construct a zero investment portfolio one has to be able to sell short at least one asset and use the proceeds to purchase (go long on) one or more as- sets. Borrowing may be viewed as a short position in the risk-free asset. Clearly, any in- vestor would like to take as large a position as possible in an arbitrage portfolio. An obvious case of an arbitrage opportunity arises when the law of one price is violated. When an asset is trading at different prices in two markets (and the price differential ex- ceeds transaction costs), a simultaneous trade in the two markets can produce a sure profit (the net price differential) without any investment. One simply sells short the asset in the high-priced market and buys it in the low-priced market. The net proceeds are positive, and there is no risk because the long and short positions offset each other. In modern markets with electronic communications and instantaneous execution, arbi- trage opportunities have become rare but not extinct. The same technology that enables the market to absorb new information quickly also enables fast operators to make large profits by trading huge volumes the instant an arbitrage opportunity appears. This is the essence of index arbitrage, to be discussed in Part VI and Chapter 21. From the simple case of a violation of the law of one price, let us proceed to a less ob- vious (yet just as profitable) arbitrage opportunity. Imagine that four stocks are traded in an economy with only four distinct, possible scenarios. The rates of return of the four stocks for each inflation-interest rate scenario appear in Table 11.1. The current prices of the stocks and rate of return statistics are shown in Table 11.2. Eyeballing the rate of return data, it is not obvious that an arbitrage opportunity exists. The expected returns, standard deviations, and correlations do not reveal any particular ab- normality. Consider, however, an equally weighted portfolio of the first three stocks (Apex, Bull, and Crush), and contrast its possible future rates of return with those of the fourth stock, Dreck. These returns are derived from Table 11.1 and summarized in Table 11.3, which     Table 11.1 Rate of Return Projections   High Real Interest Rates Real Interest Rates   High Inflation Inflation High Inflation Inflation   Probability: .25 .25 .25 .25   Apex 20 40 60 Bull 70 30 ush -20 -10 Dreck III. Equilibrium In Capital Markets