Subject: IC941208: Lecture Series (6)

From: Gray Zhu <[email-masked]>

==================    IC941208: Investment Club  ======================

1. Lecture Series (6) ........................................ Lei Xu
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   (be sure to read the Disclaimer in the end if you have not read)

Topic Six: Security Mispricing

      Finance scholars have long agreed that market is efficient in such a
sense that the market prices of all securities reflect the knowledge and
expectations of all concerned investors.  The competition among investors for
information ensures that the current prices of widely traded financial assets
are unbiased predictors of the future values of the securities.  Thus, it is
unthinkable to beat market to make a risk-free profit.  However, there have
been times, though transient, that investors do make sure profits with a zero
investment portfolio.  In a simplest case, suppose two transactions are
entered at two different places but involve the same underlying asset with
different prices.  For example, once a momentary disparity in gold prices
occurs in the Chicago and the New York markets and the price differential
exceeds all costs associated with the going transactions , an investor could
buy one contract of gold in one market and sell one contract in the other
market, locking in a sure profit with zero investment.  In this case, no risks
are involved since the long (buy) and short (sell) positions offset each
other.
      A zero investment portfolio means that the investor has to carry out at
least two transactions, in which a short position (sell) is taken towards at
least one asset and the proceeds is used to go long on (buy) one or more
assets.  In a more complicated case, assume there exist four stocks named A,
B, C, D which are traded with only four distinct and equally distributed
possible scenarios.
                             Scenario I         Scenario II        Scenario
III            Scenario IV
Probability                0.25                  0.25                    0.25 
                    0.25

      A                         -40                   30                      
40                          50
      B                          10                    70                     
  20                       -30
      C                           70                    -10                   
 10                         40
      D                          10                     20                    
 15                         15
A quick check reveals that an equally weighted portfolio of the stocks A, B, C
outperforms stock D in terms of the rate of return.
                                                Scenario I      Scenario II   
     Scenario III        Scenario IV
 Equally Weighted             
 Portfolio (A, B, C)                   26.6                   30              
        23.3                        20
  
       D                                            10                   20   
                  15                         15
Once this situation is spotted, any investor, no matter how risk averse, would
adopt a strategy to lock a risk free profit by taking a short position in D
stock to finance the long positions in stocks A, B, C.

                    Dollar Investment      Scenario I    Scenario II    
Scenario III    Scenario IV
      A              1000                           -400              300     
          400                  500
      B               1000                          100                700    
           200                  -300
      C               1000                          700                -100   
           100                 400
      D             -3000                         -300               -600     
          -450               -450
------------------------------------------------------------------------------------
Portfolio              0                        100                 300       
         250                  150

The above example shows that the initial net investment is zero, but a
positive profit is generated under any scenario.
The case described above can be stated in a way in which for any stock, the

       Expected return on stock = A + B (Factor 1) + C (Factor 2) +
.........+

The factor could be any economic factors in the marketplace such as oil price,
interest rate, etc.  Some stocks are more sensitive to some factors than
others.  In extreme, there could exist some stocks which have perfect
correlation with certain factors.  In this case, including this stock in the
portfolio is almost equivalent to buying that particular factor.  If there are
sufficient stocks, it is possible to construct a portfolio so diversified that
it has virtually zero sensitivity to each factor, and thus the portfolio is
risk free.  The return generated by such a portfolio is a sure profit.
      Though, the market is efficient, professional money managers do look for
such opportunities.  Their efforts are towards identifying the factors
affecting stock returns, and measuring the expected return on each of these
factors as well as the sensitivity of stocks to them.  In our case, it is a
sure thing that the selling and buying pressures around the stocks A, B, C, D
are to be very high within a short period of time, the price of stock D has to
come down, or/and the prices of stock A, B, C have to go up.  Soon, the free
lunch disappears.

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