Slowly creating a hypothesis.

In the financial crisis of the 2007-2008, we experienced one of the most disastrous tests of modern economic theory.
During the “sub-prime” crash, a mass scale de-leveraging occurred creating events 26 standard deviations outside the normal. Situations such as these are dubbed “Black Swans”, by author Nassim Taleb in his book “The Black Swan: The impact of the highly improbable”. This event tested equilibrium theory to its limits (this is debatable as the limits are set under money management parameters). Major Hedge Funds were hammered relentlessly as their statistical arbitrage strategies reversed, driving further away from equilibrium instead of towards it. This flight to liquidity was seen several years earlier by a firm named Long Term Capital Management (LTCM).

In 1998, a superstar Quantitative Hedge Fund, LTCM, felt that exact pain, and succumb to it. LTCM had a strategy that involved On the Run, and Off the Run US Treasury Bonds. I should start by saying that liquid assets are usually priced higher than non liquid as they are easier to sell off without a large change in price. LTCM’s strategy was to buy the non-liquid 30 year Treasury bonds, and sell short the liquid On the Run 30 year bonds. This is known as relative value investing (or arbitrage in the modern sense of the word). The theory behind the strategy is that as they are essentially the same instrument, they should have the same value, and should converge on an equilibrium level, which shows profits on being both Long the Off the Run bonds, and Short the On the Run bonds. This turned LTCM into one of the largest funds of its time. That was until the Russian Debt Crisis.
LTCM had spread its strategy into many different markets and added massive amounts of leverage to ramp up its profits. As they assumed equilibrium theory would hold, they could profit. Unfortunately LTCM didn’t calculate human error into their models. When Russian defaulted on its debt, it created a flight to liquidity. The very objects LTCM was short, were being driven to the sky, and the investments they were long, were being demolished to bargain basement deals. They decided to keep buying as equilibrium had to be met at some point, but due to their massive leverage (~40:1) they were bleeding money fast.
Could this be an ideal period for the US to introduce their leverage caps on various markets? Probably, but they decided to wait several years and spend trillions of tax payers money before pointing fingers. LTCM was the first of the great Rocket Science Quant firms to fall.

Karl Popper had a theory. He believed that scientific discoveries are theoretically correct until they are proved wrong. So for the financial markets, you may say “this is the worst event to ever happen to the market”, and that would fuel traders to sell short, pummeling the market until it reaches its exhaustion point. This point is where the panic begins to slow, and the market sentiment begins to shift and they begin to buy again. Could this be applied to quantitative models to prevent future meltdowns?

This is where my theory steps in.
In the Foreign Currency market (FX, FOREX) currencies are priced in fractions of another. I.e. when you are bullish (thinking it will go up) on Cable (British Pound), you buy Cable against another currency that you believe is going to go down against Cable. But when you have two similar base currency crosses such as EUR/USD and GBP/USD then theoretically you should be bearish USD or bullish USD, and as the currency pairs have the same base, they should move in correlation with each other, except with different rates of change. This then has the potential to create a similar, profitable situation. Possibly giving the two a value in terms of each other, then modeling the spreads between them could help prove this theory, but the two already have a cross, EUR/GBP. The problem with the cross is that you are directly selling cable for euro when you are bullish, and vice versa for bearish. That is why I want to try and prove that it is possible for one to model, and profit from this statistical relationship. I view it as a much safer trade than simply buying/selling in the spot market. Yes, you do profit on one position, and lose on the other, but the loss is a hedge which is protecting against the spread widening.

To prove this theory I am trying to create sets of rules that need to be followed in order for this to be possible.

Firstly, defining the relationship between EUR/USD, GBP/USD and EUR/GBP is needed to prove that the no arbitrage theory holds. I will continue to use these pairs, but there are many pairs that work for this style of strategy, and some that probably show much greater profits.

Currency Bid (x) Ask (y)
Euro/Usd (e) 1.50(x1) 1.51(y1)
Gbp/Usd (g) 2.00(x2) 2.01(y2)
EurGbp bid = x3 ask = y3

X3 = x1/y2 y3=y1/x2
X3=(1.50)/(2.01) y3=(1.51)/(2.00)
X3=0.7462 y3=0.7550

Therefore,
x1/y2=x3
y1/x2=y3
Else an arbitrage opportunity arises.


..more to come...want to make sure my numbers are correct, worked all day and cannot think straight.