The Calculus of Finance
Bill Scott
Financial professionals are in the business of selling financial services, and they often use Nobel prize winning theories to convince us that they should be paid to help manage our personal portfolios. Our personal investments may differ from what such advisors would recommend, and it is important for us to have a basic understanding of these theories. Such knowledge allows us to decide our own philosophy, and thereby become better purchasers of financial advice. I am a physicist, one of SAIC’s longest term employees, and the mathematics of finance theory is a hobby. Many of the current theories finance are actually quite easy to understand with a scientist’s working knowledge of calculus. Learn how Harry Markowitz derived his Nobel prize winning portfolio theory and how William Sharpe expanded it into the Capital Asset Pricing Model. You will gain an appreciation for how risk and volatility should affect your portfolio holdings. The models also recommend realistic portfolio holdings for conditions when you might disagree with your financial advisor about the prospects of a company. For example, you may have special knowledge about certain technologies. No specific financial advice will be given. No predictions of the economy or any firm or investment will be given. Rather you will learn how expectations, risk, volatilities, betas and interest rates affect the modern theory of portfolio diversification. In addition I will present some original, unpublished, not refereed work on the risk sudden bankruptcy – the Enron effect.
Caveat Added May 2005 : My goal was to derive all these Nobel prize winning finance theory using the standard calculus understood by scientists and engineers. In fact, these theories each have a deeper mathematical derivations using second order terms of stochastic calculus and Ito’s Lemma which are not nearly so familiar. Subsequent to this presentation, I have discovered that equation 3 for the weighted average of portfolio expected growth has additional second order covariance terms that I should have included. I have not been able yet to correct the rest of this paper for this error. However I believe that the inclusion of Ito’s lemma for stochastic derivatives on slides 8 and 10 will enable the Tobin and Markowitz theories to still obtain. It’s not clear to me whether this would modify my bankruptcy results.
With this caveat, I believe this is still valuable work to enable scientists and engineers to use their knowledge of standard calculus to more rapidly understand the Nobel prizes of finance.
Below is a link to a PPT file containing the full presentation:
Full presentation (Powerpoint)
