Econometrics

Question 1- Data Set I

A) Derive the estimators of the parameters (rounding up to 3 decimal points). Interpret your results briefly and precisely.

The relevant regression model for this question is: UWABIZ = β1 + β2 Market + µ; where "UWABIZ" and "Market" represent the rates of return on the UWABIZ Fund and the market portfolio, respectively. For the purposes of this question, let Y represent the rate of return on UWABIZ Fund (%), and X represent the rate of return on the Market portfolio (%).

Table 1 (on the next page) illustrates the calculations relevant for this question. The relevant formulas used in this table are:

yi = (Yi-Y)

xi = (Xi-X)

Yi= β1+ β2 Xi

μi= Yi-Yi

Estimation of Parameters:

* Slope coefficient:

β2= (xiyi)xi2= 7810.6627905.324=0.988 (3dp)

* Intercept:

β1= Y- β2X=20.97-.988 ×14.94= 6.209 (3dp)

Thus, the estimated model is Yi= β1+ β2 Xi=6.209+0.988 Xi

Interpretation of Parameters:

* Slope coefficient: A 1% increase in the rate of return on the market portfolio is estimated to lead to a 0.988% increase in the rate of return on the UWABIZ Fund.

* Intercept: When the rate of return on the market portfolio is zero, the rate of return on the UWABIZ Fund is estimated to be 6.209%. However, this is a "very mechanical interpretation of the intercept term." It may be meaningless.

Table 1: Calculations for Equation (1) [done in Excel]

| | | | | | | | | | | |

| Y | X | yi | yi2 | xi | xi2 | xiyi | Xi2 | Ŷi | μi | μi2 |

| 65.000 | 11.000 | 44.030 | 1938.641 | -3.940 | 15.524 | -173.478 | 121.000 | 17.077 | 47.923 | 2296.597 |

| 24.200 | 18.500 | 3.230 | 10.433 | 3.560 | 12.674 | 11.499 | 342.250 | 24.487 | -0.287 | 0.083 |

| -30.200 | -29.300 | -51.170 | 2618.369 | -44.240 | 1957.178 | 2263.761 | 858.490 | -22.740 | -7.460 | 55.648 |

| -37.000 | -26.500 | -57.970 | 3360.521 | -41.440 | 1717.274 | 2402.277 | 702.250 | -19.974 | -17.026 | 289.892 |

| 58.700 | 61.900 | 37.730 | 1423.553 |...