Financial Risk Manager Part 1
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The covariance between the 10-year money supply growth rates and the inflation rate is 0.007668, and the variance of the money supply growth rates is 0.02320. An investment analyst wants to explain the inflation rates using the money supply growth rates and predict the inflation rate when the money supply rate is 25%. The 10-year means for the money supply growth rate and inflation rate are 9% and 3%, respectively. The predicted inflation rate is closest to:
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TTanishq
A
7.234%
B
8.289%
C
6.345%
D
8.756%
Explanation:
Explanation
This is a linear regression prediction problem where:
- Dependent variable (Y): Inflation rate
- Independent variable (X): Money supply growth rate
Step 1: Calculate the slope coefficient (β̂)
[\hat{\beta} = \frac{\hat{\sigma}_{XY}}{\hat{\sigma}^2_X} = \frac{0.007668}{0.02320} = 0.33051]
Step 2: Calculate the intercept (β̂₀)
[\hat{\beta}_0 = \bar{Y} - \hat{\beta}\bar{X} = 0.03 - 0.33051 \times 0.09 = 0.0002541]
Step 3: Form the regression equation
[\hat{Y} = 0.0002541 + 0.33051X]
Step 4: Predict inflation rate when X = 25% (0.25)
[\hat{Y} = 0.0002541 + 0.33051 \times 0.25 = 0.0828816 \approx 8.289%]
Therefore, the predicted inflation rate is 8.289%, which corresponds to option B.
Key Concepts:
- Covariance (σXY): Measures how two variables move together
- Variance (σ²X): Measures the spread of the independent variable
- Regression coefficients: β̂ represents the slope (change in Y per unit change in X), β̂₀ represents the intercept
- Prediction: Using the regression equation to estimate Y for a given X value_
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