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Evaluacija portfolia
Factors to be Considered When Evaluating 
Portfolios 
• Differential risk levels: 
– If a unit trust provides its investor...
Factors to be Considered When Evaluating 
• Benchmarks: 
Portfolios, cont. 
– How do we determine whether portfolio perfor...
Factors to be Considered When Evaluating 
Portfolios, cont 
• Constraints on portfolio manager: 
– some unit or investment...
Risk-adjusted Measures of Performance 
• Composite measures of portfolio performance 
– incorporate return and risk in the...
Example to be Used 
We will show the application of all the measures on the example 
below: 
Return SD 
Market 0.04798 0.7...
The Sharpe Ratio 
• Reward-to-variability ratio (RVAR) 
• The Sharpe measure evaluates portfolios that are adjusted 
for t...
The Sharpe performance measure, cont. 
• The denoiminator (imenilac) measures the portfolios 
excess return - risk premium...
Sharpe Performance Measure, the Example 
Return SD Sharpe Ratio 
Market 0.04798 0.7318 0.0218 
Portfolio A 0.0793 0.8315 0...
Graphical Presentation of the Sharpe Example 
Rp 
A 
We can see from the graph that the 
slope of the CML is the Sharpe 
r...
The Treynor Ratio 
• Similar to Sharpe’s measure 
• Reward-to-volatility ratio (RVOL) 
• Treynor distinguishes between the...
The Treynor Performance Measure, cont. 
• The measure is showing the excess return per unit 
of the systematic risk (beta)...
Treynor Performance Measure, the Example 
Return SD Beta Treynor 
Market 0.04798 0.7318 1.00 0.01598 
Portfolio A 0.0793 0...
Rp 
Graphical presentation of the Treynor 
A 
B SML 
M the slope of SML is: 
Rf 
bp 
example 
We can see from the graph th...
Sharpe’s Measure vs. Treynor’s Measure 
• Sharpe and Treynor measures are similar 
• Definition of risk determines which m...
Definition of Jensen’s Alpha 
a is measuring the average rate of return 
above the return corresponding to the 
given leve...
Definition of Jensen’s Alpha, cont. 
• Therefore, Jensen’s portfolio performance measure can 
be expressed as: 
[ ( )] p p...
Information (Appraisal) Ratio 
• The source of portfolio’s excess return is the deviation 
from the market portfolio. This...
Limitations of the Portfolio Performance 
Measures 
• Derived from CAPM - depend on the 
assumptions 
• Market portfolio p...
Da se podsetimo: Beta i prinos 
• Beta measures the sensitivity of stock’s return to movements in the 
market return. 
• M...
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4 evaluacija portfolia

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4 evaluacija portfolia

  1. 1. Evaluacija portfolia
  2. 2. Factors to be Considered When Evaluating Portfolios • Differential risk levels: – If a unit trust provides its investors with the total return of 15%, is their performance good or bad? – Not possible to answer without knowing the level of risk involved – High returns v s. risk aversion – Performance evaluation on the basis of the risk adjusted returns
  3. 3. Factors to be Considered When Evaluating • Benchmarks: Portfolios, cont. – How do we determine whether portfolio performance is superior or inferior? – Need for comparison: comparable alternative – That alternative needs to be the legitimate portfolio: benchmark portfolio – Pay attention to choose the adequate benchmark: FTSE 100 index cannot be a benchmark if you invest in FTSE small companies (BELEX15 i akcije van indeksa) – Customised benchmarks can be constructed (npr. Bankarski sektor)
  4. 4. Factors to be Considered When Evaluating Portfolios, cont • Constraints on portfolio manager: – some unit or investment trusts have set constraints, such as: not allowed to short-sell or to invest in small stocks or emerging markets – investment policy determines the risk and the return of the portfolio • Other factors to be considered – evaluation of a manager v s. evaluation of a portfolio performance – diversification issues – past is not a guarantee for the future performance
  5. 5. Risk-adjusted Measures of Performance • Composite measures of portfolio performance – incorporate return and risk in the evaluation – two kinds of risk to be estimated: portfolio’s market risk (beta) and total risk (standard deviation) – the relevant measure of risk depends whether the client has other assets apart from the portfolio – Sharpe, Treynor, Jensen alpha and Information ratio measures date from 1960s and are still in use
  6. 6. Example to be Used We will show the application of all the measures on the example below: Return SD Market 0.04798 0.7318 Portfolio A 0.0793 0.8315 Portfolio B 0.06388 0.7498 Risk-free 0.032
  7. 7. The Sharpe Ratio • Reward-to-variability ratio (RVAR) • The Sharpe measure evaluates portfolios that are adjusted for their total risk, measured in terms of standard deviation (total risk), not just the systematic risk • The Sharpe ratio for portfolio p is given by: • The Sharpe ratio for the market portfolio is defined as: S r - r m sˆ m f m = • Measure is based on the ex post (historical) CML
  8. 8. The Sharpe performance measure, cont. • The denoiminator (imenilac) measures the portfolios excess return - risk premium • The numerator (brojilac) is the total risk of the portfolio • The measure shows excess return per unit of total risk • We can use Sharpe ratio to rank portfolios. The higher the value of the Sharpe ratio, the better the portfolio performance is.
  9. 9. Sharpe Performance Measure, the Example Return SD Sharpe Ratio Market 0.04798 0.7318 0.0218 Portfolio A 0.0793 0.8315 0.0568 Portfolio B 0.06388 0.7498 0.0425 Risk-free 0.032 The result of the descending order ranking is: A, B, Market.
  10. 10. Graphical Presentation of the Sharpe Example Rp A We can see from the graph that the slope of the CML is the Sharpe ratio of the market and the slope of the other two lines above CML is the Sharpe ratio for portfolios A and B. B CML M the slope of CML is: Rf sp
  11. 11. The Treynor Ratio • Similar to Sharpe’s measure • Reward-to-volatility ratio (RVOL) • Treynor distinguishes between the total risk and the systematic risk • Assumption: portfolios are well diversified, i.e. diversifiable risk can be ignored • The Treynor ratio for portfolio q is defined as: • The Traynor ratio for the market is: r r T q f b q q - = r - r T = - m r r m f m f m = b
  12. 12. The Treynor Performance Measure, cont. • The measure is showing the excess return per unit of the systematic risk (beta) • The higher the Treynor ratio, the better the investment performance is. Portfolio q will outperform the market if: r - r T > - q r r m f q f b q = • As a benchmark Treynor uses ex post SML
  13. 13. Treynor Performance Measure, the Example Return SD Beta Treynor Market 0.04798 0.7318 1.00 0.01598 Portfolio A 0.0793 0.8315 0.8223 0.05746 Portfolio B 0.06388 0.7498 0.9322 0.034198 Risk-free 0.032 The result of the descending order ranking is: A, B, Market. Note that it is the same as ranking obtained with Sharpe ratio!
  14. 14. Rp Graphical presentation of the Treynor A B SML M the slope of SML is: Rf bp example We can see from the graph that the slope of the SML is the Treynor ratio of the market and the slope of the other two lines above SML is the Treynor ratio for portfolios A and B.
  15. 15. Sharpe’s Measure vs. Treynor’s Measure • Sharpe and Treynor measures are similar • Definition of risk determines which measure to use • Ranking order of portfolios according to Sharpe and Treynor ratios can be different – if portfolio is perfectly diversified, the rankings will be the same, as it appears to be the case in our example – if portfolio is not well diversified, Treynor’s ranking will be higher than Sharpe’s
  16. 16. Definition of Jensen’s Alpha a is measuring the average rate of return above the return corresponding to the given level of risk (according to CAPM) • Positive alpha indicates that portfolio is performing better than the market on the risk-adjusted basis and vice versa .
  17. 17. Definition of Jensen’s Alpha, cont. • Therefore, Jensen’s portfolio performance measure can be expressed as: [ ( )] p p f p M f a = R - R +b R - R • Where alpha is the difference between the actual excess return of the portfolio p and the risk premium on that portfolio according to the CAPM • Alpha is estimated by regressing the excess returns of a portfolio on the excess returns of the market • It is important that it is statistically significant (t ≥ 2)
  18. 18. Information (Appraisal) Ratio • The source of portfolio’s excess return is the deviation from the market portfolio. This deviation is reflected in the extra amount of unique risk that the investor is willing to undertake. • The information ratio is the ratio of the excess return divided by the standard deviation of that excess return, where alpha is used as a measure of excess return: a p a s p IR = • The higher the information ratio, the better the performance of portfolio is
  19. 19. Limitations of the Portfolio Performance Measures • Derived from CAPM - depend on the assumptions • Market portfolio proxied by market index – benchmark error • Depending on which index you use as a proxy for market portfolio, beta can change • Global investing enhances the problem of benchmark error • Period for evaluation should be long – 10 years or longer
  20. 20. Da se podsetimo: Beta i prinos • Beta measures the sensitivity of stock’s return to movements in the market return. • Market beta is equal to 1. • Defensive vs. aggressive stocks • If the market return increases by 1%, then the following 5 stocks will exhibit the changes in returns as in the table below: Stock Beta Change in the stock return The stock is: A -0.5 -0.5% Negatively correlated and LESS volatile than the market B 0 0% Not correlated with the market C 0.5 0.5% Positively correlated and LESS volatile than the market D 1 1% Perfectly positively correlated with the market E 1.5 1.5% Positively correlated and MORE volatile than the market

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