Arbitrage Anyone?

I was looking at the historical price movement of TC-PT today.  While it is lightly traded, it should have a tight correlation with TC.  Here are the basic rules (straight from the sec {Documents}):

Unless settled earlier at the holder's option, each purchase contract will automatically settle on the mandatory settlement date of May 15, 2015 and we will deliver a number of shares of our common stock, based on the applicable market value. The applicable market value is the average of the daily volume weighted average prices, of our common stock for the 20 consecutive trading days ending on, and including the third trading day immediately preceding, May 15, 2015. On the mandatory settlement date, each purchase contract will settle, unless earlier settled, as follows (subject to adjustment):

•  if the applicable market value is equal to or greater than $5.45, you will receive 4.5855 shares of common stock for each purchase contract; 

•  if the applicable market value is less than $5.45 but greater than $4.64, you will receive a number of shares of common stock per purchase contract equal to $25, divided by the applicable market value; and 

•if the applicable market value is less than or equal to $4.64, you will receive 5.3879 shares of common stock for each purchase contract.

At any time prior to 5:00 p.m., New York City time on the third scheduled trading day immediately preceding May 15, 2015, you may settle any or all of your purchase contracts early and we will deliver you a number of shares of our common stock per purchase contract equal to: (i) if you settle purchase contracts prior to 5:00 p.m., New York City time, on November 10, 2012, 4.3562, which is 95% of the minimum settlement rate, and (ii) if you settle purchase contracts commencing on November 11, 2012, 4.5855, the minimum settlement rate, subject in either case to adjustment as described under "Description of the purchase contracts—Adjustments to the fixed settlement rates." In addition, if a fundamental change (as defined in this prospectus supplement) occurs and you elect to settle your purchase contracts early in connection with the fundamental change, you will receive a number of shares of our common stock based on the fundamental change early settlement rate, as described herein. Except for cash in lieu of fractional shares, purchase contracts will not entitle holders to any cash distributions.

The amortizing notes will pay you equal quarterly installments of $0.406250 per amortizing note (except for the August 15, 2012 installment payment, which will be $0.424306), which in the aggregate will be equivalent to a 6.50% cash payment per year with respect to each $25 stated amount of tMEDS. The amortizing notes will be our senior unsecured obligations, and will rank equally in right of payment to our existing and future senior indebtedness, including the 7.375% Senior Notes due 2018 and the Senior Notes due 2019 offered concurrently with this offering.

Ok, I think I understand it.  If I hold until May 15, 2015, I will get somewhere between 4.5855 to 5.3879 shares of TC for each share of TC-PT, dependent on the price of TC at that time.  I also have the option to exchange earlier than that date, BUT then I can only exchange at the lowest rate (4.5855).  That would be pretty stupid as then you would forgo the .406250 quarterly dividends/installments.

The whole reason I started thinking about this was by looking at the ratio of TC to TC-PT as shown in the table below:

Date	TC-PT	TC	Ratio	Rolling 20 Days
04/02/13	15.99	2.90	5.51
04/03/13	15.80	2.86	5.52
04/04/13	15.81	2.85	5.55
04/05/13	15.94	2.86	5.57
04/08/13	15.50	2.76	5.62
04/09/13	16.00	2.89	5.54
04/10/13	16.21	2.89	5.61
04/11/13	16.16	2.86	5.65
04/12/13	15.72	2.83	5.55
04/15/13	14.99	2.64	5.68
04/16/13	15.06	2.66	5.66
04/17/13	14.40	2.50	5.76
04/18/13	13.99	2.46	5.69
04/19/13	14.00	2.47	5.67
04/22/13	14.00	2.46	5.69
04/23/13	14.01	2.45	5.72
04/24/13	14.35	2.54	5.65
04/25/13	15.75	2.86	5.51
04/26/13	15.13	2.80	5.40
04/29/13	15.90	2.98	5.34	5.59
04/30/13	15.93	2.99	5.33	5.58
05/01/13	15.61	2.91	5.36	5.58
05/02/13	15.60	2.89	5.40	5.57
05/03/13	16.20	3.04	5.33	5.56
05/06/13	16.35	3.15	5.19	5.54
05/07/13	16.00	3.10	5.16	5.52
05/08/13	16.94	3.23	5.24	5.50
05/09/13	19.51	3.81	5.12	5.47
05/10/13	19.50	3.76	5.19	5.45
05/13/13	18.85	3.63	5.19	5.43
05/14/13	17.90	3.41	5.25	5.41
05/15/13	17.47	3.30	5.29	5.39
05/16/13	17.76	3.38	5.25	5.36
05/17/13	17.96	3.42	5.25	5.34
05/20/13	18.78	3.66	5.13	5.32
05/21/13	18.65	3.54	5.27	5.29
05/22/13	17.96	3.44	5.22	5.27
05/23/13	18.62	3.56	5.23	5.26
05/24/13	18.45	3.53	5.23	5.25
05/28/13	19.07	3.67	5.20	5.24
05/29/13	18.60	3.56	5.22	5.24
05/30/13	19.04	3.64	5.23	5.23
05/31/13	18.45	3.52	5.24	5.22
06/03/13	18.41	3.54	5.20	5.22
06/04/13	18.56	3.53	5.26	5.22
06/05/13	18.44	3.52	5.24	5.22
06/06/13	18.96	3.61	5.25	5.22
06/07/13	18.28	3.53	5.18	5.23
06/10/13	18.13	3.46	5.24	5.23
06/11/13	18.00	3.37	5.34	5.24
06/12/13	17.40	3.30	5.27	5.24
06/13/13	17.66	3.42	5.16	5.23
06/14/13	17.89	3.44	5.20	5.23
06/17/13	17.44	3.23	5.40	5.24
06/18/13	16.69	3.10	5.38	5.25
06/19/13	17.18	3.19	5.39	5.25
06/20/13	16.40	3.02	5.43	5.26
06/21/13	15.85	2.96	5.35	5.27
06/24/13	15.59	2.84	5.49	5.28
06/25/13	15.30	2.84	5.39	5.29
06/26/13	15.45	2.77	5.58	5.31
06/27/13	16.00	2.93	5.46	5.32
06/28/13	16.37	3.03	5.40	5.33
07/01/13	16.77	3.08	5.44	5.34
07/02/13	16.29	2.99	5.45	5.35
07/03/13	16.05	2.93	5.48	5.36
07/05/13	15.90	2.94	5.41	5.37
07/08/13	15.90	2.88	5.52	5.39
07/09/13	15.82	2.84	5.57	5.41
07/10/13	15.86	2.84	5.58	5.42
07/11/13	15.82	2.86	5.53	5.43
07/12/13	15.95	2.87	5.56	5.45
07/15/13	15.60	2.86	5.45	5.46
07/16/13	15.82	2.90	5.46	5.47
07/17/13	16.45	3.00	5.48	5.47
07/18/13	16.23	2.93	5.54	5.48
07/19/13	15.99	2.87	5.57	5.49
07/22/13	16.46	2.99	5.51	5.49
07/23/13	17.00	3.12	5.45	5.49
07/24/13	16.71	3.04	5.50	5.50
07/25/13	16.82	3.04	5.53	5.49
07/26/13	16.81	3.06	5.49	5.50
07/29/13	16.03	2.98	5.38	5.50
07/30/13	15.93	2.92	5.46	5.50
07/31/13	16.06	2.98	5.39	5.49
08/01/13	16.06	2.95	5.44	5.49
08/02/13	15.94	2.93	5.44	5.49
08/13/13	18.32	3.48	5.26	5.48
08/14/13	18.81	3.63	5.18	5.46
08/15/13	19.00	3.68	5.16	5.44
08/16/13	19.33	3.75	5.15	5.42
08/19/13	19.10	3.64	5.25	5.40
08/20/13	18.90	3.66	5.16	5.39
08/21/13	18.88	3.58	5.27	5.38
08/22/13	18.91	3.66	5.17	5.37
08/23/13	19.54	3.77	5.18	5.35

As you can see, the higher the share price of TC, the lower (typically) the ratio of TC-PT to TC.  That kind of makes sense as as the likelihood of the TC share price exceeding $4.64 then the ratio (per the formula) starts to drop.

Not sure if my patient readers care, but it helped me to walk through it as I could not understand why the current ratio is 5.18 when it had been more in the 5.5 range in the past and I thought as long as price was under $4.64 I could exchange at 5.3879 ratio.

More tomorrow.