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The Nobel Series: Valuators of derivatives

Amid the wide-ranging works of Robert Cox Merton and Myron Samuel Scholes in financial theory, the valuation of options by eliminating the need of risk premium stands out — but not without criticism

The Nobel Series: Valuators of derivatives
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The Nobel Prize in Economic Sciences in 1997 was awarded to Robert C Merton of Harvard University, Cambridge, USA and Myron S Scholes of Stanford University, USA, "for a new method to determine the value of derivatives".

Merton had been a science and engineering student at Bachelors and Masters level and began studying economics only during his doctorate studies. He got Bachelor of Science degree in engineering mathematics from Columbia University and did Masters in science from California Institute of Technology. Merton completed his doctorate in economics from MIT under the guidance of Paul Samuelson in 1970. After his PhD, he joined MIT as a faculty and stayed there until 1988. Merton then moved to Harvard where he stayed from 1988 to 2010, before returning back to MIT.

Scholes did his Bachelors in economics from McMaster University in Canada in 1962. After this, he finished his MBA from Booth School of Business in Chicago in 1964. He completed his PhD in economics from the University of Chicago in 1969 under the supervision of Eugene Fama and Merton Miller. While doing his PhD he joined as faculty member at the Sloan School in MIT in 1968. In 1973, Scholes moved to the Booth School of Business in Chicago and, in 1981, he moved to Stanford University, from where he retired in 1996.

Main works

Both Merton and Scholes focussed on financial theory — including lifecycle finance, optimal intertemporal portfolio selection, capital asset pricing, pricing of options, risky corporate debt, loan guarantees and measurement of risk. Merton has also written on operation and regulation of financial institutions. His works are published widely, with well-known works such as 'Continuous-Time Finance', 'Cases in Financial Engineering: Applied Studies of Financial Innovation', 'The Global Financial System: A Functional Perspective' and 'Finance; and Financial Economics'. Scholes also published widely but became famous for his 2012 article titled 'Not All Growth Is Good' in 'The 4% Solution: Unleashing the Economic Growth America Needs', published by the George W Bush Presidential Centre.

The best-known work of Merton and Scholes is the Black-Scholes-Merton model, which they proposed along with Fischer Black in 1973. The model basically provides a formula for valuing options. As we know, options are a type of derivative, which give the investor a right (but not an obligation) to buy or sell a security in the future at a previously agreed price. This allows the investor to hedge against the risk of fluctuating security prices. The main problem in such a valuation is to decide on which risk premium to use. It is here that the model provides a valuable insight: It is not necessary to use any risk premium since the risk is already included in the stock price. As per the model, the value of the call option is given by the difference between the expected share value and the expected cost if the option right is exercised at maturity.

As the Nobel website tells us:

Black, Merton and Scholes made a vital contribution by showing that it is in fact not necessary to use any risk premium when valuing an option. This does not mean that the risk premium disappears; instead, it is already included in the stock price.

The idea behind their valuation method can be illustrated as follows:

Consider a so-called European call option that gives the right to buy one share in a certain firm at a strike price of $ 50, three months from now. The value of this option obviously depends not only on the strike price, but also on today's stock price: the higher the stock price today, the greater the probability that it will exceed $ 50 in three months, in which case it pays to exercise the option. As a simple example, let us assume that if the stock price goes up by $ 2 today, the option goes up by $ 1. Assume also that an investor owns a number of shares in the firm in question and wants to lower the risk of changes in the stock price. He can actually eliminate that risk completely, by selling (writing) two options for every share that he owns. Since the portfolio thus created is risk-free, the capital he has invested must pay exactly the same return as the risk-free market interest rate on a three-month treasury bill. If this were not the case, arbitrage trading would begin to eliminate the possibility of making a risk-free profit. As the time to maturity approaches, however, and the stock price changes, the relation between the option price and the share price also changes. Therefore, to maintain a risk-free option-stock portfolio, the investor has to make gradual changes in its composition.

Both Merton and Scholes became active participants in the stock market. In 1990, Scholes became a special consultant with Salomon Brothers and then became managing director and co-head of its fixed-income-derivative group. In 1994 Scholes, Meriwether and Merton co-founded a hedge fund called Long-Term Capital Management (LTCM). The fund, which started operations with USD one billion of investor capital, performed extremely well in the first years, realising annualised returns of over 40 per cent. However, following the 1997 Asian financial crisis and the 1998 Russian financial crisis, the fund lost USD 4.6 billion in less than four months and collapsed abruptly. The collapse of LTCM brought legal problems for Merton and Scholes and, in 2005, the courts disallowed the firm's claim of USD 40 million in tax savings.

Apart from the Black-Scholes-Merton model, both Merton and Scholes have also contributed to other areas in financial economics. Merton generalised the Capital Asset Pricing Model (CAPM) which was proposed by William Sharpe — the Nobel Prize winner in 1990. Scholes worked with the other Merton (Merton Miller, the Nobel laureate in 1990) on various determinants of the stock market value.

Conclusion

While there is no doubt that the work of Merton and Scholes has been applied by many investors and brokers to value options, their work has also found application in the valuation of various securities as well as in valuations involved in contracts, disinvestments, and mergers and acquisitions. Their work has also been criticised for failing to predict crises and not being robust enough even in the valuations' estimates. Some critics even blamed the model for the 2008 subprime financial crisis since the model made everyone complacent and did not value the risk properly. The most stringent criticism has come from the famous economist Nicholas Nassim Taleb (of Black Swan fame). He suggested that the model was not in much use; it was not needed and that it wasn't even original. As I pointed out in my article in these columns in November 2020, Taleb blamed Merton and Scholes for not predicting the failure of the Long-Term Capital Management (LTCM) in 1998. In fact, they had claimed that the probability of LTCM failing was one in a trillion.

The writer is an IAS officer, working as Principal Resident Commissioner, Government of West Bengal. Views expressed are personal

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