## Exotic securities: “Detachable GDP linked Greek warrant” – Valuation approach

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.

Plaidon,

you are absolutely right. I have read it again and it is the differen *1.5.

Thank you very much.

MMI

I think the Payout is defined by (actual yoy GDP minus reference GDP growth rate) times 1,5 on Page 54 in the pdf-document

instead you wrote “the difference of the actual yoy GDP growth rate times 1.5 minus a reference GDP growth rate.

as result GDP growth “required for max” for 2014 should be 3,01%.

(3,01% – 2,35%) * 1,5 = 1,00%

What do you think?

I think the Payout is defined by (actual yoy GDP minus reference GDP growth rate) times 1,5 on Page 54 in the pdf-document

instead you wrote “the difference of the actual yoy GDP growth rate times 1.5 minus a reference GDP growth rate.

as result GDP growth “required for max” for 2014 should be 3,01%.

(3,01% – 2,35%) * 1,5 = 1,00%

What do you think?

they can carry it at the new nominal value as far as I understood.

mmi

Hi, i am an owner of one of these bonds, i would like to know what will happen in 2042 when it expires. This is unclear. Do i get back the nominal value of the bond or an amount resulting from all the conditions stated in your article?

i.e. carry them at 100% instead of the 1%? wouldn’t it have been possible to structure a loan and carry it impairment-only? just saying…

hi jan hendrik,

re a):I think its much easier if you view them as independent.That might not be mathematically correct,but in reality it could be.

So for instance due to Oil rice shock the nominal GDP can reach the target but no real growth happens.

c) They set this up to allow some financial institutions a non mark-to-market accounting. From what I heard, in Italy they can book it at nominal value if they keep the warrant. So the “rip-off” is done with the regulator/accountant/shareholder.

mmi

I tried to build a (backof the envelope) model for this and stopped, for three reasons:

a) it’s much more complexe than it looks as all probabilities are dependend on each other. I.e. the nominal criteria is not independent from the real ciriteria is not independent from the probability of default etc etc. Still thinking about how to solve this.

b) the 30 day call option by the greek state. This makes the security impossible to hold as every undervaluation can get locked in.

c) seriously, why did they set that up? it’s immaterial to the entire package, it’s a nightmare to value and it definitly took some time to structure. whose idea was it? who is ripping whom of? until I cannot answer this- caveat emptor.

You forgot the factor 1.5 (resulting in lower required real gdp growth, thus increasing value) and the buy back option of the issuer (resulting in a lower value of the gdp warrant).

thanks for reminding me.Was already quiet late last night…..

The buy back option in my opinion is not a real option as there is no fixed strike.

the 1.5 factor indeed increases value toacertain extent. 10% more probability of bet 2 ? I don’t know.

mmi