Thursday, June 7, 2007

Kurtosis baby

Whoa baby, 2+ standard deviation move in the bond markets today! For those of you who are looking to get on the street but don't keep track of markets, you probably should start doing so. Big move, no good explanation, it seems? Rates market up 20bps today (10yr swap)! That's a huge move. S&P down some 1.75%. Prize to whoever can give me an explanation that I'll actually believe for the rates fallout today.

By the way, kurtosis is what statisticians call what market practitioners often call "fat tails." A lot of theory involves assuming that market returns are normally distributed (follow a normal distribution). In practice, we often see the distributions have a lot higher probability of a big move than a normal distribution would explain. Thus they say the distribution has "fat tails" or higher kurtosis compared to a normal distribution. Basically, days like today should not happen as frequently as they do if markets were normally distributed. But because of the high kurtosis, we actually expect days like today about three times a year.

For many of you, you will never view the markets like this. Most of the desks/traders today said "HUGE sell-off in rates markets." Only the quantitative types (only me, as far as I can tell) looked at it relative to the expected distribution. I'm a nerd, but I warn those less quantitative that we nerds are proliferating quite quickly on the street.

Ask for volatility and you shall receive. . .

6 comments:

Anonymous said...

How about volatility clustering? Big movements (not as large) in yesterday's markets and the day before. Do we expect just as big absolute movements in the near future??

Quant_Trader said...

Well, I just asked for vol, not a vol cluster. . .

I know our GARCH models tell us that we should expect more vol in the next few days. Volatility clustering has been shown in many empirical papers to occur, so yes I do expect some heightened vol. I am a bit long gamma at the moment. I would not, however, expect "just as big" absolute movement. Even with kurtosis, that 12-18 basis point day (depending on when you marked it) was a BIG day. I don't expect much more of it.

That being said, it is important not to just look at this from an academic point of view (I am criticized for this a lot, so I pass it on to you). Let's assume vol will cluster. So what? It's priced into the market. It's bloody expensive to buy option because implied vol is way way up. I am, in fact, slightly short vega because I expect the market moves to be not as big as are priced into the options right now.

To your point, today looked like it would be another big day. Markets were sold off when I walked into the office. Markets came roaring back mid-day. Looking only at closes does not show the extent of vol we saw intra-day today.

Anonymous said...

Hi again, didn't mean to sound like I was challenging your points just wanted to make another comment about vol.

Yes I agree, the red day was a BIG day, shook my local markets quite a bit too (Aus, All Ords) and as empirical evidence does support the move on Friday was predictedly large too! Our local markets however aren't as trigger happy as the Dow, largly because we are a lagging market. More often than not we will see a jump(or fall) in our markets on open and then a nice little drift either way.

Anonymous said...

Rates movement reaction to ECB and New Zeeland perhaps? As catalysts to the prevailing need of counter-inflationary measurements given strong growth?

Quant_Trader said...

The ECB rate change was largely expected. Surprise move by New Zealand really doesn't seem like a big deal (no offense to any Kiwis, but who really cares what rates are in New Zealand?).

The real disconnect I see is why the entire world would suddenly decide that monetary policy would need to be tightened globally. There was no economic data (in fact no trading these days seems to be data driven). I don't think New Zealand is a big enough economy to set off the sort of sell-off we saw. If it were a surprise hike in England (there was a 20% chance or so priced into the futures markets), I'd find it more believable.

Good thought, though. Your theory is a relatively common one on the street.

Anonymous said...

quant_trader... common because my understanding of what happened is solely based on the FT and WSJ. I don't gain much info about the markets from any other source really. I'm a newbie trying to learn.