代写金融线性计量经济学-Linear Econometrics代写

BU.232.620 (Linear Econometrics for Finance)

Homework 2

代写金融线性计量经济学 Suppose we only change the unit of yi to percentage points, i.e., the IBM stock return yi will be 5 for the 5% monthly return.

1.For the SLR model yi = 0 + 1xi + ui , with yi as the IBM stock return and xi as the market return (CAPM) that are both in original units, e.g., 0.05 means 5% monthly return. 代写金融线性计量经济学

Suppose we only change the unit of xi to percentage points, i.e., the market return xi will be 5 for the 5% monthly return. Does this change the values of

β0 , and β1 ? If so, by how much?

Answer: Changing the unit of ; to percentage points means we multiply x; byAnswer:100, with the new regressor defined as z; = 100.;. Let the new regression model be

Compare this regression equation to the original regression yi = , + i + ui,we have

Therefore. the value of 6, does not change, while that of , get divided by 100 代写金融线性计量经济学

Suppose we only change the unit of yi to percentage points, i.e., the IBM stock return yi will be 5 for the 5% monthly return. Does this change the values of β0 ,and β1 ? If so, by how much? 代写金融线性计量经济学

Answer:Changing the unit of yi to percentage points means we multiply yi by 100. with the new regressand defined as gi = 100y. Let the new regression model be

which is equal to

Compare this regression equation to the original regression yi = + Bi + ui,we have

Therefore, the values of both 6, and 6, get multiplied by 100.

Do the two changes of units above make R²different? Use the definition of R²to prove it.

Proof: We have by definition:

In the first case, i.e., changing the unit of x; to percentage points, we observe fromabove that neither y; or y changes. As a result the denominator does not changeIn the numerator, we just need to show y; does not change, which follows from 代写金融线性计量经济学

where we used

which follows from the sample counterpart of (2)In the second case, i.e.. changing the unit of y to percentage points, the denominator of R²is . Then we just need to show gets multiplied by 100, which follows from the sample counterpart of (1).

2.For the SLR model yi = 6x; + ui, i.e., regression without intercept,. 代写金融线性计量经济学

Use the OLS principal to derive the OLS estimator of 6, for this model.

Answer: The OLS minimization problem is:

Taking the first order derivative, we have

Then the OLS estimator is

Compare the OLS estimator for this regression with that for the regression withintercept. Under what conditions are the two estimators equal to each other?

Answer: From the OLS, we have the estimator for SLR as