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2 Concepts of Finance
2.6 Efficient Market Hypothesis
Another basic assumption is that in a large market with many tradeable goods and
many trading agents there always will be someone willing to participate in a trade. I
may try to short large quantities of a stock because I believe its value will decrease,
but there is still someone believing that the value increases and buys all the stock I
want to sell. Likewise, we assume that a farmer, who is interested in a smaller, but
guaranteed, later price to sell his wheat, always finds a trading partner who accepts
the other side of the trade.
A consequence of the large number of eager trading agents and the existence
of an investment opportunity at the risk-free rate r f , the market as a whole will
grow at the risk-free rate r f on average, though large fluctuations can occur. Why
is that so? Well, if the average rate of the entire market were lower then all traders
would invest money in risk-free bonds and nobody would invest in companies. The
companies would need to react by promising a higher rate of return, albeit at some
risk for investors. But some investors will take the risk and some will make money
and some will lose, but on average the overall gain will be at the risk-free rate.
Note, that the same mechanism will work between other trading partners. As soon
as there is an imbalance of rate of return and risk, someone will exploit it and the
average growth is restored by supply and demand. This is called the efficient market
hypothesis, namely that supply and demand will always exploit any imbalance until
it is removed. The exploitation of a small trading imbalance without incurring a risk
is called arbitration, an example is the difference in gold price in the US and UK. If
it gets larger than the handling costs, it makes sense to buy Gold where it is cheaper,
transport it across the Atlantic and sell it at a profit. This only works until the demand
on gold is so large that the Gold price rises to a level that makes the deal unprofitable.
After this discussion it should become a bit clearer that stocks fluctuate randomly,
but the market as a whole maintains an average growth rate equal to the risk-free
interest rate r f . This already hints at the diffusion equation with a drift term, which
will occupy us in the coming chapters.
Before progressing, let us briefly summarize the “rules of the trade,” a number of
basic assumptions the characterize markets in a somewhat idealized form, mainly to
make the theoretical analysis in later chapters feasible.
2.7 Theoretical Markets
The markets and mechanisms are based on assumptions that we list in the following.
Some of the rules are rather generic to enable fair trading with equal information
available to all participants and others are somewhat idealized in order to make
analytic methods feasible. These rules are nevertheless largely valid even in real
markets.
2 Concepts of Finance
2.6 Efficient Market Hypothesis
Another basic assumption is that in a large market with many tradeable goods and
many trading agents there always will be someone willing to participate in a trade. I
may try to short large quantities of a stock because I believe its value will decrease,
but there is still someone believing that the value increases and buys all the stock I
want to sell. Likewise, we assume that a farmer, who is interested in a smaller, but
guaranteed, later price to sell his wheat, always finds a trading partner who accepts
the other side of the trade.
A consequence of the large number of eager trading agents and the existence
of an investment opportunity at the risk-free rate r f , the market as a whole will
grow at the risk-free rate r f on average, though large fluctuations can occur. Why
is that so? Well, if the average rate of the entire market were lower then all traders
would invest money in risk-free bonds and nobody would invest in companies. The
companies would need to react by promising a higher rate of return, albeit at some
risk for investors. But some investors will take the risk and some will make money
and some will lose, but on average the overall gain will be at the risk-free rate.
Note, that the same mechanism will work between other trading partners. As soon
as there is an imbalance of rate of return and risk, someone will exploit it and the
average growth is restored by supply and demand. This is called the efficient market
hypothesis, namely that supply and demand will always exploit any imbalance until
it is removed. The exploitation of a small trading imbalance without incurring a risk
is called arbitration, an example is the difference in gold price in the US and UK. If
it gets larger than the handling costs, it makes sense to buy Gold where it is cheaper,
transport it across the Atlantic and sell it at a profit. This only works until the demand
on gold is so large that the Gold price rises to a level that makes the deal unprofitable.
After this discussion it should become a bit clearer that stocks fluctuate randomly,
but the market as a whole maintains an average growth rate equal to the risk-free
interest rate r f . This already hints at the diffusion equation with a drift term, which
will occupy us in the coming chapters.
Before progressing, let us briefly summarize the “rules of the trade,” a number of
basic assumptions the characterize markets in a somewhat idealized form, mainly to
make the theoretical analysis in later chapters feasible.
2.7 Theoretical Markets
The markets and mechanisms are based on assumptions that we list in the following.
Some of the rules are rather generic to enable fair trading with equal information
available to all participants and others are somewhat idealized in order to make
analytic methods feasible. These rules are nevertheless largely valid even in real
markets.