Simple model for effect of bond convexity on Stock Index Futures

[nitro]

Hi,

Can someone point me to a paper for a simple model of how bond Convexity theoretically affects prices of Stock Index Futures? I think the spirit of the correlation is the same as that of Credit Default Swaps to SIFs, but I am not sure...

I have looked through the web but found nothing explicit. Maybe I am using the wrong keywords... I understand the basic idea, but I want to understand the theory as deeply as possible.

Ultimately it is obvious how IRs affect stocks, but why should convexity have such a powerful effect on the stock market is not completely obvious to me. Convexity is like gamma (in fact they are the same concept in different domains), in that it is not readily obvious (observable) unless you compute it, second order non-linear effect.

Thanks,

nitro

 

[ig0r]

Why concern yourself with theory when it rarely plays out like that in the market?

Convexity hedging moves the treasuries, and the correlation between treasuries and equities comes and goes (usually based on whether the move is rate-related or not)

 

[nitro]

Quote from ig0r:

Why concern yourself with theory when it rarely plays out like that in the market?

Convexity hedging moves the treasuries, and the correlation between treasuries and equities comes and goes (usually based on whether the move is rate-related or not)

Right, good point. The reason I want to become more familiar with convexity is because I believe we are heading to a mini-1980s style market (6% to 7% FFFs, with maybe an inverted curve), where markets will have a more significant IR component correlation. IOW, the stock/bond intermarket play is about to become vogue again. Timeline is 2008-2010. I remember those days as I was an arb clerk at the MERC in the TB pit when IRs were 17% and gold was $800 an ounce in 1980 dollars (about $1200 an ounce in today dollars.)

I agree the correlation has been weak for years, but I think it is coming rather than going. Thing is, I don't think it will be a first order effect, I think the effect will be in the second order, i.e., convexity. The play will be far less obvious than it was then, imo.

I don't see what trend could possibly derail SPX from 1600 or so by year end, and 1800 or so by 2008-2010. Perhaps not extending Bush's lower dividend taxationby a new prez. Inflation will be rampant. China will be a net importer of inflation and a net exporter of deflation for only so long. If you think commodities are expensive now, wait...

nitro

 

[dhpar]

I am with ig0r on this one.

The study of asset correlations in conjunction with higher orders is something nobody gives a damn (I mean dealers a la GS/JPM/MER/MS/BSC). It is much more interesting to add credit factor (1st order) if you want more granularity.
With recent spike in rates there is a lot of talk about effects on P/Es etc. Personally I am skeptical but maybe - you never know.
It is interesting what you say about correlation between rates and stocks in the first place - there was a plenty of research about this topic and it is far from conclusive.
I think the IR/EQ link is going to be (statistically) blurred even more than it was before - largely due to globalization and easy access to cheap credit.

Anyway, some help: when you speak about '80s and bond convexity the first thing that comes to my mind is Salomon Brothers and Mr. Ilmanen - google it - I am lazy to attach it as it has 6 parts.

 

[nitro]

Interesting. Thanks. I found it here at the bottom of the thread:

http://www.wilmott.com/messageview.cfm?catid=11&threadid=7633

How do you add a credit factor? What instrument would you look at? Credit Default Swaps? I need something that has a symbol and is traded, or can be computed in realtime, so that I can input it into a realtime ATS model as a parameter.

It is funny you mention Solomon Brothers. Back when I was in the TB pit, they were the 800 lb gorrilla.

nitro

Quote from dhpar:

I am with ig0r on this one.

The study of asset correlations in conjunction with higher orders is something nobody gives a damn (I mean dealers a la GS/JPM/MER/MS/BSC). It is much more interesting to add credit factor (1st order) if you want more granularity.
With recent spike in rates there is a lot of talk about effects on P/Es etc. Personally I am skeptical but maybe - you never know.
It is interesting what you say about correlation between rates and stocks in the first place - there was a plenty of research about this topic and it is far from conclusive.
I think the IR/EQ link is going to be (statistically) blurred even more than it was before - largely due to globalization and easy access to cheap credit.

Anyway, some help: when you speak about '80s and bond convexity the first thing that comes to my mind is Salomon Brothers and Mr. Ilmanen - google it - I am lazy to attach it as it has 6 parts.

 

[nitro]

Quote from nitro:

...
Ultimately it is obvious how IRs affect stocks, but why should convexity have such a powerful effect on the stock market is not completely obvious to me. Convexity is like gamma (in fact they are the same concept in different domains), in that it is not readily obvious (observable) unless you compute it, second order non-linear effect...

From reading the paper that dhpar suggested above, in the section on convexity it explains clearly why convexity is desirable to the point that investors are willing to take a lower yield relative to another bond with lower convexity, because convexity raises expected return. It all makes nearly perfect sense now.

nitro

 

[annaland]

Quote from nitro:

Hi,

Can someone point me to a paper for a simple model of how bond Convexity theoretically affects prices of Stock Index Futures? I think the spirit of the correlation is the same as that of Credit Default Swaps to SIFs, but I am not sure...

I have looked through the web but found nothing explicit. Maybe I am using the wrong keywords... I understand the basic idea, but I want to understand the theory as deeply as possible.

Ultimately it is obvious how IRs affect stocks, but why should convexity have such a powerful effect on the stock market is not completely obvious to me. Convexity is like gamma (in fact they are the same concept in different domains), in that it is not readily obvious (observable) unless you compute it, second order non-linear effect.

Thanks,

nitro

I’m not familiar with papers that explicitly show the relationship between convexity and stock futures prices – there is a lack of consensus among academics on whether bonds lead stocks or stocks lead bonds and I’ve found that some of the debate ends there. However, if you’re interested, you can check out the following:
“Firm-specific information and the correlation between individual stocks and bonds” (Kwan 1996)
“The Informational Efficiency of the Corporate Bond Market: An Intraday Analysis” (Hotchkiss and Ronen 2002)
“Modeling the Conditional Covariance Between Stock and Bond Returns: A Multivariate GARCH Approach” (Peter de Goeij and Wessel Marquering 2004)

 

[nazzdack]

Post your question at wilmott.com. The quants over there might have an answer.

 

[dhpar]

Quote from nitro:

Interesting. ..... nitro

re Salomon papers: I see that in the thread you posted are all 6 parts but in addition at the bottom there is a part 7 which I thought never got published. Looking forward to read this one cheers
These are classic papers for fixed income - in fact probably the most influential of all - and it does not matter that they are quite basic. They always made for good interview questions.

re Wilmott: I used to post there quite a bit (under different username). But since about 2005 the quality disintegrated because many good quants left for http://www.nuclearphynance.com/ (which is not a very active forum).
In any case it is a good place to fish for papers - if you bring CDS in ATS you should try for something with "Capital Structure Arbitrage" in the heading.

re CDS: almost impossible to get intraday tick data. Creditex has platform (I think without API) which is kind of live screen with quotes - but it will cost you dear. The best source for daily data is certainly Markit - but they will likely screw you up too.
You may be lucky though. Coincidentally today CBOT starts to trade a new product (ticker CX). It is a future on index of 50 US investment grade credits. (see this thread: http://www.elitetrader.com/vb/showthread.php?s=&threadid=97404&highlight=cx) But here you will have to wait for some data history and mainly if the product succeeds.

gl (and keep it simple

 

[nitro]

Thanks for the websites annaland.

nitro

Quote from annaland:

I’m not familiar with papers that explicitly show the relationship between convexity and stock futures prices – there is a lack of consensus among academics on whether bonds lead stocks or stocks lead bonds and I’ve found that some of the debate ends there. However, if you’re interested, you can check out the following:
“Firm-specific information and the correlation between individual stocks and bonds” (Kwan 1996)
“The Informational Efficiency of the Corporate Bond Market: An Intraday Analysis” (Hotchkiss and Ronen 2002)
“Modeling the Conditional Covariance Between Stock and Bond Returns: A Multivariate GARCH Approach” (Peter de Goeij and Wessel Marquering 2004)