First of all a hat tip to Profitlich & Schmidtlin which had mentioned this idea in their first quarterly letter.
Piraeus Bank is one of the “survivors” of the Greek Banking sector. As with other Greek banks, the bank was “rescued” by the Government via a dilutive capital increase, with the Greek Government as a majority shareholder. Those private investor who participated in the capital increase got as a kind of “compensation” (and exit vehicle) some Warrants “for free” which allows them to buy back the shares until 2018 from the Greek Government. Those Warrant are traded quite actively on the Athens Stock Exchange.
Maybe in order to make it more fun, the Greek Government spiced up the Warrants with some extra features which are ( a kind of term sheet can be found here)
– one Warrant gives the right to purchase 4,476 shares from the Hellenic Stability Fund (so its non dilutive”)
– the final maturity is 02.01.2018, however there seems to be a kind of “forced” exchange possibility on 02.07.2016
– the Warrants can be exercised every 6 months, so its technically a “Bermudan option”
– the strike price increases every 6 months after a predetermined formula
At a first glance, this “thing” seems to be really hard to value. Bloomberg for instance does not offer to value “Bermudan Equity options” in its standard option valuation tool (OVME).
Let’s take a step back and look at principal option types. The two classical types are:
– European Option: This option can only be exercised at the final maturity date
– American Option: This option can be exercised on every day during the term of the option
Nevertheless, there is normally very little difference in the value of an European option and American one if all other things are equal. The main reason for this is that in normal cases, the “time value” of an option is usually positive until the very last day. Exercising an American option early and “throwing away” the time value normally doesn’t make sense. For “normal” stock options, the only reason to exercise early would be a large dividend payment before maturity which will reduce the value of a (long Call) option, but in most cases one can ignore the valuation difference between an European and American option.
On the other hand, the increasing strike price of the Piraeus Warrant is economically equal to a dividend, so we cannot just ignore this feature and value it as a European Option.
This is the call schedule and the corresponding strike prices for the Warrant:
From what I know, Piraeus Bank is not supposed to pay out any dividends in the foreseeable future. So in order to replicate the increasing strike, we could assume that the increasing strike is similar to a dividend assumption and we model this as an option with a strike of 1,734 EUR and dividends as shown in the column “Delta”.
Using the Bloomberg Option Valuation tool “OVME”, the same volatility and the assumption of a July 2016 maturity, the value difference between an European and American Option would be almost 20%, i.e. the American Option with the possibility to exercise at any day is 20% more valuable than the European one. This is due to the fact that I can basically wait until the last day before the synthetical dividend is paid an exercise then. So I don’t lose any time value and save myself the full dividend compared to an European exercise.
In our case however, I have to exercise 6 months earlier. With the OVME tool, I can for instance also calculate the value of an American vs. European Option for 6 months, “simulating” the time between for instance 03.07.2014 and 02.01.2015. For those 6 months, the valuation difference between an American and an European Option is only ~ 10%. Again, the “Bermudan” option is worth less than an American.
If I am actually in the last 6 months of the warrant maturity, the day after the last exercise possibility, the option will be exactly worth the value of a European Option. The day before it will be worth slightly less.
Anyway, as a very simple working assumption, I will assume that the “Bermudan” feature overall is worth 5% more than a European option.
Valuation of Piraeus Warrant
In order to value the Pireaus Warrant, we will have to make one further assumption: What is the final maturity ? If I understand correctly, the Greek Government has the possibility, to sell the shares after July 2016 without compensation to the Warrant holders if the Warrant holders do not convert. So as a realistic assumption one should use July 2016 as final maturity and not January 2018.
By the way, this “mechanic” of selling the shares without compnesation is a very strange featre for a Warrant.
In the following exercise I will use as the share price for Pireaus the level of 1.73 EUR, for the warrant 0.94 EUR (price at the time of writing)
As the first valuation steps, we can now do the following:
1) calculate the price of the warrant per share which equals the current traded warrant divided by 4,475. This would be 0.94/4,475= 0,21 EUR per share
2) “plug in” the price into the option calculator and solve for implied volatility (based on the current strike of 1.734 EUR and the “synthetic” dividends)
As a result we get an implied volatility of ~31.3% for the European Option, 26.2% for the American . This is rather at the low side for Piraeus. It is always a big question which volatilities to use, short-term (10 day) or longer term. Only 10 day historical volatility would justify such levels, trailing 305,50 and 100 day volatility is more in the 40-50% range.
We can now do a third step and
3) plug in for instance 45% as volatility and add 5% premium on the price of the European option to get to our value estimate. In this case this would result in a fair value of 0.33*1.05= 0.35 EUR per share or ~1.56 EUR for the Warrant. Compared to the 0,94 EUR per share, this would mean that the warrants trade at around 40% discount to their “fair value” which is quite significant.
So should one now run out and buy this undervalued security ? I would say: Not so fast, we need to consider at least one other factor
Potential shortening of maturity
The Greek Government as counterpart has quite a bad reputation for sticking to its terms. By googling a little bit, i found this quite revealing story from Reuters.
Two quotes here:
Some of Greece’s biggest banks and their advisors are starting to press the country’s banking rescue fund to look at ways to speed up their return to wider private ownership, banking sources say.
“They recognize that there are arguments to support the early retirement of the warrants,” he said, adding that the proposals would be favorable for the HFSF because it would no longer face a ‘cliff’ of all the warrants being exercised together.
However, any changes would have to be approved by the troika of European Commission, European Central Bank and IMF officials overseeing Greece’s bailout, who would be keen to make sure any changes did not disadvantage the HFSF or gift overly generous terms to the private investors.
In my opinion, this should make any holder of the Warrants really nervous. Currently, the Piraus Warrants do not have any intrinsic value, as the price of the share is below the strike. So all value is time value. With the option valuation tool we can play around a little bit with the maturity. Shortening the maturity (all other things equal) by 6 months for instance reduces the value of the Warrant by -10%, shortening it to July 2015 would reduce the value by more than -20%. The “break even” based on a 45% volatility would be some kind of “forced exercise” at the end of October 2014.
I do not know under which law the warrant has been issued, but if it’s under Greek law, then anything could be possible.
Valuation of Piraeus Bank
Finally a quick glance at the valuation of Piraeus Bank itself. Piraeus is currently valued at around 1,2 times book value. This is on a level with banks like Standard Chartered or Banco Santander, high quality diversified banks. However this is much higher than other domestic or regional players like for instance Unicredit (0.74) , Intesa (0,84), Credit Agricole (0,64) or even HSBC (1.05).
So without going into much detail, Piraeus bank looks rather expensive and a lot of recovery expectations seem to be priced in already.
At a first glance and under some critical assumptions, the Piraeus Warrants do look undervalued by around 40% based on historical volatilities and the price of the Piraeus share. However there seems to be significant risks, that the terms of the Warrant could be subject to change with a negative impact on the warrant. ALso the valuation level of Piraeus bank itself looks rather optimistic.
I would not want to own the Warrants “outright”. For someone who is ale to short the shares, a delta hedged position could be interesting in order to “harvest” to low implied volatility, although there would still be the risk of the change in Warrant terms.
I haven’t looked at the other Greek banks where similar warrants have been issued.