value and opportunity

In the first post i quickly looked at the features of the “Detachable GDP linked Greek warrant” (ISIN GRR000000010)

With securities like this, there are usually many ways to try to value this. You could eiher lock up a handfull of rocket scientists into an office and only let them out if they produce a model which is mind boggingly difficult, including at least features like “Monte Carlo simulation, path dependend barrier option etc.” or you can try a “common sense” approach to get a feeling about the risks and value drivers of such a complex structure. As anon-rocket scientist, I prefer the second one.

In order to get a rough idea how to evaluate this, we have to make sure to understand the following issues and risk factors:

Default risk

If Greece defaults, we don’t have to worry about GDP growth anymore. We should assume zero value (no recovery) in this scenario.

Maximum pay out

As discussed, the bond pays out a maximum of 1% on outstanding notional starting 2015. Based on the amortisation schedule (by the way: here is the Reg_S_Invitation_Memorandum1 GDP warrant starts at page 52) we can compute the best case cashflows:

	Nominal	Coupon max	Payment in % of original amount
2012	100.0%
2013	100.0%
2014	100.0%
2015	100.0%	1%	1.00%
2016	100.0%	1%	1.00%
2017	100.0%	1%	1.00%
2018	100.0%	1%	1.00%
2019	100.0%	1%	1.00%
2020	100.0%	1%	1.00%
2021	100.0%	1%	1.00%
2022	100.0%	1%	1.00%
2023	100.0%	1%	1.00%
2024	95.2%	1%	0.95%
2025	90.5%	1%	0.90%
2026	85.7%	1%	0.86%
2027	81.0%	1%	0.81%
2028	76.2%	1%	0.76%
2029	71.1%	1%	0.71%
2030	66.0%	1%	0.66%
2031	61.0%	1%	0.61%
2032	55.9%	1%	0.56%
2033	50.8%	1%	0.51%
2034	45.7%	1%	0.46%
2035	40.6%	1%	0.41%
2036	35.6%	1%	0.36%
2037	30.5%	1%	0.30%
2038	25.4%	1%	0.25%
2039	20.3%	1%	0.20%
2040	15.2%	1%	0.15%
2041	10.2%	1%	0.10%
2042	5.1%	1%	0.05%
2043	0.0%	1%	0.00%
Total			18.62%

So in the “perfect recovery case” and ignoring the option of the Government, the bond will pay out a maximum total of 18,62% of nominal value over its life.

Bond equivalent

If we then forget for a moment about the GDP triggers, we could calculate a market value for a bond with a fixed payement schedule resembling the best case of the GDP linker. For this we can use the current traded yield of the new greek Bonds, which is around 16% p.a.

	Nominal	Coupon max	Payment in % of original amount	NPV at 16%
2012	100.0%
2013	100.0%
2014	100.0%
2015	100.0%	1%	1.00%	0.6%
2016	100.0%	1%	1.00%	0.6%
2017	100.0%	1%	1.00%	0.5%
2018	100.0%	1%	1.00%	0.4%
2019	100.0%	1%	1.00%	0.4%
2020	100.0%	1%	1.00%	0.3%
2021	100.0%	1%	1.00%	0.3%
2022	100.0%	1%	1.00%	0.2%
2023	100.0%	1%	1.00%	0.2%
2024	95.2%	1%	0.95%	0.2%
2025	90.5%	1%	0.90%	0.1%
2026	85.7%	1%	0.86%	0.1%
2027	81.0%	1%	0.81%	0.1%
2028	76.2%	1%	0.76%	0.1%
2029	71.1%	1%	0.71%	0.1%
2030	66.0%	1%	0.66%	0.0%
2031	61.0%	1%	0.61%	0.0%
2032	55.9%	1%	0.56%	0.0%
2033	50.8%	1%	0.51%	0.0%
2034	45.7%	1%	0.46%	0.0%
2035	40.6%	1%	0.41%	0.0%
2036	35.6%	1%	0.36%	0.0%
2037	30.5%	1%	0.30%	0.0%
2038	25.4%	1%	0.25%	0.0%
2039	20.3%	1%	0.20%	0.0%
2040	15.2%	1%	0.15%	0.0%
2041	10.2%	1%	0.10%	0.0%
2042	5.1%	1%	0.05%	0.0%
2043	0.0%	1%	0.00%	0.0%
Total			18.62%	4.23%

This table shows us, that the value of such a bond would be currently 4.23% based on the yields of the traded Greek Goevernment bonds

So let’s summarize this:

If the GDP linker would be a bond with a fixed payout amounting to the maximum payout of the discussed mechanism, its current value would be 4.23% of nominal value.

Next step: Assuming a “binary” option

Now just for fun, we could assume that the bond would only contain one option: If the first threshold is reached (2014 GDP 210 bn EUR, real 2014 yoy GDP growth of >= 2.34%) we could approx. work out the implied probabilityin current market prices.

So very simplistic (and mathematically not correct), with a curent price of the GDP warrant of ~0.80 % of nominal, the implied probability would be 0.80 EUR / 4.23 = 18.93% of achieving the required GDP scenario

Next step: More options !!!!!

As each years coupon payment of the bond depends independently on each years YoY real GDP growth, in theory each coupon would have to be valued as a seperate option. So theoretically, ignoring the nominal GDP hurdle, we have 29 single options packed into this security !!!

However, as we have seen in the second table, the options in the later year are worth almost nothing due to the high discount rate.

They payout itself is defined as the difference of the actual yoy GDP growth rate times 1.5 minus a reference GDP growth rate.

The reference rates are the following rates,the second colum shows the required rates for max.payout:

	ref GDP yoy	required for max
201400.00%	2.35%	2.23%
201500.00%	2.90%	2.60%
201600.00%	2.85%	2.56%
201700.00%	2.77%	2.51%
201800.00%	2.60%	2.40%
201900.00%	2.50%	2.33%
202000.00%	2.25%	2.16%
202100.00%	2.00%	2.00%

If we look at the Eurostat page, which publishes the relevant rate we can see that from 1996 until 2007, Greece had growth rates usually north of 3.5% with few exceptions. Interestingly they offer projections for 2012 and 2013 as well.

GDP hurdle: more fun

Maybe late at night during those negotiations an advisor thought: “hmm 29 different options with a non traded underlying is not difficult enough, so lets add some funky stuff !!!”.

As I described in the first post, no matter what the actual yoy growth rate looks like, the security only pays if certain nominal GDP thresholds are reached.

The thresholds are as follows:

year	nominal GDP	yoy
2014	210.1
2015	217.9	3.71%
2016	226.4	3.90%
2017	235.7	4.11%
2018	245.5	4.16%
2019	255.9	4.24%
2020	266.47	4.13%
therafter	266.47	0.00%

To compare this with current data, I downloaded the GDP numbers directly from the official Greek statistical service, ELSTAT.

YEAR	2001	2002	2003	2004	2005	2006*	2007*	2008*	2009*	2010*	2011*
gdp	142	151	166	180	189	204	215	222	225	223	212

Interestingly, all numbers since 2006 are “provisional” whatever that means.

So in order to hit the nominal trigger, Greek GDP hast to reach 2011 levels in 2014.

Purchase Option

According to the prospectus, Greece has the “option” to purchase the warrants back. Howver this “option” isnot based on a fixed strike price but atrailing 30 day market price. Theoretically, an option at market price does not have any theoretical option value. However it introduces some “moral hazard” into the scheme. Greece could give a very bad outlook and then buy the Warrants back cheaply beforethen revising the outlook upwards.

So before this gets boring, let’s apply some common sense instead indulging in further quant dreams. In my opion one could think about the two main features as two “bets”:

A) Nominal GDP “bet”

This is basically a bet that Greece doesn’t fall in a deflationary trap and regains Nominal GDP around 2014.

B) Back to historical growth “bet”

This is the second bet that Greece goes back to historical growth and we get the full payout

In order to win this “game” one has to win both bets, winning only one is not enough.

If we further assume that the possibility of a Greek bankruptcy is independently reflected in our calculated discounted cash flows, we can value the security in the following way:

Probability of “Nominal GDP bet” times probability of “Historical growth bet” times NPV of max payout

With this assumption one can calculate a very simple valuation grid based on the NPV of 4.23% for the maximum payout:

	Nominal bet
Back to Growth	10%	20%	30%	40%	50%
10%	0.04%	0.08%	0.13%	0.17%	0.21%
20%	0.08%	0.17%	0.25%	0.34%	0.42%
30%	0.13%	0.25%	0.38%	0.51%	0.63%
40%	0.17%	0.34%	0.51%	0.68%	0.85%
50%	0.21%	0.42%	0.63%	0.85%	1.06%

So the picture is relatively clear: Only if one asumes for both, the non-deflation scenario and the return to historical growth bets a chance of 40-50% EACH, then the current market prices of around 80 cents might makes sense.

Personally, I don’t see the returns to historical growth rates any time soon, although I might accept a chance of maybe 50% that they can reach the nominal target.

At the moment, I would not buy this at any price. I think this is one of the securities which will “sleep” for a long time eventually die or maybe become interesting in 5 years when everyone has forgotten about them and Greece for some reason avoided bankruptcy again and one can get this for virtually nothing.

Edit:Some changes made with regard to the GDP growth formula and the repurchase option.Thanks to Dante for reminding me.