Quote from Daal:
I'm not sure these theoretical values will matter for those wanting to hold for a few weeks gunning for a quick 10-15% profit. Most trading AAMRQ will use the JPM formula even if it is wrong.
By using a figure between JPM's and the beta I think I will be protected against a big tank in these stocks.
My guess is that the "correct" ratio, the number that will avoid underhedging and overhedging is between the 2 figures.
If you disagree, I would like to know why
If LCC doesn't move much (to be more precise, let's say it remains in a range between $20 and $25), then the linear function provided by JPM should be close enough.
But if LCC falls to $14.26, then the value of the AAG preferred stock approaches zero.
If you are hedging your long AAMRQ dollar for dollar with short LCC, then you probably won't gain enough on the LCC short to cover your AAMRQ losses.
eg. LCC at $23. 1.582 * 23 - 22.56 = 13.83.
But if LCC falls by 38% to $14.26, then AAMRQ be worth approx $2 (haven't looked up the exact amount) because the value of the AAG preferred stock is zero.
Let's assume you shorted 1,000 LCC shares at $23, and cover at $14.26. Gain of $5,740.
The value of the LCC shares was 1,000 * 23 = 23,000.
LCC share price $23 * 1.582 - 22.96 = $13.42
23,000 / $13.42 = 1,713 AAMRQ shares
If you bought 1,713 AAMRQ shares at $11, total paid = $18,843.
If they fall to $2, then you lose 1,713 * 9 = $15,417.
Gain $5,740 on LCC
Lose $15,417 on AAMRQ.
So the correct way to hedge long AAMRQ is with a combination of short LCC and short LCC call options, to more accurately reflect the behavior of the AAG preferred stock.