Portfolio Selection
The PORTFOLIO command
provides features for calculating efficient portfolios.
Example
Berndt [1991, Chapter 2] provides a data set of monthly returns
for a number of companies for the period January 1978 to December 1987.
From this data set, a file
(filename: P.txt )
was prepared with returns for
Mobil, IBM, Weyerhauser and Citicorp as well as the return on
30day Treasury Bills (a measure of the riskfree return) and
a valueweighted composite monthly market return based on all stocks listed
at the New York and American Stock Exchanges.
The SHAZAM commands below solve a portfolio selection problem.
SAMPLE 1 120
READ (P.txt) DATE MOBIL IBM WEYER CITCRP MARKET RKFREE / SKIPLINES=1
* Convert to percentages
GENR MOBIL=100*MOBIL
GENR IBM=100*IBM
GENR WEYER=100*WEYER
GENR CITCRP=100*CITCRP
* Set a riskfree rate of return
GEN1 RF=100*(RKFREE:120)
PORTFOLIO MOBIL IBM WEYER CITCRP / INRATES RISKFREE=RF EQUALW PFRONT &
GRAPHDATA GRAPHLINE
STOP

Below is SHAZAM output generated by the
PORTFOLIO command.
_PORTFOLIO MOBIL IBM WEYER CITCRP / INRATES RISKFREE=RF EQUALW PFRONT &
 GRAPHDATA GRAPHLINE
PORTFOLIO ANALYSIS  RATES OF RETURN 4 ASSETS 120 OBSERVATIONS
MEAN RISKFREE RATE OF RETURN = 0.27700
VARIABLE MEAN ST.DEV SHARPE
MOBIL 1.6192 8.0308 0.16713
IBM 0.96167 5.9024 0.11600
WEYER 0.96333 8.5066 0.80682E01
CITCRP 1.1858 8.0972 0.11224
COVARIANCE MATRIX
MOBIL 64.493
IBM 15.225 34.838
WEYER 26.403 24.694 72.363
CITCRP 20.227 20.250 37.195 65.564
MOBIL IBM WEYER CITCRP
EFFICIENT PORTFOLIOS
MINIMUMVARIANCE RISKFREE=ZERO RETURN=ZERO ACTUAL
MEAN 1.1521 1.3300 0.44409E15 1.1825
VARIANCE 27.751 32.037 207.44 32.828
STDEV 5.2680 5.6602 14.403 5.7296
SHARPE 0.16612 0.18604 0.19233E01 0.15804
PORTFOLIO WEIGHTS
MOBIL 0.23486 0.48422 1.3797 0.25000
IBM 0.59096 0.39925 1.8322 0.25000
WEYER 0.13607E01 0.10732 0.79655 0.25000
CITCRP 0.16057 0.22385 0.24910 0.25000
 
The figure below shows the minimumvariance riskreturn frontier.
The xaxis measures the standard deviation of return.
The portfolios marked M and Z are the
MINIMUMVARIANCE and RISKFREE=ZERO
portfolios respectively.
The curve that extends upward from point M gives the efficient frontier.
That is, all portfolios on the efficient frontier have greater expected
return than the portfolio with the global minimum variance.
The portfolio A is the equalweighted portfolio calculated with the
EQUALWEIGHT option and reported on the SHAZAM output in
the ACTUAL column.
Clearly, this is not an efficient portfolio since it is possible
to find an alternative portfolio with the same risk but a higher
expected return.
The straight line with an intercept at the riskfree rate of return
r that is tangential to the efficient frontier at point Q has a slope
that is the maximimum Sharpe ratio of all possible portfolios.
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