April 14, 2013
by Patrick
Comments Off on Finance Engineering 102: Derivatives
The housing crises was a Fed induced asset bubble that started to pop in 2007. It’s now 2013 and we can still see the affects of the crises as more homes in foreclosure slowly make their way to market. To understand the housing melt-down, one must understand only one thing: derivatives. Just like derivatives in calculus, the derivatives in the financial world derive their value from some other function.
Take the example of the stock option. It derives it’s value from the value of a stock, which is just another function:
Think about the function:y=mx+b
This function is the value of a stock where y is the dollar amount it costs to buy one share of a stock and x being the time value. The slope m is the merits of the company’s fundamentals, and the y-intercept, or amplitude, is determined by the animal spirits of human beings. If more people place a higher value on the prospects for the future of the company, they will naturally think the companies fundamentals deserve to be valued higher, and the slope will increase. The value of the stock is not a linear function as in this example; the linear line of y=mx+b only illustrates how to think about the value of a stock. To understand a stock’s price, we have to have some knowledge beyond Algebra and delve into the world of Calculus. But don’t worry, no calculation is required! The value of a stock is not a straight line, but rather, it is often times a curve. So it will have some exponents in the function. If you can imagine the shape of a parabola, you know what an exponential function looks like.
So now, we know how the stock option derives it’s value. Just like a derivative is the slope of the tangent to a point on a curve for a value of x, the option’s value is the slope of the tangent to the curve of a stock’s value at a point in time. Thus, an option’s integral is a stock, and a stock’s derivative is an option. Simple!
Derivates can be stock options, or the toxic stuff like CDS and MBS that financials like AIG sold, and lost so much money, and had to be bailed out by the government. The CDS’s are Credit Default Swaps. They are the derivative of the MBS- the Mortgage Backed Security. The MBS got there value from the value from the payment of mortgages of all the houses in the country, so they are like the the function of the Stock in the example above. As the MBS lost value, the CDS gained value because they protected against default of the mortgages of all the houses in the country. So the MBS is the inegral to a CDS and the CDS is the derivative of the MBS. And that’s as simple as the housing crises is. Unfortunately, just like sketching the graph of a curve is difficult and requires the use of calculus (until the TI-83 came along!), the solution to fixing the housing crisis is complicated and so far the Fed has not been able to fix the problem. Houses still take months to come to market in foreclosure. Just like the price of gasoline goes up when there is not enough coming to the gas stations, the prices of houses are being kept up by not enough coming to the market. As soon as all the supply is allowed to go through the foreclosure process, the supply will increase as we are still building new houses and no major home-builder went under in the greatest housing burst we’ve seen, because they were the recipients of a “back-door-bailout” in the form of first-time-homebuyer subsidies paid for by the tax payer.
