Hey guys, I’m trying to figure out how to assess the value or returns of GDP-linked warrants for various countries. I have access to Capital IQ, Bloomberg, and FactSet. Basically, I’d like to create a spreadsheet whereby given projected GDP growth of X% and inflation of Y%, the GDP-linked warrants are worth $Z. Anyone here have thoughts on how I can do this?
The world would be better off with GDP futures. Anyway, Damodaran has some options spreadsheets that you could start from: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/spreadsh.htm#basicoption It depends on whether you get any dividends (I assume not, but not sure). I also would assume this would be a longer-term warrant, which means that Black-Scholes may not be the most accurate (I’m not sure if this is only in the case of dividend payments?), but could be a good starting place. As an aside, I have argued to some advocates of nominal GDP targeting, like Scott Sumner, that it would be a pain in the ass to implement based on levels since GDP growth is constantly revised. If I were looking at this, I would want to check the prospectus on how revisions are handled and what exactly the terms are. You may have to make some simplifying assumptions.
I dunno. The simplistic way would be to use X% growth and Y% inflation (plus error bars), you then project an expected GDP and an expected standard deviation, then plug into Black Scholes with a very long time horizon. The problem is that one of the things that Black Scholes assumes is that you can hedge the underlying by holding part of it. You wouldn’t actually be able to hedge GDP. Perhaps the best you can do is to try to create a portfolio that replicates GDP and then issue an option on that. Of course, then you have an optimization process and the risk that the replication will stop working, and the fact that the underlying hedging will be on a bunch of things and have lots of transaction costs, but you’d at least get a lower limit on o price.
Argentina EUR warrants? Given the instrument/market, I’d imagine the purpose of the exercise could be more relevant - are you trying to mark a position on the books, trade, or just doing it for the sake of learning? The IMF went through a modeling exercise: “Experience has shown that the poor design and low quality of statistics have been major problems in the history of GLWs.” They found the price changed significantly based on estimated growth rates and real GDP volatility…also significant FX risk (not sure if that’s applicable). Seems like kind of a crapshoot at the end of the day. My 2c.
…to add some context I worked at a place that had some Venezuelan Oil Warrants on their books and from personal experience the fudge factor in marking those positions was high to quite high, er “liquidity premium”.
Guys, thanks for the thoughtful feedback. It sounds like everyone’s on the same page here, the key takeaways being as follows: (1) Black Scholes could be useful in approximating the value of GDP-linked warrants; (2) However, valuations will be highly sensitive to assumptions; and (3) Empirically (per IMF and others), trying to model values of these securities too far in the future can be a cumbersome and perhaps evan an academic exercise. However, I did find a number of equity research reports on GDP-linked warrants which I guess anyone interested in reading more about can easily find by running a Thomson or TheMarkets.com search for “warrants” in the title. That’s probably the most time-efficient way of getting at this stuff in case anyone really needs it. (I was looking into this topic because my portfolio manager had a specific question…this is obviously outside my realm of personal expertise and is more of a one-off project)
Does anyone know why someone would buy GDP warrants and not options/warrants on broad market indexes? It seems that the latter would be far more liquid, easier to value, and would offer the same exposure.
i was thinking country etf - never heard of a ‘GDP-linked warrant’
ohai Wrote: ------------------------------------------------------- > Does anyone know why someone would buy GDP > warrants and not options/warrants on broad market > indexes? It seems that the latter would be far > more liquid, easier to value, and would offer the > same exposure. the vols aren’t the same.
justin88 can you elaborate on that, and specifically the implications therein? thanks
I should caveat this by saying I don’t know anything about GDP warrants, but nonetheless it would appear to me that, %-wise, Variance(GDP) << Variance(Market Index).
Furthermore they are not perfectly correlated. One could go up while the other goes down, e.g. GDP coming in below estimates (but still positive) and the market falls on that news.
i’ve never heard of these things before - how is the payoff determined in simple terms? i think bchad had a strong point about unability to hedge by trading the underlying… which means that risk-neutrality doesnt apply here and black-scholes would be extremely imprecise, hence the need to throw in fudge factors such as illiquidity premium to get to a risk-adjusted discounted rate
I’m not really sure if the vol argument is valid. If you trade options, you are basically leveraging your bet on the underlier. For instance, you could get the same delta of a $100 market index by buying maybe an option worth $10. If you want a highly volatile investment, you can always buy more options. I suppose you are right that GDP and stock indexes are not the same thing, so I guess if you want very specific exposure, you can buy whatever you want. Also, maybe for a country like Argentina, the index option market is not so liquid (I don’t really know - just guessing). Edit: I’m just very wary of illiquid, hard-to-value investments. Investment banks make a lot of money by structuring and marketing illiquid structures with nice spreads.
Mobius - here’s the IMF paper I referenced, seems pretty case specific and can be absolute GDP levels, % of actual-strike spread levels, etc. http://www.imf.org/external/pubs/ft/wp/2006/wp0685.pdf
Robert Shiller has advocated the development of GDP linked bonds wherein the coupon payment is somehow linked to GDP. It’s an interesting issue in public finance, since it would mean that a sovereign could have some automatic relief in the event of an economic slowdown and fall in revenues to support interest. Obviously, there would have to be an additional risk premium on top of it because the creditor would be taking on additional uncertainty as to the income stream, but because the terms of the bond are linked to GDP, it would be less prone to true default. Presumably a warrant on GDP might be a way to generate this synthetically. It still seems a bit strange to me. First of all, one would need an independent arbiter of what GDP actually is, or a country could simply understate its GDP in order to reduce its obligations. Secondly, growth in GDP isn’t really tradeable in substantial quantities. You’d have to own a large and representative portion of the economy and have shares in it. Potentially you could have futures on an index and then trade the futures, but that would depend on having a sufficient number of counterparties to make a market. I always try to be open to creative thinking, but I still don’t see how this really works in practice. Here are a few citations that might be relevant. http://en.wikipedia.org/wiki/GDP-linked_bond http://www.nytimes.com/2009/12/27/business/economy/27view.html http://blogs.wsj.com/economics/2011/02/17/worried-about-us-debt-shiller-pushes-gdp-linked-bonds/
why wouldn’t this be an otr treasury swaption? the rate s/b current gdp growth (+/- currency effects.)
numi Wrote: ------------------------------------------------------- > Guys, thanks for the thoughtful feedback. It > sounds like everyone’s on the same page here, the > key takeaways being as follows: > > (1) Black Scholes could be useful in approximating > the value of GDP-linked warrants; Just as a caveat: B-S assumes GBM for the underlier process; GDP, in contrast, exhibits considerable mean reversion. This might justify Justin’s intuition: > Variance(GDP) << Variance(Market Index). …though this also begs a few observations: + I think economic theory suggests that, over the long run, equity markets can’t grow faster than their surrounding economy. So even though their variance might differ, their long-run growth can’t, which suggests that options on the two should price similarly? + B-S is often applied to individual stocks, which can violate mean reversion for long periods of time
DarienHacker Wrote: ------------------------------------------------------- > + I think economic theory suggests that, over the > long run, equity markets can’t grow faster than > their surrounding economy. So even though their > variance might differ, their long-run growth > can’t, which suggests that options on the two > should price similarly? the option price is based on the forward price (net of dividends etc), which is simply TVM, so the EV of the underlier (GDP, economy in our case) doesn’t matter. the variance/stdev is primarily what determines the option (and warrant) price.
DarienHacker Wrote: ------------------------------------------------------- > numi Wrote: > -------------------------------------------------- > ----- > > Guys, thanks for the thoughtful feedback. It > > sounds like everyone’s on the same page here, > the > > key takeaways being as follows: > > > > (1) Black Scholes could be useful in > approximating > > the value of GDP-linked warrants; > > Just as a caveat: B-S assumes GBM for the > underlier process; GDP, in contrast, exhibits > considerable mean reversion. I might quibble with this… For the US (not necessarily for other countries), you could say that GDP is trend stationary, but I wouldn’t necessarily say it is mean-reverting (I tested it for an Ornstein-Uhlenbeck process and did not find it was significant with a 5-year or 10-year trend). For a first approximation you could probably just assume log changes in GDP are stationary.