PORTFOLIOS

PORTFOLIO PERFORMANCE : DO INVESTORS MAKE ADEQUATE RISK-RETURN ASSESSMENTS ?

MOST INVESTORS HAVE A GENERAL IDEA OF RISK BUT USUALLY FIND THE CONCEPT DIFFICULT TO EXPLAIN IN CONCRETE TERMS…

WE LIVE IN AN EXTREMELY COMPLEX BUSINESS ENVIRONMENT. NOT ONLY DO MANY DOMESTIC FACTORS INFLUENCE AND INVESTMENT’S RETURN, BUT WE ALSO MUST CONSIDER INTERNATIONAL FACTORS AS WELL.

THIS DIFFERENCE RESULTS FROM DIVERSIFICATION OF ASSETS AND THE RETURN CORRELATIONS AMONG THEM : POORLY OR NEGATIVELY CORRELATED ASSET RETURNS REDUCE RISK PORTFOLIO, WHILE HIGHLY CORRELATED RETURNS LEAVE RISK UNCHANGED.

THE CORRELATION COEFFICIENT IS A STATISTICAL MEASUREMENT OF THE CORRELATION BETWEEN 2 VARIABLES. IT RANGES IN VALUE FROM +1.0 ( PERFECTLY POSITIVELY CORRELATED-NOT REDUCING RISK AT ALL ) TO -1.0 (PERFECTLY NEGATIVELY CORRELATED-COMPLETELY ELIMINATE RISK ). BETWEEN ZERO AND +1.0 (POSITIVELY CORRELATED-REDUCING RISK SLIGHTLY : THE LOWER THE VALUE, THE MORE THE REDUCTION). BETWEEN ZERO AND -1.0 (NEGATIVELY CORRELATED-VIRTUALLY ELIMINATING RISK ). 0.0 (UNCORRELATED-REDUCING RISK CONSIDERABLY).

IF SECURITIES ARE PICKED RANDOMLY AND ADDED TO A PORTFOLIO, PORTFOLIO RISK DECLINES AS MORE SECURITIES ARE ADDED.

THE RISK ELIMINATED IS CALLED DIVERSIFIABLE RISK.

SOME RISK CANNOT BE ELIMINATED REGARDLESS OF THE NUMBER OF SECURITIES ADDED. THIS RISK IS CALLED NONDIVERSIFIABLE RISK. ALTHOUGH IT CANNOT BE ELIMINATED, IT CAN BE MANAGED. A RISK STATISTIC USED IN THIS EFFORT IS A SECURITY’S beta WEIGHT, WHICH MEASURES THE RESPONSIVENESS OF A SECURITY’S RETURN IN RELATION TO CHANGES IN RETURN FOR THE OVERALL SECURITIES MARKET.

HIGH beta VALUES INDICATE HIGH RISK, WHILE LOW beta VALUES SHOW LOW RISK.

THE RISK ASSOCIATED WITH HOLDING AN INDIVIDUAL ASSET CAN BE MEASURED BY USING 3 STATISTICS IN EVALUATING THE ASSET’S HISTORICAL RETURNS :

  1. THE VARIANCE
  2. THE STANDARD DEVIATION
  3. THE COEFFICIENT OF VARIATION
  • THE VARIANCE IS THE MEASUREMENT OF DISPERSION THAT REFLECTS DIFFERENCES BETWEEN POSSIBLE RETURNS AND THE EXTECTED RETURN.
  • THE EXPECTED RETURN IS THE INVESTMENT’S WEIGHTED AVERAGE RETURN WHICH CONSIDERS PAYOFFS AND PROBABILITIES.
  • THE REQUIRED RETURN IS THE RATE OF RETURN AN INVESTOR MUST EARN ON AN INVESTMENT TO BE FULLY COMPENSATED FOR ITS RISK.
  • THE STANDARD DEVIATION IS A STATISTIC USED TO MEASURE THE DISPERSION (VARIATION) OF RETURNS AROUND AN ASSET’S AVERAGE OR EXPECTED RETURN. IT IS THE SQUARE ROOT OF THE VARIANCE.
  • THE COEFFICIENT OF VARIATION(CV) IS A STATISTIC USED TO MEASURE THE RELATIVE DISPERSION OF AN ASSET’S RETURNS; IT IS USEFUL IN COMPARING THE RISK OF ASSETS WITH DIFFERING AVERAGE OR EXPECTED RETURNS.

DURING THE PAST 50 YEARS MUCH THEORITICAL WORK HAS BEEN DONE ON THE MEASUREMENT OF RISK AND ITS USE IN ASSESSING RETURNS.

THE 2 KEY COMPONENTS OF THIS THEORY ARE beta, WHICH IS A MEASURE OF RISK, AND THE CAPITAL ASSET PRICING MODEL (CAPM), WHICH RELATES THE RISK MEASURED BY beta TO THE LEVEL OF REQUIRED OR EXPECTED RETURN.

  • beta IS A MEASURE OF NONDIVERSIFIABLE, OR MARKET, RISK THAT INDICATES HOW THE PRICE OF A SECURITY RESPONDS TO MARKET FORCES. IT IS FOUND BY RELATING THE HISTORICAL RETURNS FOR A SECURITY TO THE MARKET RETURNS, THE HISTORICAL RETURNS FOR THE MARKET. IN OTHER WORDS, beta IS A MEASUREMENT OF AN ASSET’S RISK BASED ON ITS RETURN CO-MOVEMENTS WITH THE MARKET’S RETURN.
  • THE MARKET RETURN IS THE AVERAGE RETURN ON ALL STOCKS.

THE MORE RESPONSIVE THE PRICE OF A SECURITY IS TO CHANGES IN THE MARKET, THE HIGHER THAT SECURITY’S beta.

  • (CAPM) IS A MODEL THAT USES beta, THE RISK-FREE RATE, AND THE MARKET RETURN TO HELP INVESTORS DEFINE THE REQUIRED RETURN ON AN INVESTMENT. (CAPM) FORMALLY LINKS THE NOTION OF RISK AND RETURN.

 

WHEN INDIVIDUAL ASSETS ARE HELD SIMULTANEOUSLY, A PORTFOLIO IS CREATED THAT MAY HAVE A RISK CHARACTERISTIC DIFFERENT FROM THAT OF THE ASSETS OF WHICH IT IS COMPOSED.

PORTFOLIO MANAGERS GENERALLY MAKE 2 TYPES OF DECISIONS :

  1. THE INVESTMENT PROPORTIONS IN VARIOUS ASSET CLASSES ( BONDS, STOCKS, CASH ).
  2. THE SELECTION OF INDIVIDUAL SECURITIES OUT OF THESE CLASSES.

ASSESSING THE PERFORMANCE OF THE ACTIVITIES THAT MAKE UP PORTFOLIO MANAGEMENT IS KNOWN AS PERFORMANCE ATTRIBUTION.

CALCULATING PORTFOLIO PERFORMANCE IS USUALLY DONE USING 3 PERFORMANCE INDEXES :

  1. SHARPE’S INDEX
  2. TREYNOR’S INDEX
  3. JENSEN’S INDEX

  • SHARPE’S PERFORMANCE INDEX COMPARES PORTFOLIO PERFORMANCE WHERE THE STANDARD DEVIATION MEASURES THE RISK. IT IS APPROPRIATE FOR PORTFOLIOS IN ISOLATION. SHARPE’S INDEX IS A MEASURE OF PORTFOLIO PERFORMANCE THAT GIVES THE RISK PREMIUM PER UNIT OF TOTAL RISK, WHICH IS MEASURED BY THE PORTFOLIO’S STANDARD DEVIATION OF RETURN.
  • TREYNOR’S PERFORMANCE INDEX COMPARES PORTFOLIO PERFORMANCE WHERE BETA SERVES AS THE MEASURE OF RISK. IT IS APPROPRIATE FOR PORTFOLIOS IN THE CONTEXT OF THE ENTIRE MARKET PORTFOLIO. TREYNOR’S INDEX IS A MEASURE OF PORTFOLIO PERFORMANCE THAT GIVES THE RISK PREMIUM PER UNIT OF NONDIVERSIFIABLE RISK, WHICH IS MEASURED BY THE PORTFOLIO’S beta.
  • JENSEN’S PERFORMANCE INDEX IS ALSO BASED ON BETA AS A RISK INDEX, BUT IT GIVES PERFORMANCE MEASURE RESULTS IN TERMS OF RATES OF RETURN. JENSEN’S INDEX IS A MEASURE OF PORTFOLIO PERFORMANCE THAT USES THE PORTFOLIO’S beta AND CAPM TO CALCULATE ITS EXCESS RETURN, WHICH MAY BE POSITIVE, ZERO, OR NEGATIVE.

 CONCLUSION

WE LIVE IN AN AGE OF MEASUREMENT – HOW HIGH, HOW HEAVY, HOW MUCH, HOW MANY? -

MONEY IS A STUPID MEASURE OF ACHIEVEMENT BUT UNFORTUNATELY IT IS THE ONLY UNIVERSAL MEASURE WE HAVE  WHILE KEEPING IN MIND THAT YOU CAN’T MANAGE WHAT YOU CAN’T MEASURE !

PHLDUCX

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