Pg. 129-132

In the fall of 1969 Fischer and Myron Scholes started working on their model for option pricing. It started in a meeting that they were in together and developed in less than a year of them working together on it. This is not to imply that it only took a year to find this model. Both Black and Scholes had been thinking about this for a long time. One of the interesting methods that they used to develop this was to find out what needed to not be in the formula. From there they could get closer to what actually needed to be in the model.

After they had finished it they addressed the issue of why someone should care about what they developed. Black and Scholes wanted this to be useful for more people than just speculators. They concentrated on the fact that their model could actually be used to value the stock of a firm. Allowing people to eventually find the measure of discount due to the chance of default, among other things. I also like that they did give credit to Robert Merton in their first paper about this.

124-129

The prevailing logic of Black's day (and ours too) is that investors should be more risky when they are younger, and less risky when they are older and have a greater dependence on their investment income.
However, Black suggested that risk should be spread out over an investor's lifetime, rather than being reserved only for youth.
He suggested that the dollar amount spent on risky investments should be a function of a leverage parameter, which remains constant over a person's lifetime, b, and the amount of investment in a safe asset w. Multiplying b and w gives you the amount a person should invest in riskier assets over their lifetime.
His assumptions on lifetime risk tolerance lead to the formation of Wells Fargo's Stagecoach Fund, a constantly leveraged fund.

Black claims to have found the solution to option pricing in June 1969. Despite his brilliance however, Black did not yet recognize what he found when he figured it out.
Departing from conventional logic, Black began by assuming that an option's price was only a function of the underlying stock's price x, and time, t. Using CAPM, and adding variables to account for systematic and unsystematic risk, Black came to the following equation:

w₂=rw-rxw₁-½v²x²w₁₁

This equation, though Black did not realize it at the time, was the secret to option pricing.

Pages 121-124

In the summer of 1968, the MIT professor Paul Samuelson proposed to one of his students, Robert C Melton a partnership in order to write a thesis on how to price warrants. Samuelson already published a first attempt elaborating a formula to estimate the value of warrant at a point in time but the weakness was that the assumed expected returns are unknown and unlikely to be constant over time.

After writing the paper together, the new idea was to propose an equilibrium model in which both alpha and beta quantities are determined period by period, by supply and demand, given the risk preferences of investors.

Later, for his PhD work, Melton pioneered writing on the problem of continuous-time stochastic processes. According to his analytical framework, at every immeasurably small instant in time the die that determines the return on an asset is rolled again implying that the return over any limited interval of time is the sum of many rolls.

Pages 116-118

According to Fischer, when there is a lack of correspondence between the data and the theory, it is safer to assume that the theory is correct implying that Wells Fargo was right to prefer the market index fund suggested by the CAPM rather than the low-beta fund implied by the data.

Besides, Fischer had the will to improve his theory using recalcitrant experience referring to stimulating theoretical work with empirical anomalies. He criticized econometrics models because of the exclusive focus on data combined with less theoretical considerations. He said: “A crooked yield curve or unexplained stock price is suggestive, but I generally want to know why these patterns exist before I trade”.

Pages 109-111

Wells Fargo did not change its practices in order to adapt to Black and Scholes orientations; CAPM was still only an academic theory.

Several months later, the new trend was to offer to clients a market index fund (S&P 500) aiming only to match the market no to beat it. Thus, the main issue was to reduce costs of trading. Fischer had the idea to consider that the index fund manager as a liquidity trader who does not care about which particular stock he buys or sells. That flexibility could be exploited by advertising a list of stocks and prices at which one was prepared to trade, so that he would not lose to other markets.

For a leveraged fund, Fischer thought that borrowing at a rate that would change daily could solve the equation. Besides, the banks would prefer such an arrangement that guarantees a profitable loan even if interest rates rise.

Pages 105-109

CAPM states that expected return on a specified stock can be divided into two components, the risk-free rate of interest and a term multiplying the price of risk times the quantity of risk in the stock. The consequence is that low-beta stocks have higher returns and high-beta ones have lower returns than the theory predicts. Besides, CAPM suggests that the best passive portfolio strategy is to hold a value weighted market portfolio.

During the 70s, everyone was looking for inefficiencies to beat the market. For Black and Scholes, there is evidence on mispricing stocks suggesting the existence of a factor called the alpha effect. Indeed, low-betas stocks were underpriced and high-beta ones overpriced.

In order to exploit the anomaly, Black and Scholes proposed three strategies more efficient than the high-beta strategy:

The first is a market portfolio levered to have the same risk as the high-beta portfolio.

The second is a portfolio of low-beta stocks levered to have the same risk as the high-beta one.

The third is a mixture of long positions in low-beta stocks and short positions in high-beta stocks.

PG 102-105

Wells Fargo Bank was established during the gold rush because gold miners needed a way to convert their gold into cash. The bank also operated an express service to ship goods and mail. McQuown wanted to change investment management strategies from the unsophisticated ways of “water walkers” (having a magic touch to pick stocks) to a more quantitative and scientific method. McQuown heard about Fischer-Lorie results on common stock returns. A meeting with Lorie was arranged, and his popularity began to increase. As he was giving a talk in 1963 to IBM, the CEO from Wells Fargo was in the audience. McQuown was hired by Wells Fargo to further develop a quantitative technology for money management.

McQuown was suspicious that stock prices could not be easily exploited for profit, and hired Wagner and Cuneo, who were non-finance minds so he could teach them whatever he wanted. Scholes disapproved of their research, and they turned their focus to efficient market portfolio strategies. The strategy was to gather many great minds together in conferences and focus on helping Wells Fargo; in return wells Fargo financed all the research. The first conference was held in 1969 and focused turned to the CAPM.