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Posted on Oct 07, 2024

3. Suppose you have 1,000 shares of your assigned company as of Oct 1st, 2021. Compute the optimal number of S&P500 Futures contract to fully

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3. Suppose you have 1,000 shares of your assigned company as of Oct 1st, 2021. Compute the optimal number of S&P500 Futures contract to fully hedge your position until Dec 31st, 1 2021. For simplicity, assume each S&P500 Futures contract is written on 10 times the index (Hint: Compute the (beta) using 2-years of historical data). Using the theoretical price of S&P500 Futures contract you have computed in Question 2, track the PnL of your hedged portfolio until the Futures maturity date of Dec 31st, 2021. Comment on the successfulness of the hedging and analyze potential reasons behind any issues. (Lecture 3) Berkshire Hathaway Inc. Date Adj Close Theoretical price FO 2021-10-01 275.709991 279.168435 2021-10-04 273.640015 276.9586517 2021-10-05 278.049988 281.3835594 2021-10-06 280.220001 283.5407451 2021-10-07 282.950012 286.2638911 2021-10-08 284.140015 287.4284548 2021-10-11 280.929993 284.0645194 2021-10-12 278.619995 281.6901569 2021-10-13 277.899994 280.9237367 2021-10-14 281.640015 284.6654538 S&P 500 Date Adj Close Theoretical price FO 01-Oct-21 4,357.04 4411.693729 04-Oct-21 4,300.46 4352.614888 05-Oct-21 4,345.72 4397.821308 06-Oct-21 4,363.55 4415.260202 07-Oct-21 4,399.76 4451.289501 08-Oct-21 4,391.34 4442.162329 11-Oct-21 4,361.19 4409.850754 12-Oct-21 4,350.65 4398.590564 13-Oct-21 4,363.80 4411.28114 14-Oct-21 4,438.26 4485.936762 15-Oct-21 4,471.37 4518.783383 18-Oct-21 4,486.46 4532.170475 19-Oct-21 4,519.63 4565.053037 20-Oct-21 4,536.19 4581.151869 21-Oct-21 4,549.78 4594.247179 22-Oct-21 4,544.90 4588.690853 25-Oct-21 4,566.48 4608.584452 26-Oct-21 4,574.79 4616.338655 27-Oct-21 4,551.68 4592.38963 28-Oct-21 4,596.42 4636.894544 29-Oct-21 4,605.38 4645.297057 01-Nov-21 4,613.67 4651.746841 2021-10-15 284.209991 287.2236886 2021-10-18 282.589996 285.4691754 2021-10-19 284.829987 287.692576 2021-10-20 287.48999 290.3395372 2021-10-21 286.820007 289.6232363 2021-10-22 289.23999 292.0268645 2021-10-25 290.26001 292.9363031 2021-10-26 290.850006 293.4915319 2021-10-27 287.779999 290.3538656 2021-10-28 289.720001 292.2711789 2021-10-29 287.01001 289.4976647 2021-11-01 286.23999 288.6023425 2021-11-02 287.929993 290.2665279 4668.227451 2021-11-03 288.720001 291.0230778 4697.746679 2021-11-04 287.690002 289.9451414 4716.745974 2021-11-05 287.880005 290.0968918 4733.70442 2021-11-08 288.799988 290.904385 4735.959848 2021-11-09 286.350006 288.3970416 4718.743534 2021-11-10 285.320007 287.3203178 4679.28698 2021-11-11 284.649994 286.6063437 4681.22362 2021-11-12 285.98999 287.916106 4714.388559 2021-11-15 284.670013 286.4694877 4712.401221 2021-11-16 283.359985 285.1121195 4729.967651 2021-11-17 281.589996 283.2923761 02-Nov-21 03-Nov-21 04-Nov-21 05-Nov-21 08-Nov-21 09-Nov-21 10-Nov-21 11-Nov-21 12-Nov-21 15-Nov-21 16-Nov-21 17-Nov-21 18-Nov-21 19-Nov-21 22-Nov-21 23-Nov-21 24-Nov-21 26-Nov-21 29-Nov-21 30-Nov-21 01-Dec-21 02-Dec-21 03-Dec-21 4,630.65 4,660.57 4,680.06 4,697.53 4,701.70 4,685.25 4,646.71 4,649.27 4,682.85 4,682.80 4,700.90 4,688.67 4,704.54 4,697.96 4,682.94 4,690.70 4,701.46 4,594.62 4,655.27 4,567.00 4,513.04 4,577.10 4,538.43 4717.015817 2021-11-18 280.630005 282.2879091 4732.333451 2021-11-19 279.98999 281.6055343 4725.067264 2021-11-22 284.970001 286.4965175 4708.025396 2021-11-23 288.559998 290.0660075 4715.181005 2021-11-24 287.279999 288.739772 4725.349809 2021-11-26 283.089996 4616.701894 284.4505358 283.3593999 2021-11-29 282.119995 4675.721455 2021-11-30 276.690002 277.8674853 4586.435347 2021-12-01 275 276.1324624 4531.624902 2021-12-02 279.089996 280.2009148 4595.319165 2021-12-03 277.429993 278.4961514 4555.871104 2021-12-06 281.380005 282.3452871 06-Dec-21 4607.421854 2021-12-07 284.970001 285.9084305 07-Dec-21 4702.18385 2021-12-08 283.720001 284.615323 08-Dec-21 4716.04539 2021-12-09 284.519989 285.3787399 4681.537505 09-Dec-21 10-Dec-21 2021-12-10 288.230011 289.0603596 4725.594642 2021-12-13 290.01001 290.7259855 13-Dec-21 4680.496734 2021-12-14 295.029999 295.7178558 14-Dec-21 4644.894292 2021-12-15 294.579987 295.2263499 4720.18428 2021-12-16 300.170013 300.7874348 15-Dec-21 16-Dec-21 17-Dec-21 4678.27302 2021-12-17 293.660004 294.223728 4,591.67 4,686.75 4,701.21 4,667.45 4,712.02 4,668.97 4,634.09 4,709.85 4,668.67 4,620.64 4,568.02 4,649.23 4,696.56 4,725.79 4,791.19 4,786.35 4,793.06 4,778.73 4,766.18 4629.510004 2021-12-20 289.609985 290.0467126 4574.908506 2021-12-21 293.23999 293.6419639 4655.603172 2021-12-22 294.410004 294.7731991 4702.35385 20-Dec-21 21-Dec-21 22-Dec-21 23-Dec-21 27-Dec-21 28-Dec-21 2021-12-23 294.48999 294.8128957 4730.971787 2021-12-27 296.670013 296.8326165 4793.816029 2021-12-28 298.290009 298.4126191 4788.317397 2021-12-29 299.459991 299.5420461 29-Dec-21 4794.373347 2021-12-30 299.980011 300.021107 4779.384665 30-Dec-21 31-Dec-21 2021-12-31 299 299 4766.18 3. Suppose you have 1,000 shares of your assigned company as of Oct 1st, 2021. Compute the optimal number of S&P500 Futures contract to fully hedge your position until Dec 31st, 1 2021. For simplicity, assume each S&P500 Futures contract is written on 10 times the index (Hint: Compute the (beta) using 2-years of historical data). Using the theoretical price of S&P500 Futures contract you have computed in Question 2, track the PnL of your hedged portfolio until the Futures maturity date of Dec 31st, 2021. Comment on the successfulness of the hedging and analyze potential reasons behind any issues. (Lecture 3) Berkshire Hathaway Inc. Date Adj Close Theoretical price FO 2021-10-01 275.709991 279.168435 2021-10-04 273.640015 276.9586517 2021-10-05 278.049988 281.3835594 2021-10-06 280.220001 283.5407451 2021-10-07 282.950012 286.2638911 2021-10-08 284.140015 287.4284548 2021-10-11 280.929993 284.0645194 2021-10-12 278.619995 281.6901569 2021-10-13 277.899994 280.9237367 2021-10-14 281.640015 284.6654538 S&P 500 Date Adj Close Theoretical price FO 01-Oct-21 4,357.04 4411.693729 04-Oct-21 4,300.46 4352.614888 05-Oct-21 4,345.72 4397.821308 06-Oct-21 4,363.55 4415.260202 07-Oct-21 4,399.76 4451.289501 08-Oct-21 4,391.34 4442.162329 11-Oct-21 4,361.19 4409.850754 12-Oct-21 4,350.65 4398.590564 13-Oct-21 4,363.80 4411.28114 14-Oct-21 4,438.26 4485.936762 15-Oct-21 4,471.37 4518.783383 18-Oct-21 4,486.46 4532.170475 19-Oct-21 4,519.63 4565.053037 20-Oct-21 4,536.19 4581.151869 21-Oct-21 4,549.78 4594.247179 22-Oct-21 4,544.90 4588.690853 25-Oct-21 4,566.48 4608.584452 26-Oct-21 4,574.79 4616.338655 27-Oct-21 4,551.68 4592.38963 28-Oct-21 4,596.42 4636.894544 29-Oct-21 4,605.38 4645.297057 01-Nov-21 4,613.67 4651.746841 2021-10-15 284.209991 287.2236886 2021-10-18 282.589996 285.4691754 2021-10-19 284.829987 287.692576 2021-10-20 287.48999 290.3395372 2021-10-21 286.820007 289.6232363 2021-10-22 289.23999 292.0268645 2021-10-25 290.26001 292.9363031 2021-10-26 290.850006 293.4915319 2021-10-27 287.779999 290.3538656 2021-10-28 289.720001 292.2711789 2021-10-29 287.01001 289.4976647 2021-11-01 286.23999 288.6023425 2021-11-02 287.929993 290.2665279 4668.227451 2021-11-03 288.720001 291.0230778 4697.746679 2021-11-04 287.690002 289.9451414 4716.745974 2021-11-05 287.880005 290.0968918 4733.70442 2021-11-08 288.799988 290.904385 4735.959848 2021-11-09 286.350006 288.3970416 4718.743534 2021-11-10 285.320007 287.3203178 4679.28698 2021-11-11 284.649994 286.6063437 4681.22362 2021-11-12 285.98999 287.916106 4714.388559 2021-11-15 284.670013 286.4694877 4712.401221 2021-11-16 283.359985 285.1121195 4729.967651 2021-11-17 281.589996 283.2923761 02-Nov-21 03-Nov-21 04-Nov-21 05-Nov-21 08-Nov-21 09-Nov-21 10-Nov-21 11-Nov-21 12-Nov-21 15-Nov-21 16-Nov-21 17-Nov-21 18-Nov-21 19-Nov-21 22-Nov-21 23-Nov-21 24-Nov-21 26-Nov-21 29-Nov-21 30-Nov-21 01-Dec-21 02-Dec-21 03-Dec-21 4,630.65 4,660.57 4,680.06 4,697.53 4,701.70 4,685.25 4,646.71 4,649.27 4,682.85 4,682.80 4,700.90 4,688.67 4,704.54 4,697.96 4,682.94 4,690.70 4,701.46 4,594.62 4,655.27 4,567.00 4,513.04 4,577.10 4,538.43 4717.015817 2021-11-18 280.630005 282.2879091 4732.333451 2021-11-19 279.98999 281.6055343 4725.067264 2021-11-22 284.970001 286.4965175 4708.025396 2021-11-23 288.559998 290.0660075 4715.181005 2021-11-24 287.279999 288.739772 4725.349809 2021-11-26 283.089996 4616.701894 284.4505358 283.3593999 2021-11-29 282.119995 4675.721455 2021-11-30 276.690002 277.8674853 4586.435347 2021-12-01 275 276.1324624 4531.624902 2021-12-02 279.089996 280.2009148 4595.319165 2021-12-03 277.429993 278.4961514 4555.871104 2021-12-06 281.380005 282.3452871 06-Dec-21 4607.421854 2021-12-07 284.970001 285.9084305 07-Dec-21 4702.18385 2021-12-08 283.720001 284.615323 08-Dec-21 4716.04539 2021-12-09 284.519989 285.3787399 4681.537505 09-Dec-21 10-Dec-21 2021-12-10 288.230011 289.0603596 4725.594642 2021-12-13 290.01001 290.7259855 13-Dec-21 4680.496734 2021-12-14 295.029999 295.7178558 14-Dec-21 4644.894292 2021-12-15 294.579987 295.2263499 4720.18428 2021-12-16 300.170013 300.7874348 15-Dec-21 16-Dec-21 17-Dec-21 4678.27302 2021-12-17 293.660004 294.223728 4,591.67 4,686.75 4,701.21 4,667.45 4,712.02 4,668.97 4,634.09 4,709.85 4,668.67 4,620.64 4,568.02 4,649.23 4,696.56 4,725.79 4,791.19 4,786.35 4,793.06 4,778.73 4,766.18 4629.510004 2021-12-20 289.609985 290.0467126 4574.908506 2021-12-21 293.23999 293.6419639 4655.603172 2021-12-22 294.410004 294.7731991 4702.35385 20-Dec-21 21-Dec-21 22-Dec-21 23-Dec-21 27-Dec-21 28-Dec-21 2021-12-23 294.48999 294.8128957 4730.971787 2021-12-27 296.670013 296.8326165 4793.816029 2021-12-28 298.290009 298.4126191 4788.317397 2021-12-29 299.459991 299.5420461 29-Dec-21 4794.373347 2021-12-30 299.980011 300.021107 4779.384665 30-Dec-21 31-Dec-21 2021-12-31 299 299 4766.18