
                                            
                     MODERN PORTFOLIO THEORY

                       Copyright 1990-1997
                               By
                   STAFFORD FINANCIAL SERVICES 
                           CORPORATION

                          Distributed By
                      STAFFORD ENTERPRISES
                           Denver, CO


Selection of portfolio investments is not just limited to the
size of returns.  Usually the greater the return, the greater the
risk.  The objective of portfolio management is to balance
expected gain and risk, consistent with gain expectations and
risk tolerances of the client.

Prior to the work of  Harry Markowitz (1990 Nobel Prize Winner),
portfolio management theory was limited to picking the highest
quality stocks with the best expected returns.  Markowitz
revolutionized portfolio management by pointing out  that the
"best stock" theory was contrary to portfolio diversification,
since it would logically concentrate funds in a few assets with
the greatest expected returns.  Portfolio diversification,
Markowitz asserted, expressed investor concern with risk.  His
"mean-variance" theory quantifies risk as the variance from each
security's expected return; then combines securities having
opposing market movement characteristics to reduce overall
portfolio risk.

By combining assets in a portfolio with returns that increase or
decrease differently (are less than perfectly correlated)
portfolio risk can be reduced without sacrificing portfolio
return.  As the correlation (covariance)  between asset returns
combined in a portfolio decreases, the volatility (standard
deviation) of the return on the entire portfolio decreases.


** Definitions **

To aid understanding a few definitions are in order:
 
     o Rate of Return  is the average (mean) percent of return    
     generated by a security's appreciation (price increase)      
     plus income.

     o Standard Deviation is a measure of fluctuation of return   
     from a linear trendline (which is to say that it measures    
     the general ups and downs in return over time).  One
     standard deviation defines the normal boundaries of actual
     results in either direction from the average return about
     68% of the time.  Standard deviations can be
               statistically refined to reflect 80%, 90%, etc. probability.

     o Covariance and Correlation are  measures of the            
     interrelationship between  assets and whether they move      
     in sinc or opposed to each other.

     o Efficient Sets or efficient frontiers maximize        
     risk/return utility by the mathematical technique of
     quadratic optimization.  They provide a higher expected
     return at the same level of risk or a lower level of risk at
     the same expected return than any other alternatives.

     o Portfolio Optimization is achieved by selection of
     portfolios at given levels of return from within the
     efficient sets. 


** Measuring the Individual Investment **

The total gain of an individual investment during a given period
equals the dividends or interest income received plus the
increase in the value of the investment.  This rate of return can
be stated as: 

R = (D + (Pp - Pb) \  Pb

R  = Rate of Return during the period
D  = Dividends
Pp = Price at the end of the period
Pb = Price at the beginning of the period 

Historical returns are not expected returns.  Expected returns
are not always realized.  It is this quantification of investment
risk or exposure to loss, for which Markowitz is famous.

Markowitz' studies in the 1950's quantified investment risk as
the variance about an asset's expected return.  Given the
following probabilities of occurrence and expected returns for
each probability, the mean or expected return of this
investment's probability distribution (expected return denoted by
E) is equal to 8%.

    Return          Probability
                    of Occurrence

     15%                  .40
     10%                  .30
      0%                  .20
    -10%                  .10
                        -------            
                         1.00         

E (R) = (.40*15%) + (.30x10%) +
           (.20*0%) + (.10*-10%) = 8%
The variance of expected returns measures the dispersion of
possible outcomes.  In our example, the probability of each
occurrence is multiplied by the square of the difference from the
mean.  The variance would be ,0064.  Or stated in its more usual
form of conversion to the standard deviation or square root of
the variance, it would be 8%.  The larger the variance or
standard deviation, the greater the potential risk. 

Var(R) = .40*(15%-8%)2 + .30*(10%-8%)2
      + .20*(0%-8%)2 + .10*(-10%-8%)2  = .0064
                                             
SD(R) =  square root of Var(R)  = .08 = 8%

This says that 68% of the time, the actual return will be 8%
below or 8% above the weighted portfolio return (ie. 0% to 16%).



** Measuring Portfolio Return **

The return of a given portfolio of assets equals the sum of the
returns on each asset in the portfolio weighted by its percentage
of the portfolio.  For example, a portfolio composed of three
assets representing 50%, 40% and 10% of the portfolio
respectively; with the assets returning 10%, 12% and 14%
respectively would result in a portfolio return of 11.2%.

R = (.50*10%) + (.40*12%)
           + (.10*14%) = 11.2%

The variance of a portfolio of assets depends not only on the
variance of each asset in the portfolio but how the assets track
each other asset in the portfolio.  This introduces the concept
of covariance or correlation; that is to say the degree by which
the returns of two assets vary or change together.  To determine
the variance of a portfolio of assets, the sum of the weighted
variances of the individual assets and the sum of the weighted
covariances of the assets are added together.

Correlation and covariance are analogous.  A correlation
coefficient of +1.0 notes perfect co-movement in the same
direction, while -1.0 notes perfect co-movement in opposite
directions.  We will see that the selection of investments that
move in opposite directions are of primary importance in
diversification theory. 


** Diversification **

Diversification is intended to assemble a portfolio of assets in
order to reduce risk.  Systematic or market risk cannot be
diversified away.  However, unsystematic risk is capable of being
reduced by diversification.  

There are basically two diversification strategies to lessen
portfolio risk: naive and Markowitz.  The naive strategy ranges
from seat-of-the-pants to what many refer to as the interior
decorator approach. The seat-of-the-pants approach combines
investments because "one is supposed to combine investments". 
There is a guessed at basis for their combination in the
portfolio.  The interior decorator  approach "designs" portfolios
for individuals (such as widows  with high current income needs)
that concentrate investments in single asset categories that
"fit" the individual (such as bonds).  These approaches invite
the very risk that the asset manager is attempting to avoid.
Markowitz diversification combines assets with returns that are
less than perfectly correlated in order to lower overall risk
without sacrificing overall return.  Concentrations in single
asset categories are avoided.  The magic of Markowitz
diversification is the degree of correlation between expected
asset returns.  Portfolio returns may be maintained while
obtaining lower risk through assets with low to negative
correlations.  


** Efficient Portfolio **

Having established the methodology for combining individual
portfolios, the question now shifts to which portfolio is best
for the investor.

Markowitz defined efficient portfolios as those with the highest
expected return at a given level of risk.  A mathematical
technique called quadratic optimization is coupled with the
computer to solve for the portfolio that minimizes risk at each
level of return.  A set of efficient portfolios is then selected
that have higher expected returns and lower risk levels than any
other potential portfolio combinations.  Portfolios are not
included in the efficient set if there exists some other
portfolio that would provide a lower level of risk at the same
return or a higher anticipated return at the same level of risk.


** Selection of the Efficient Portfolio **

Efficient Portfolio analysis presupposes that investors will only
want to hold portfolios in the efficient set.  That is to say
those with the lowest risk and highest return.  Once the
efficient sets are determined, the problem is reduced to fitting
a specific portfolio from among the efficient sets to the
investor.

Usually the portfolios with higher returns also carry higher
risk.  Selecting the portfolio from the efficient sets that best
fits the investors risk/reward temperament is professional key to
this process of modern portfolio management.

** Betas **
Betas are a adaptation of Markowitz theory advanced by William
Sharpe (another 1990 Nobel Prize recipient.  I effect they are
correlations (volatility) measured RELATIVE TO THE MARKET
(usually the S&P 500).  Betas vary by the periods (usually 36
months) selected by those setting the beta.  Computer statistical
programs are used to compute the relative betas.

The Market (S&P 500) has a beta of 1.0 or supposedly neutral
risk.  A bond would have a lower (lower fluctuation/volatility)
beta .. for example .65.  A merging growth stock might have a
beta of 1.50 (higher volatility).  When the market's price rises
or falls 10%, the bond example would have a tendency to rise or
fall only 6.5%, while the example merging growth stock would have
tendency to rise or fall 15%.

Weighting individual portfolio items by their beta, gives the
overall beta for the portfolio (relative to market for the period
selected).  The investor then determines what risk (portfolio
beta) he is willing to take and tries portfolio  adjustments
accordingly.


** Conclusions **

Risk is often ignored in investing.  It's so much more pleasant
to talk about those big potential rewards.  Unfortunately, the
greater the potential gain (reward) the greater the potential
pain (risk).

Markowitz' mean-variance work and Sharpe's beta market
adaptations have brought risk onto equal footing with its more
glamorous cousin, return.  These techniques are universally
recognized.  Today's prudent investor should understand their
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