Archive for February, 2011

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Gunning for Stop Orders in HFT

A prudent risk management strategy in financial markets is using stop losses to protect your downside - even if you are short - but is this yet-to-be-fulfilled order able to be gamed by other market participants?

Short answer is YES but first lets define what we mean by stop orders, in the context of a short position.

A buy stop order is an order to buy a given security at a specified buy stop order price. This order is only activated once the security's market price rises above the specified buy stop price. The advantage of a stop order is you don't have to monitor how a stock is performing on a daily basis. However, the disadvantage is that the stop price could be activated by a short-term fluctuation in a stock's price and worst, once your stop price is reached, your stop order becomes a market order and the price you receive may be quite different to the stop price, especially in a fast-moving market where stock prices can change rapidly.To mitigate this risk investors can use buy stop-limit orders...

A buy stop-limit order is the same only the order is a limit order once the buy stop price has been reached. Thus a stop-limit buy order, if triggered and fulfilled (it's not guaranteed to be executed), buys the security at or below the specified limit price.

So why buy something in the future at a higher price than it is trading at now? There are several reasons:

  1. you have short-ed the security and want to limit the loss (you lose when the stock goes up);
  2. you are a momentum trader and want to buy only when you see a certain amount of momentum (momentum traders reason that the current trend in prices is more likely to continue in the same direction, rather than revert);
  3. in a declining market you expect a stock to "rebound" and want to buy just after the turn-around.

How can such stop orders be manipulated? Well, large market participants can look at price movements over time and perform similar analysis that "chartists" do and figure out where clusters of stop orders might be - in the near vicinity of trades by people with limited downside tolerance, or at so-called "levels of resistance". With deep enough pockets, large participants can buy the security to force the price up until it triggers the anticipated stop order prices. When that happens market forces drive the price even higher and the manipulator can sell out with a profit. Of course, the risk for the manipulator is that the stop orders do not exist, or the price doesn't reach them and they must close out their positions at a loss.

Apparently, this is called "gunning the stops".

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Market-Based Estimation of Implied Corporate Credit Risk

Corporations that raise capital in the debt markets need to pay a spread over risk-free instruments to compensate the investor for the increased default risk that they assume when buying bonds issued by the said corporation. Thus the buyer of such "credit-risky" bonds need to be able to estimate the likelihood of default and compare this to the default rates implied by the current trading spread of the bond. Sure, credit rating agencies do dish out ratings such as AA, AAA, BBB etc but these are far too broad and not that useful here.

There are more exotics techniques but lets first examine a simplistic back-of-the-envelope approach to calculate implied credit risk. Assume p is the probability of default of the corporation, and r is the recovery rate if/when a default happens.

Assume a corporate bond is currently yielding 12% and government bonds with the same term are yielding 10%. Further suppose that if the corporate bond defaulted the recovery rate would be 50%.

By definition, the (US) government bond is default-free and thus returns $1.1 annually for every $1 of face value. During this same time period, an investor holding a corporate bond could have one of two things happen. The issuer could default, with probability p, or it might not with probability (1-p). The payouts associated with these events are, respectively, $1.12 and $0.5 per dollar of face value. Generalising this it it would look as follows:


The efficient-market hypothesis implies that all available information is used in pricing the instrument thus the corporate bond price/yield already has the credit risk probability embedded in it. Thus an investor should be indifferent to investing in the government bond or the corporate bond. We can therefore look at the expected value of both instruments after one period and solve for the implied credit risk.


1.1 = (1-p)1.12 + 0.5p
=> 1.1 = 1.12 - 1.12p + 0.5p
=> 0 = 0.02 - 0.62p
=> p = .02/.62 = 3.226%

In other words, this crude approach indicates that there is a 3.226% chance of default in the next 12 months for the said corporation.

As an aside, because only two events can happen, and we look only at distinct time epochs, this approach is effectively a one-period, discrete-time binomial tree model. Of course it is flawed in many ways (the real-world is continuous not discrete), but it's a good enough quick guess.