# Who invented these key notions in Finance?

We often give credit to the origins of academic achievements. The Black-Scholes equation or the Gibbons Ross Shanken (GRS) test etc.

• Net Present Value (NPV),
• Internal Rate of Return (IRR),
• Duration of bonds,
• Law of One Price (LOP),
• Time value of money,
• Stochastic Discount Factor (SDF) or pricing kernel?

These are fundamental things which are taught to undergraduates in one way or the other. But who first came up with these ideas?

Net Present Value (NPV) as a soft concept existed probably even in antiquity but it was formalized and made popular by Irving Fisher in his book the Rate of Interest.

Internal rate of return is basically a special application of NPV. It was also first formally introduced in Fisher's book although he called it 'rate of return over costs'.

Duration of bonds was introduced by Canadian economist Frederick Macaulay, but the concept was later greatly expanded by none other than Fisher together with Weil.

Law of One Price I was not able to trace this idea back to any single person. According to this article:

The intellectual history of the concept can be traced back to economists active in France in the 1760-70’s, which applied the “law” to markets involved in international trade. Most of the modern literature also tends to discuss the “law” in that context.

But no exact names are mentioned. It might be that the original authors are unknown. As @Henry pointed out in his comment, these were most likely the French Physiocrats.

Time value of money this like the NPV, a vague notion that existed already in antiquity. You can find a lot of antique quotes that boil down to saying “time is money”, but more formally, it was introduced to the west by Martín de Azpilcueta of the School of Salamanca.

Stochastic Discount Factor - as in its modern mathematical representation can be traced back to the works of Harrison and Kreps (see 1), and Hansen et al (see [2-5]). However, as pointed out in @Michael +1 comment, the concept can be already traced back all the way to Arrow-Debreu and Radner. Of course, on this subtopic, the list of sources is not exclusive.

1 Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20, 381-405.

[2] Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50, 1029-1054.

[3] Hansen, L. P., & Jagannathan, R. (1991). Implications of Security Market Data for Models of Dynamic Economies. Journal of Political Economy 99(2), 225-262.

[4] Hansen, L. P., & Richard, S. F. (1987). The role of conditioning information in deducing testable restrictions implied by dynamic asset pricing models. Econometrica 55(3), 587-613.

[5] Hansen, L., & Singleton, K. (1983). Stochastic Consumption, Risk Aversion and the Temporal Behavior of Asset Returns. Journal of Political Economy 91(2), 249-265.

• Thank you very much!! – Alex Mar 14 '20 at 15:03
• Seminal papers on GMM and the Hansen-Jagannathan bound, etc, are not really relevant to the question of when the notion of SDF came about. Harrison-Kreps did not use the "SDF" terminology and the entire math finance community still does not today. "Super-martingale price deflator" is the correct description of SDF as a mathematical object. Economically, the notion of SDF really goes back to Arrow-Debreu and Radner. SDF are AD price densities. – Michael Mar 14 '20 at 17:27
• @Michael oh okay I will update my answer to reflect that – 1muflon1 Mar 14 '20 at 17:36
• The French economists of the 1760s were probably the Physiocrats, of which there were several – Henry Mar 14 '20 at 22:32