Financial Econometrics Harvard Case Solution & Analysis

Financial Econometrics Case Solution

Question 1

The correlation coefficient of the US dollar and inflation is:

Correlation coefficient = (Slope of the regression line * Standard-deviation of inflation) / Standard deviation of US dollar

To find the correlation, we have the slope of the regression line but the standard deviation of inflation and standard deviation of the US dollar are missing. The F Test formula is the variance of inflation divided by the variance of the US dollar. So, the under route of F Test score will be used to find out the correlation. Then, the under route of F Test will be multiplied by the slope of the regression line.

The correlation coefficient will be = - 1.1652 * (15.8665) ^ (1/2)

The correlation coefficient will be = - 1.1652 * 3.9833

The correlation coefficient = - 0.0464

Question 2

Wald test to check if the multiple regression lasts significant improvement in the simple regression; we have used the Z score to calculate the p value for this test.

The Z score formula is = (Intercept of simple regression – Intercept of multiple regression) / Pooled variance

The Z score formula is = (0.01799 - 0.014461) / 0.002333

The Z score = 1.512373457

P value = 0.1310434

Do not reject null hypothesis which states that the multiple regression does not have a significant improvement over the simple regression.

Question 3

The 95% confidence interval for the Slope of Semiconductor in the multiple regression is:

Confidence interval = Slope of Semiconductor in the multiple regression± Z * (Standard deviation / Total number of observations ^ (1/2))

Confidence interval = 0.875988± 1.96 * (0.002333418 / 2520 ^ (1/2))

Confidence interval = 0.875988± 0.00009111

Lower Bound = 0.875896894

Upper Bound = 0.876079106

The 95% confidence interval for the Slope of Semiconductor is:

0.875896894 <Slope of Semiconductor< 0.876079106

Question 4

Slope of the regression equation is:

Slope = Correlation * (Standard deviation of small cap / Standard deviation of market cap)

Slope = 0.855282718

Intercept = Average return of small cap – Slope of the regression equation * Average return of market cap

Intercept = 0.04681429

The null value of the slope is 1.

The estimated value of slope is 0.855282718.

The regression equation test statistics is:

T = (0.855282718 – 1) / 0.002545323

T = -56.85615835

P value < 0.000001

Reject the null hypothesis which states that the regression equation is not significant as well as the slope of the equation is equal to 1. It means that we are accepting the alternate hypothesis and are concluding that the regression equation is significant and the slope of the equation is not equal to 1.

Question 5

1. When the predicted return of next year’s market index is 10%, the foretasted return for small cap will be:

Small cap return = 0.04681429 + 0.855282718 * 10%

Small cap return = 13.234%

1. If Small Cap ends up delivering a 35% return while the Market Index comes in at 10% as expected; the small cap performance significantly would be different than predicted.

T Test = (13.234% - 35%) / 0.002496022

T Test = -87.20172365

P value < 0.000001

Reject null hypothesis which states that the small cap performance is not significantly different than predicted. It means that we are accepting the alternate hypothesis and concluded that the small cap performance is significantly different than predicted.

Question 6

1. These results are indicating the problem with non-stationary based on a Dickey-Fueller test of a random walk with drift because

The null value of the slope is 1.

The estimated value of slope is 0.855282718.

The regression equation test statistics is:

T = (-0.103 - 0.9007) / 2.2076

T = -0.454656641

P value =0.650656

Do not reject null hypothesis, which indicate that there is not any problem with non-stationary, based on a Dickey-Fueller test of a random walk with drift.

1. Based on the above conclusion; it has been found that there is not any problem with non-stationary based on a Dickey-Fueller test of a random walk with drift, so we can use the regression model for an ongoing research.

Question 7

GARCH Model = Intercept + Slope return * (Slope return – Expected Return) ^ 2 + Slope Volume * Variance + SSE

GARCH Model = 0.045790783

The annual volatility would be:0.045790783 or 4.5790783%

Question 8

1. In order to estimate the KRD for the 6^th year; I have calculated the compound growth rate and multiplied it for the 5^th year KRD to found the 6^th year KRD

Compound growth rate = (KRD 5 / KRD 1) ^ (1/4) – 1

Compound growth rate = 44.973%

Estimated KRD 6 = KRD 5 * (1 + Compound growth rate)

Estimated KRD 6 = -0.268773596

1. The estimated percentage change in the value of the bond will be:

Change in the value of bond = (Bond value at 6^th year / Bond Value at 1^st year) – 1

Change in the value of bond = 1.563%..........................

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