One thing that I would find interesting though is the question of what the optimal decision criterion here should be for instrument selection and roll decisions (in general terms ... as the actual decision would depend on the input assumptions such as probability of price going up, down or staying the same at each roll decision).

So for example, take another stock (to stay away from the emotionally charged BAC), TFSL at approximately 60% TBV (excl. MHC shares). I don't know when it will trade to book but since they are buying back shares as fast as they can there is some trajectory for this. The longest dated option is for July, so about 6 months out. A $12.5 put is about $0.3 with the stock at ~$14. You enter a synthetic long, the cost of that non recourse leverage (or more precisely leverage with a capped loss of $1.5) is (1+0.3/14)2 = ~4.3%. Dividend runs at 2.1% currently, so if one could ignore taxes, leverage would be financed at ~2.2%. Not bad.

Ok, so the stock can go up, down or stay the same (a trinomial tree). I haven't done this with an option pricing model (where you'd again have to make volatility assumptions along the way) but intuitively, it's probably worthwhile to look at the stock going down to exactly the strike as well.

So if we focus on the $12.5 and below range - this is what we know:

- PnL Put: $12.5 - stock price - $0.3

- PnL Stock: $14 - stock price

- PnL Combined (MTM and realised, at least at IB): $14- $12.5- $0.3 = $1.8

What is the right decision now? You can roll to the same strike, down to something lower or to a higher strike (or do nothing). Again, what do we know? (The following depends on market factors though, so for simplicity assume these stay the same, i.e. vol not increasing tremendously, etc.):

A) Roll to higher: We invest significantly more capital in the position. As the put is DITM, the cost for buying this protection is also significantly higher (e.g. another 6 month put for strike = $15 would be at least $15-stock price+ $0.2 ... so a fairly hefty annualised costs. This cost is of course locked in because if the stock increases, the put loses value at a similar rate (until it gets much closer to the strike, at which point one could recapture some of the premium ... but this requires yet another decision with a view on the future trajectory).

B) Roll to same: Assume $12.5 strike. So the premium and the cost will be less than in the above scenario.

C) Roll to lower: Assume, first, it's an at-the-money put. Premium will be elevated vs. second option, an OTM put. The latter would provide the cheapest cost for the non-recourse debt we implicitly take on (vis-a-vis the alternatives above, ceteris paribus)

Rolling to a higher option seems to not be a good choice. Rolling to the same strike basically leaves the investor in the same position as before. She only paid the cost of the initial option and the second option for this strategy and has taken the initial loss on the stock move ($1.8 above). However, this cost is increasing (the degree of which depends on how far that old strike is now above the stock price).

Rolling to a lower strike. The investor opens herself up to another loss, e.g. $2.5 if rolling down to $10. The benefit is a cheaper cost for non recourse debt. Is this worthwhile? Again one would have to make an assumption as to how much of that loss the investor will have to take (she cannot "wait it out" as the option forces her to recognise the loss at expiration). Let's compare the costs at either end of the extreme:

0. The cost for buying the $10 put, assuming a $12.5 stock might be in the region of $.2 - $.3 so cost approximately 0.25/14 ~3.6% p.a.

1. At a minimum this is a $0 loss (price above $12.5 original strike). Investor only pays 3.6% annualised

2. At a maximum this is a $2.5 loss (price below $10 new strike ... the implied cost basis is now $12.5 as the losses down to that point where recognised with the first expiration). Investor "pays" ($2.5 + $0.25)/14 ~43% annualised.

So, if the investor is agnostically pessimistic (yes, probably an oxymoron) then she may not want to end up in scenario 2 and therefore choose to not roll down. That cost for an ATM call may be ~$0.9, cost of that is 11%.

... long winded thought to work out the following: The investor can only make an "optimal" decision in the context of an assumed stock price by expiration, for she can only choose the "cheapest" option on every roll (rolling lower) if she is able to keep contributing capital. In other words, it all comes back to "How low do you think it can go?" If you're convinced that it can only go down to $7 (50% down, trading at ~30% TBV) then you can use this to size the position. Lever up so that you're not getting margin called on a loss of $7 x Number of synthetic calls x 100. If you want to be extremely conservative, assume that this happens on the first roll (as the costs of any rolls before the one that gets down to $7 add to the costs incurred).

Another question that should be asked in this strategy is which option expiry to choose? The near term one or the one further away?

-> Option further out has more TV, therefore is more expensive. Rationally (and ignoring trading costs), one should therefore use the nearest term option and roll persistently.

Eric, Mungerville - do you see this differently, or do you have any other/better heuristics to guide your decision-making?

Oh and one more thing - I think the above also demonstrates quite clearly that perhaps a longer term option is actually a more conservative choice (when faced with limited capital). It will be more expensive, but it does not force the frequent "recognition" of the MTM losses that is required at each expiry. Another way to illustrate this is to say that the theoretical max downside in this strategy is still the whole stock price ... i.e. one could end up rolling ever lower. Or, coming back to the original discussion: Choosing a short term vs. a long term call option is right iff you believe that the stock will rise sufficiently within the time frame of the shorter option. If you have to assume a number of rolls and you have a limit of how much capital you're able to contribute to the strategy, you may well be served better with the longer term option to begin with (and, of course, you pay for that extended optionality = extended time period someone lends you money with limited recourse).