How hard is it to establish a new theory?

Investment theories are to measure the average returns of different investments. There are two ways to measure an average, arithmetic average and geometric average. Arithmetic average provides an accurate measurement of various outcomes at the same time. Geometric average provides an accurate measurement of various outcomes over a period of time.   Since people need to measure investment outcomes over a period of time, we might expect the standard investment theory is built on geometric average. However, this is not the case. The standard investment theory, represented by Markowitz’s portfolio theory and CAPM (Capital Asset Pricing Model), is based on arithmetic return.

We will use an example of Ponzi scheme to illustrate the difference between measurement with arithmetic return and geometric return. Suppose one invests a thousand dollar in a Ponzi scheme, which lasts for four years. A typical outcome will look like,

The returns of such investment of each year are

Average return per year, with arithmetic average, is 50%. Average return per year, with geometric average, is -100%.

With arithmetic return, the investment performance of the Ponzi scheme is quite stellar. With geometric return, it shows clearly that such investment is a Ponzi scheme. In general, arithmetic return is higher than geometric return for the same investment. That is why people in charge prefer to use arithmetic return.

Many government programs, such as bank bailouts and inflation policies, are really Ponzi schemes that transfer wealth from the general public to the elites. If we use geometric return, various Ponzi schemes will be very easy to spot. Losses to the public will reduce greatly. At the same time, most profit opportunities for the finance industry will disappear as well.

As an example of such government programs, we will look at CPP (Canada Pension Plan). The deduction rates of CPP over the years are

The deduction rates have been increasing steadily over time. This pension system is clearly a Ponzi scheme. With geometric return, the performance measure will be dismal. The opposition to such pension systems will (hopefully) be much louder. This is probably why geometric return based investment theory has been aggressively resisted. Such a theory has been developed since 1956, almost seventy years ago.

Most people are aware of the struggle in getting Copernicus’ theory established. We often angrily denounce the church authority for persecuting Galileo and others. But few recognize that today’s environment is much more oppressive than the time of Galileo. Galileo was widely admired at his time, by Pope and many others. He held prestigious academic positions. Today’s pioneers, on the other hand, languish in poverty and obscurity, abused by the authority and despised by the public.