Many investors mistakenly base the success of their portfolios on returns alone. Few consider the risk that they took to achieve those returns. Since the 1960s, investors have known how to quantify and measure risk with the variability of returns, but no single measure actually looked at both risk and return together. Today, we have three sets of performance measurement tools to assist us with our portfolio evaluations. The Treynor, Sharpe and Jensen ratios combine risk and return performance into a single value, but each is slightly different. Which one is best for you? Why should you care? Let's find out. Portfolio performance measures should be a key aspect of the investment decision process. These tools provide the necessary information for investors to assess how effectively their money has been invested (or may be invested). Remember, portfolio returns are only part of the story. Without evaluating risk-adjusted returns, an investor cannot possibly see the whole investment picture, which may inadvertently lead to clouded investment decisions.

1. PERFORMANCE
EVALUATION

2. INTRODUCTION
• The portfolio performance evaluation involves the determination of
how a managed portfolio has performed relative to some comparison
benchmark.
• The evaluation can indicate the extent to which the portfolio has
outperformed or under-performed, or whether it has performed at
par with the benchmark.

3. INTRODUCTION (CONTD.)
The evaluation of portfolio performance is important for several reasons:
• First, the investor, whose funds have been invested in the portfolio, needs to
know the relative performance of the portfolio.
• The performance review must generate and provide information that will help
the investor to assess any need for rebalancing of his investments.
• Second, the management of the portfolio needs this information to evaluate
the performance of the manager of the portfolio and to determine the
manager’s compensation, if that is tied to the portfolio performance.
• The performance evaluation methods generally fall into two categories,
namely conventional and risk-adjusted methods.

4. CONVENTIONAL METHODS
Benchmark Comparison
• The most straightforward conventional method involves comparison of the
performance of an investment portfolio against a broader market index.
• The most widely used market index in the United States is the S&P 500
index, which measures the price movements of 500 U.S. stocks compiled by
the Standard & Poor’s Corporation.
• If the return on the portfolio exceeds that of the benchmark index, measured
during identical time periods, then the portfolio is said to have beaten the
benchmark index.

5. CONVENTIONAL METHODS (CONTD.)
While this type of comparison with a passive index is very common in the
investment world, it creates a particular problem.
• The level of risk of the investment portfolio may not be the same as that of
the benchmark index portfolio.
• Higher risk should lead to commensurately higher returns in the long term.
This means if the investment portfolio has performed better than the
benchmark portfolio, it may be due to the investment portfolio being more
risky than the benchmark portfolio.
• Therefore, a simple comparison of the return on an investment portfolio with
that of a benchmark portfolio may not produce valid results.

6. CONVENTIONAL METHODS (CONTD.)
Style Comparison
• A second conventional method of performance evaluation called ”style-
comparison” involves comparison of return of a portfolio with that having a
similar investment style.
• While there are many investment styles, one commonly used approach
classifies investment styles as value versus growth.
• The ”value style” portfolios invest in companies that are considered
undervalued on the basis of yardsticks such as price-to-earnings and price-to-
topic value multiples.
• The ”growth style” portfolios invest in companies whose revenue and
earnings are expected to grow faster than those of the average company.

7. RISK-ADJUSTED METHODS
The risk-adjusted methods make adjustments to returns in order to take account
of the differences in risk levels between the managed portfolio and the
benchmark portfolio. While there are many such methods, the most notables are:
• Sharpe Ratio
• Treynor Ratio
• Jensen’s Alpha
• Modigliani and Modigliani and;
• Treynor Squared

8. RISK-ADJUSTED METHODS (CONTD.)
Sharpe Ratio
The Sharpe ratio computes the risk premium of the investment portfolio per unit
of total risk of the portfolio. The risk premium, also known as excess return, is
the return of the portfolio less the risk-free rate of interest as measured by the
yield of a Treasury security.

9. RISK-ADJUSTED METHODS (CONTD.)
Illustration:
Return of Portfolio = 20%
SD = 32%
Return on Treasury Bill = 4%
Market Return = 13%
SD = 20%
Risk Premium of Portfolio = (20 – 4) = 16% | Sharp Ratio = 16/32 = .50
Risk Premium of Market = (13 – 4) = 9% | Sharp Ratio = 9/20 = .45
Accordingly, for each unit of standard deviation, the managed portfolio earned
a risk premium of 0.50 percent > the market portfolio of 0.45 percent,
suggesting that the managed portfolio outperformed the market after adjusting
for total risk.

10. RISK-ADJUSTED METHODS (CONTD.)
Treynor Ratio
• The Treynor ratio computes the risk premium per unit of systematic risk. The
risk premium is defined as in the Sharpe measure.
• The difference in this method is in that it uses the systematic risk of the
portfolio as the risk parameter.
• The systematic risk is that part of the total risk of an asset which cannot be
eliminated through diversification.
• It is measured by the parameter known as ‘beta’ that represents the slope of
the regression of the returns of the managed portfolio on the returns to the
market portfolio.

11. RISK-ADJUSTED METHODS (CONTD.)
Further to the previous Illustration:
Beta of Portfolio = 1.5
Beta of Market = 1
Treynor Ratio:
Portfolio – (20 - 4)/1.5 = 10.67
Market – (13 - 4)/1 = 9
Thus, after adjusting for systematic risk, the managed portfolio earned an
excess return of 10.67% for each unit of beta while the market portfolio earned
an excess return of 9.00% for each unit of beta.
Thus, the managed portfolio outperformed the market portfolio after adjusting
for systematic risk.

12. RISK-ADJUSTED METHODS (CONTD.)
Jensen’s Alpha
• Jensen’s alpha is based on the Capital Asset Pricing Model (CAPM).
• The alpha represents the amount by which the average return of the portfolio
deviates from the expected return given by the CAPM.
• The CAPM specifies the expected return in terms of the risk-free rate,
systematic risk, and the market risk premium.
• The alpha can be greater than, less than, or equal to zero. An alpha greater
than zero suggests that the portfolio earned a rate of return in excess of the
expected return of the portfolio.

13. RISK-ADJUSTED METHODS (CONTD.)
Using the same set of numbers from the previous illustration:
Expected return of the portfolio = 4 + 1.5 (13 - 4) = 17.5 %
Therefore, the alpha of the managed portfolio is equal to the actual return less the
expected return, which is (20 - 17.5) = 2.5 percent.
Since we are measuring the expected return as a function of the beta and the
market risk premium, the alpha for the market is always zero. Thus, the managed
portfolio has earned a 2.5 percent return above that must be earned given its
market risk.
In short, the portfolio has a positive alpha, suggesting superior performance.

14. Major Stakeholders
External
Investor
Investment Consultant
Competitor
Regulator
Internal
Portfolio Manager
Marketing Officer
Risk Manager
Performance Analyst

15. Investment Performance Presentation
Manager Selection
Performance Appraisal
Performance Attribution
Performance Measurement
Performance Evaluation: Major Component Activities

16. • Performance Management – Measurement of risk and return
• Performance Attribution - Identifying and quantifying the sources
of performance of portfolio includes asset class investment weights,
exposure to market sectors, individual assets within mkt. sect. etc.
• Performance Appraisal – Identifying and measuring investment
skill includes technical aspects of the portfolio.
• Manager Selection – Whether to hire, retain or dismiss a portfolio
manager.
• Investment Performance Presentation – Providing information
about the investment portfolios. (i.e perspective clients and existing clients)
Performance Evaluation: Major Component Activities

18. PERFORMANCE ATTRIBUTION ANALYSIS
Performance Attribution interprets how portfolio managers achieve
their performance and measure the sources of value added to a portfolio. To
determine success, these managers seek to outperform their scheme returns with
respect to a benchmark.
This excess return with respect to the benchmark is called active return. A fund
manager’s skill is generating returns that are not attributable to any obvious
reason like sector driven performance or market capitalization driven gains.
*Active Return - Active return is the percentage gain or loss of an investment
relative to the investment's benchmark.

19. PERFORMANCE ATTRIBUTION ANALYSIS
Methodology for Performance Attribution (Returns Based)
Arithmetic Approach
•Relies on arithmetic approach to calculate active return
•Arithmetic excess return is the profit in excess of a benchmark fund expressed
as a percentage of the initial amount invested.
Geometric Approach
•Relies on geometric approach to calculate active return
•Geometric Excess return is the profit in excess of the benchmark fund expressed
as a percentage of the final value of the benchmark fund

20. PERFORMANCE ATTRIBUTION ANALYSIS
Illustration to show the difference between two approaches
Arithmetic
Market start value = $1,000,000 Market end value = $1,070,000
Hence, profit = $70,000
Fund return = 7% Benchmark Return = 5%
Added value = Fund return – Benchmark return = 7% - 5% = 2%
Geometric
Added Value = (Fund Return-Benchmark Return) / Benchmark Return =
($1,070,000-$1,050,000)/$1,050,000
= $20,000/$1,050,000 = 1.9 %

21. SCOPE OF PERFORMANCE APPRAISAL

22. SCOPE OF INVESTMENT PERFORMANCE
PRESENTATION

23. JARGON
BUSTER

24. MONEY-WEIGHTED RATE OF RETURN
• A money-weighted rate of return is a measure of the rate of return
for an asset or portfolio of assets.
• It is calculated by finding the rate of return that will set the present
values of all cash flows and terminal values equal to the value of the
initial investment.
• The money-weighted rate of return is equivalent to the internal rate
of return (IRR).

25. TIME-WEIGHTED RATE OF RETURN
The time-weighted rate of return is a measure of the compound rate of
growth in a portfolio. Because this method eliminates the distorting
effects created by inflows of new money, it is used to compare the
returns of investment managers.

26. TWRR - ILLUSTRATION
Investor 1 invests $1 million into Mutual Fund A on December 31. On August 15 of
the following year, his portfolio is valued at $1,162,484.
At that point, he adds $100,000 to Mutual Fund A, bringing the total value to
$1,262,484. By the end of the year, the portfolio has decreased in value to
$1,192,328.
The first period return, from December 31 to August 15, would be calculated as
follows:
Return = ($1,162,484 - $1,000,000) / $1,000,000 = 16.25%

27. TWRR - ILLUSTRATION
The second period return, from August 15 to December 31, would be calculated as:
Return = ($1,192,328 - ($1,162,484 + $100,000)) / ($1,162,484 + $100,000) = -5.56%
The time-weighted over the two time periods is calculated by geometrically linking
these two returns as follows:
Time-weighted return = (1 + 16.25%) x (1 + (-5.56%)) - 1 = 9.79%

28. VOLATILITY
• Volatility is a statistical measure of the dispersion of returns for a given security or
market index. Volatility can either be measured by using the standard deviation or
variance between returns from that same security or market index. Commonly, the
higher the volatility, the riskier the security.
TRACKING ERROR
• Tracking error or active risk is a measure of the risk in an investment portfolio that
is due to active management decisions made by the portfolio manager; it indicates
how closely a portfolio follows the index to which it is benchmarked.
• The best measure is the standard deviation of the difference between the portfolio
and index returns.

29. Thank you
“Be fearful when others are greedy and greedy when others are
fearful”