stock's returns are normally distributed.

TTanishq

Explanation:

Explanation

For a 90% 2-sided confidence interval with normally distributed returns, we use the formula:

β1±Zα2×se(β1)\beta_1 \pm Z_{\frac{\alpha}{2}} \times \text{se}(\beta_1)

Where:

  • β1=2.8%\beta_1 = 2.8\% (estimated slope coefficient)
  • se(β1)=0.52%\text{se}(\beta_1) = 0.52\% (standard error)
  • α=0.10\alpha = 0.10 (for 90% confidence)
  • Z0.05=1.645Z_{0.05} = 1.645 (critical value from standard normal distribution)

Calculation: 2.8%±1.645×0.52%=2.8%±0.8554%2.8\% \pm 1.645 \times 0.52\% = 2.8\% \pm 0.8554\%

Lower bound: 2.8%−0.8554%=1.9446%≈1.9%2.8\% - 0.8554\% = 1.9446\% \approx 1.9\%

Upper bound: 2.8%+0.8554%=3.6554%≈3.7%2.8\% + 0.8554\% = 3.6554\% \approx 3.7\%

Therefore, the 90% confidence interval is approximately (1.9%, 3.7%), which matches option D.

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