# Market Fluctuation: Data, Observations and Questions

#### TyndallDisperse

Hi, folks. I'm new here.

So, here are a few observations:
http://www.richmondfed.org/banking/...nds/pdf/delinquency_and_foreclosure_rates.pdf

The maximum fixed subprime mortgage delinquency rate hit a little over 25% after the market crashed and caused the wonderful unemployment rates that we contend with today. That maximum is in roughly 2010 Q2. Wikipedia describes the Great Recession as beginning in December 2007, but there was a "sharp downturn" in September 2008.

I've read several stories from several different perspectives on the crisis that caused the Euro-American economies to melt... the terms that get thrown around are "leverage", "securities", "swaps", "CDS (Credit Default Swap)", etc...

Here's an investment banker's perspective:
http://video.mit.edu/watch/a-bankers-perspective-of-the-financial-crisis-5224/

Notable quote:
15:04 -- ""It's not that debt has become more expensive over the years; it has become cheaper!""

A nice little example:
The Black Schole's Equation is a model in the form of a PDE that calculates what the price of a derivative should be based on a kind of statistical equilibrium. It was a brilliant concept that was developed by Fischer Black, Myron Scholes, and Robert Merton. Scholes and Merton received the Nobel Prize for their efforts in 1997 , unfortunately; Black was no longer alive to be credited as a Laureate.

(disclaimer: please feel free to correct me where my descriptions are faulty; I have no MFE, but some of you do)

Their model could do something that nothing could ever do before... it allowed traders to create two portfolios sell the option to interested clients in the market, if the market behaves nicely and in a way that closely approximates the state within the market that is assumed by the model... then the traders can let their clients bet on a stock in the market going up, or going down and the balance on the portfolio should remain zero (as opposed to horribly, badly, negative... which is undesirable).

So, anyways, this is a cool trick. People were excited about it. The Nobel Laureates and a few other folks decided to start a business based on their nifty new theory in 1994 called LTCM. They were brilliant, all of them. They knew what they were doing; or at least, as much as anyone was likely to know at that time. Up through 1997, the appreciation in value of the investments looked a lot like an exponential curve. Perhaps it was over exuberance, maybe it was arrogance, was it gamblers ruin? In 1998 LTCM's profits disappeared like dynamite detonating on the back of an elephant, then LTCM was no more. If the Nobel Laureates who created the theory cannot manage the risk associated with it's practice, then ultimately who can?

See:
http://en.wikipedia.org/wiki/File:LTCM.png

Other interesting little beasties exist in our market these days. High frequency trading based on bets of short term gain. Flash crashes can occur. If trading can be done en bulk millions of times in a fraction of a second, does this destabilize the market? How does this alter liquidity and volatility for the average joe investor? A Fourier series analysis can be done on any stock curve that you are interested in, so you can get a sense of the frequencies of the different oscillations in the market; historically, people who have invested in the stock market have been financially better off, but has the character of the market changed? Is it going to continue to be wise for the average investor to invest in stocks and bonds anymore? If a microsecond flash crash occurs as soon as an investor tries to sell their bonds, and they lose their entire investment... if this becomes a frequent scenario, then it would no longer be wise to invest in the market. (What is the variance of a stock's value given a time delay of "k" when it is sold?)

How does one estimate the value of a security when it has mixed with it the cumulative risk of several derivatives from multiple equity markets where the stochastic characteristics and assumptions of each market are inherently different? How does one estimate the risk associated with derivatives mixed in and leveraged and mixed with other bonds which also came from derivatives many hundreds of times, bundle it with several equity security, leverage it again, and hope for your risk calculation to be accurate? How can you possibly calculate risk accurately for something like this when some of the securities came from proprietary models developed by private banks whose underlying assumptions you don't know?!

Do scenarios like what I've outlined above really happen in practice?

I look forward to hearing your thoughts. I hope you'll forgive the mistakes that I've made in the statements above, like I said; I am not an MFE.

If you made it this far, thanks for humoring me.

Tyndall off.

#### C S

Some misconceptions:

1) Black--Scholes theory is not needed for traders to hedge options. They knew how to do this since long ago. The work of Black--Scholes--Merton legitimized option pricing in the eyes of academics and subsequently brought greater interest to the use of derivatives by financial practitioners. This is roughly analogous to how Newton is given credit for the gravitational law, but the actual law was known to others (like Hooke) from an experimental viewpoint. Newton gave a nice mathematical derivation of the law, which is why he's often given the sole credit.

2) LTCM was not "based" on Black--Scholes theory, nor the reason it failed. There's a nice book on LTCM by Lowenstein, "When Genius Failed" that goes into considerable detail. Yes, LTCM did do volatility trades, and yes, a key insight, perhaps THE key insight, of BS is that call/put option prices come from volatility not direction. But this insight wasn't wrong per se. LTCM just bet on the wrong side of the vol trade, which happens. Perhaps LTCM did underestimate the irrationality of the market, but John Meriweather is a top-notch trader. You don't get to where he is without understanding the markets are irrational.

3) You make it seem like normal investors can lose money because of some mysterious flash crash. This has yet to happen. Prices have recovered and stabilized within seconds even when the ultra high frequency guys are going nuts. If the closing price were affected, you'd have a strong point. It's quite debatable how unsafe this makes the markets, but don't mistake this as undeniable fact. Also, for the scenario you envision of some Joe selling his bonds and losing everything, he'd have to be placing market orders, and why would he be doing that?

#### TyndallDisperse

First of all, C S; thank you for outlining my misconceptions, I knew I probably had a few, I do appreciate it.

1) I didn't know this. That's very interesting.

2) In that case... it should be perfectly safe for the trader to sell options, right? Because the trader will never lose any money on the bet whether or not it goes awry unless they themselves also put money; their commission into the same option.

3) This is very comforting. Does anyone collect data on flash crash occurrences; if so, where can I find it? And what does it look like with respect to say... US Cancel To Trade Ratio.
What about data on closing price? You are a mathematician; please show me data, don't tell me.

To be honest, I'm looking into the possibility of investing myself, and I would rather lose my shirt to my own foolish investing decisions than because of intrinsic variability in closing price. I want to understand what can happen with a flash crash... and I am particularly interested in knowing exactly what types of things can happen if I try to sell when a flash crash occurs?

http://money.cnn.com/2013/03/20/investing/mini-flash-crash/

If I make hundreds of trades in my lifetime, and if the number of flash crashes exceeds 100/second, then you wouldn't be able to make a trade without having several crashes in between. If high frequency trading and flash crashes become more common it's inevitable that it will happen. You could easily imagine a stock price that is made up by a bunch of delta stacked at some frequency next to one another and zero everywhere else. If the microsecond that you click the button to close the trade, and it's value registers in the system the microsecond after the value hits 0 from 600 (say that this was the price of the stock before). So what can happen when it does? How can I control the damage to my investment when it does happen?

In theory, can you lose money if you make a trade precisely when a flash crash occurs? Can you have the closing price as the average value of a stock over a period of time; say ask for the closing price of the average of a stock price over a period of 1 minute to avoid your assets getting damaged by the microsecond crashes?

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#### C S

Couple quick comments. About hedging options, you are only perfectly safe if you are continuously adjusting the hedge at every possible moment of time and the underlying is perfectly liquid with no transaction costs of any kind. In reality, you do not hedge every instant because: 1) that's impossible. 2) you wouldn't even try to accurately approximate that impossibility because every transaction DOES cost you (not just fees/commissions but market impact) 3) there's no such thing as something that is perfectly liquid and that you can always buy and sell in any quantity you want.

Not sure what kind of trading you're talking about in your long series of questions, but it doesn't sound like you know about basic order types or what a brokerage does. I'd read about basic trading first on sites like Investopedia. That will answer most of your questions thus far (I think).

#### TyndallDisperse

My main question was simple:

What would happen if stock assets are sold the moment a flash crash occurs? A $600/share stock crashes to$20/share in the fraction of a second that the stocks are sold then in the fraction of a second after that the stock jumps back to it's original value... can this happen?

#### C S

My main question was simple:

What would happen if stock assets are sold the moment a flash crash occurs? A $600/share stock crashes to$20/share in the fraction of a second that the stocks are sold then in the fraction of a second after that the stock jumps back to it's original value... can this happen?

I think it's better to go even simpler, as even that is not so simple. What happens if you try to sell your stock shares right now? What price will you get for it? To answer this, you should know there are many prices, many "bids" for your stock shares, and each will have a limit on how many they will buy from you at that price.

When you submit an order through your broker, it will take time to execute. Unlike the straightforward scenario which I think you're imagining, the submitted order may travel through multiple systems before it even hits an exchange or dealer. Your broker will try to arrange it so you get the best execution given the constraints on the order. This may involve splitting up the order and/or routing order(s) to different venues and/or crossing orders with other clients. Note different venues may very well be listing different bids and some may allow hidden, or partially hidden, orders.

If you submit a market order, you are in effect saying, I don't care if the best price is radically different from when I sent the order, that's what I want -- execution now. A market order to sell will hit bid(s), including hidden ones, until it is completed. The first bid it hits is not necessarily anything like the price that was observed when you submitted.

So you see, price fluctuations arising from the shifting sea of bids will get you all the time, regardless of these flash crash scenarios you like to imagine. If you care about price fluctuations, you would submit a limit order, which, as name suggests, has a limit on the price.

#### TyndallDisperse

Thank you. That is more detailed an explanation than most of what I have found so far, reading around.

But I did find this:
http://www.dbresearch.com/PROD/DBR_INTERNET_EN-PROD/PROD0000000000269468.pdf

This article alludes to an interesting new set of incentives in the market. There is maker-taker trade pricing in the market these days. Meaning that prices shift based on whether or not the broker is producing more liquidity in the market. High frequency trading produces higher liquidity, therefore is less expensive per trade. I was concerned because a broker that I was speaking to led me to believe that the latency between hitting the trigger on buying a stock and actually having it traded was one the order of days.

I had heard of some HF Trading facilities locating right next to the exchange buildings. Latencies on something like this, I can imagine; might be as fast as MHz to perhaps GHz (probably unlikely in this regime). The Ultra-High Frequency trading mentioned in the article runs at MHz.

So, roundtrip latency time these days is around milliseconds.

"In terms of market volatility, neither Hendershott and Riordan (2009) nor Brogaard (2010) find any evidence for a detrimental impact of either AT or HFT."

I am almost convinced now, my fears allayed. What is the typical buy-in or per-share price to participate as an individual investor with a low latency (milli-second/trade) broker? (What would it be to work with an UHF (micro-second/trade) broker?)

And here is an interesting chart:
Watch what happens in 2010.

Surely all people can take advantage of the benefits of millisecond latency on their trades? Otherwise they would hopelessly disadvantaged...

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