## The Midas Formula: Trillion Dollar Bet

The history behind perhaps the greatest formula ever created in finance: the Black-Scholes-Merton options pricing model. Two of its creators were awarded the Nobel Prize in Economics in 1997. A year later their hedge fund Long Term Capital Management (LTCM) had collapsed with staggering losses of $100 billion due to significant leverage of the strategy.

The Black-Scholes Formula was derived by observing that an investor can precisely replicate the payoff to a call option by buying the underlying stock and financing part of the stock purchase by borrowing. Only five variables were needed: the price of the stock; the exercise price of the option; the risk-free interest rate; and the time to maturity of the option. The only unobservable is the volatility of the underlying stock price.

The main problem with the framework (which assumes the ability to use risk-free arbitrage and dynamic hedging in continuous time) is that it doesn’t consider how a change in market dynamics (specifically liquidity risk and default) can affect overall market sentiment.

This means the prices of assets can in some extreme cases depart from what the formula says should hold. LTCM was brave and took a contrarian view. It borrowed even more in the face of the perceived profitable outcome. Instead the reverse happened (things just kept getting worse day after day).

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