BOSTON COLLEGE

Department of Economics

EC 362

Financial Markets

Prof. Baum

Fall 1998

PROBLEM SET TWO

Due Wednesday, 21 October 1998, at classtime

Enclosed are monthly data for 1986-1990 on the CME British Pound contract. Using these data, answer the following questions. You may use any appropriate software (StataQuest, Excel, StatView, etc.).

1) What is the variance in the spot price of £ for the 1986-1990 period?

(2) What is the variance of the futures price of £ for this period?

(3) What is the simple correlation between the two series? Does it appear to be large enough to generate a reliable hedge?

(4) Calculate the optimal hedge ratio for this period using ordinary least squares (OLS) regression. What is the coefficient of determination (R-squared) of this regression? What does it tell you?

(5) Calculate your gains or losses (in US $) from a spot position of £ 625,000, using the appropriate (integer) number of futures contracts over the period. (Ignore the fact that this would be a rolling hedge).

(6) How would the optimal hedge ratio change if you used only the data from 1989 to calculate the OHR? How reliable is this estimate?

These are beginning-of-month quotes, derived from daily data. The Yr Mo Da refer to the quote date. W is the weekday (1=Monday). The "Con" is the contract used to provide the futures quotation (generally the near contract). Spot £ and Fut £ are quotations in $/£.

Yr Mo Da W Con Spot £ Fut £

86 1 2 4 8606 1.447700 1.425000

86 2 3 1 8606 1.390200 1.362000

86 3 3 1 8609 1.434000 1.401500

86 4 1 2 8609 1.470800 1.443500

86 5 1 4 8609 1.530500 1.516000

86 6 2 1 8612 1.475500 1.457500

86 7 1 2 8612 1.543600 1.520500

86 8 1 5 8612 1.489800 1.476500

86 9 2 2 8703 1.491200 1.457500

86 10 1 3 8703 1.443000 1.415000

86 11 3 1 8703 1.412700 1.388000

86 12 1 1 8706 1.435500 1.397000

87 1 2 5 8706 1.492500 1.467500

87 2 2 1 8706 1.517500 1.493500

87 3 2 1 8709 1.556000 1.527000

87 4 1 3 8709 1.603000 1.583000

87 5 1 5 8709 1.671500 1.656500

87 6 1 1 8712 1.625000 1.611500

87 7 1 3 8712 1.619500 1.610000

87 8 3 1 8712 1.591300 1.582500

87 9 1 2 8803 1.638000 1.620000

87 10 1 4 8803 1.620000 1.609500

87 11 2 1 8803 1.730000 1.720000

87 12 1 2 8806 1.811500 1.805000

88 1 4 1 8806 1.873500 1.861000

88 2 1 1 8806 1.756300 1.747000

88 3 1 2 8809 1.773000 1.754000

88 4 5 2 8809 1.881000 1.873000

88 5 3 2 8809 1.871700 1.864000

88 6 1 3 8812 1.824000 1.821000

88 7 1 5 8812 1.701200 1.686000

88 8 1 1 8812 1.712300 1.697800

88 9 1 4 8903 1.680000 1.652000

88 10 3 1 8903 1.696000 1.673200

88 11 1 2 8903 1.766000 1.746400

88 12 1 4 8906 1.845800 1.822000

89 1 3 2 8906 1.824000 1.800000

89 2 1 3 8906 1.750000 1.726600

89 3 1 3 8909 1.723000 1.704000

89 4 3 1 8909 1.680300 1.666000

89 5 2 2 8909 1.682700 1.662400

89 6 1 4 8912 1.576000 1.533000

89 7 3 1 8912 1.572000 1.538000

89 8 1 2 8912 1.655500 1.627000

89 9 1 5 9003 1.565300 1.525200

89 10 2 1 9003 1.617500 1.579000

89 11 1 3 9003 1.582000 1.542000

89 12 1 5 9006 1.565500 1.512000

90 1 2 2 9006 1.610500 1.575000

90 2 1 4 9006 1.683000 1.644000

90 3 1 4 9009 1.664500 1.612000

90 4 2 1 9009 1.629800 1.575000

90 5 1 2 9009 1.638000 1.600600

90 6 1 5 9012 1.683000 1.628400

90 7 2 1 9012 1.760500 1.709000

90 8 1 3 9012 1.854500 1.808600

90 9 4 0 9103 1.876000 1.818000

90 10 1 1 9103 1.888000 1.839000

90 11 1 4 9103 1.951500 1.898000

90 12 3 1 9106 1.917800 1.867000