8/8/2019 Portfolio Performance Measures1
1/53
Portfolio Management
The art and science of making decisionsabout investment mix and policy, matching
investments to objectives, asset allocation
for individuals and institutions, and
balancing risk against. performance.
8/8/2019 Portfolio Performance Measures1
2/53
What we have learnt till date
Concept and calculation of factors affecting
portfolio performance.
Risk and Return
Performance of a portfolio depends on the balanceof Return V/s Risk
8/8/2019 Portfolio Performance Measures1
3/53
Factors for Portfolio Performance
Risk
Variance
Standard Deviation Beta
Correlation Coefficient
Covariance
8/8/2019 Portfolio Performance Measures1
4/53
Factors for Portfolio Performance
Return
Expected Rate of Return
Require Rate of Return Risk Free Rate of Return
Market Return
8/8/2019 Portfolio Performance Measures1
5/53
Factors for Portfolio Performance
Risk Return relationship
Coefficient of variation
Sharpe measure Treynors measure
Jensens Alpha
Benchmark
8/8/2019 Portfolio Performance Measures1
6/53
Portfolio management is all about
strengths, weaknesses,
opportunities and threats in thechoice of tradeoffs encountered in
the attempt to maximize return at a
given appetite for risk
8/8/2019 Portfolio Performance Measures1
7/53
Trade offs
debt vs. equity
domestic vs. international
growth vs. safety Sector Specific vs Market
Mid Cap vs Large Cap
etc
8/8/2019 Portfolio Performance Measures1
8/53
Portfolio Performance Measures
What do we require of portfolio
managers?
1. Earn an average (or fair) return for the
level of risk in the portfolio
2. Ability to manage risk
3. Eliminate unnecessary risks
8/8/2019 Portfolio Performance Measures1
9/53
Portfolio Performance
Measurement Benchmarking
Gives us a reference point for comparison
Comparison of return and risk
8/8/2019 Portfolio Performance Measures1
10/53
Portfolio Performance
Measurement Choosing a benchmark
The most important consideration for
portfolio performance measurement is
bench
mark ch
oice. All portfolio evaluationis dependent on benchmark choice
1. Make sure the benchmark is unambiguous
2. Make sure the benchmark is an investable
index
3. Make sure the benchmark has a
measurable value
8/8/2019 Portfolio Performance Measures1
11/53
Portfolio Performance
Measurement Choosing a benchmark
4. Make sure that the benchmark is
appropriate for the style of portfolio that you
are evaluating
5. Make sure the benchmark is specified in
advance
6. Make sure the benchmark reflects currentknowledge and opinion
7. Dont change indices. Be consistent
across portfolios
8/8/2019 Portfolio Performance Measures1
12/53
Portfolio Performance Measures
Treynors measure
i
fi
i
RR
T F
!
8/8/2019 Portfolio Performance Measures1
13/53
Portfolio Performance Measures
Treynors measure
Treynors measure basically gives us a
measure of return per unit of market risk (or
systematic risk) that our investment earns
Strictly speaking, the larger the Treynor
measure the better. However, we would like
tohave some benc
hmark wit
hwhich
tocompare our individual Treynor measures.
8/8/2019 Portfolio Performance Measures1
14/53
Portfolio Performance Measures
Tryenors measure
Benchmark comparison
fmm
fm
m RR
RR
T !
! F
8/8/2019 Portfolio Performance Measures1
15/53
Portfolio Performance Measures
Treynors measure
If Ti > Tm, the portfolio would plot above the
security market line, indicating superior
performance by the portfolio manager.
If Ti < Tm, the portfolio would plot below the
security market line, indicating poor
performance by the portfolio manager.
8/8/2019 Portfolio Performance Measures1
16/53
Portfolio Performance Measures
Sharpe performance measure
i
fi
iSW
!
8/8/2019 Portfolio Performance Measures1
17/53
Portfolio Performance Measures
Sharpe performance measure
Thus, the Sharpe measure gives us a
measure of return per unit of total risk.Again, the higher the Sharpe measure, the
better the performance. We can also
compare individual Sharpe measures to a
benchmark:
m
fm
m
RRS
W
!
8/8/2019 Portfolio Performance Measures1
18/53
Portfolio Performance Measures
Sharpe performance measure
Instead of plotting deviations from the security
market line, like the Treynor measure, we are
plotting deviations from the market determine
price of risk as defined by the capital market
line (CML).
8/8/2019 Portfolio Performance Measures1
19/53
Portfolio Performance Measures
Sharpe measure
If Si > Sm, the asset earn more than the risk
premium required by the capital market line,
indicating superior performance by the
portfolio manager.
If Si < Sm the asset earn less than the risk
premium required by the capital market line,indicating poor performance by the portfolio
manager.
8/8/2019 Portfolio Performance Measures1
20/53
Portfolio Performance Measures
Comparing the Treynor and Sharpe
measures
For a completely diversified portfolio of
assets, the Sharpe and Treynor measures
would be identical in what they are measuring
Treynor measures performance relative to
systematic risk Sharpe measure s performance relative to
total risk
8/8/2019 Portfolio Performance Measures1
21/53
Portfolio Performance Measures
Comparing the Treynor and Sharpe
measures
Sharpe measure gives some indication ofhow
good the portfolio manager is at diversifying
away unsystematic risk
A poorly diversified portfolio could have a high
Treynor ranking
8/8/2019 Portfolio Performance Measures1
22/53
Portfolio Performance Measures
Jensens Alpha Jensens alpha is based on the ideas
contained in the CAPM. It, like the Treynor
measure, measures how well a portfolio
manager does at dealing with systematic
risk
To calculate Jensens alpha we need to
estimate the following regression model:
)( ,,,, tftmiitfti RRRR ! FE
8/8/2019 Portfolio Performance Measures1
23/53
Portfolio Performance Measures
Jensens Alpha
E measures the degree to which managers
are earning significant returns after
accounting for market risk, as measured by
beta. If the manager is earning a fair return
for the given portfolios systematic risk, then E
would be zero.
8/8/2019 Portfolio Performance Measures1
24/53
Portfolio Performance Measures
Jensens Alpha
(+) E indicates good performance
(-) E indicates poor performance Jensens alpha allows us to statistically test
whether the return the manager earns is
significantly more (or less) than what we
would expect using the CAPM. Jensens alpha allows us to get a
performance measure that incorporates
information from more than one time period.
8/8/2019 Portfolio Performance Measures1
25/53
Portfolio Performance Measures
Jensens Alpha
The validity of the Jensen performance
measure is tied to the validity of the CAPM.
Thus, some individuals will choose estimate
Jensen's alpha performing the regression
model without subtracting the risk-free rate.
This gives us the alpha from the characteristic
line. Its interpretation is the same as the
interpretation of Jensen's alpha.
8/8/2019 Portfolio Performance Measures1
26/53
Portfolio Performance Measures
Fama and French (1993) three factor
model
The alpha in this model can be interpreted in
the same way as the Jensen's alpha. A
positive Fama/French alpha would indicate
performance better than expectations.
Given that the Fama/French model predictsreturns better than the CAPM, the
Fama/French alpha should be a more precise
measure of portfolio performance than the
Jensen's alpha.
8/8/2019 Portfolio Performance Measures1
27/53
Portfolio Performance Measures
Famas performance measure
Fama breaks performance by a portfolio
manager into two categories: selectivity and
diversification. Famas measure incorporates
measures for managing both systematic and
unsystematic risk.
8/8/2019 Portfolio Performance Measures1
28/53
Portfolio Performance Measures
Famas performance measure
Selectivity: measures the ability of the
portfolio manager to earn a return that is
consistent with the portfolios market
(systematic) risk. The selectivity measure is:
))((( fmifi RRRR F
8/8/2019 Portfolio Performance Measures1
29/53
Portfolio Performance Measures
Famas performance measure
(+) selectivity indicates that the manager
earned a higher return than the systematic
risk of the portfolio would indicate. Basically,
you are just comparing the return on the asset
with the return earned by the CAPM.
8/8/2019 Portfolio Performance Measures1
30/53
Portfolio Performance Measures
Famas performance measure
Diversification: Diversification measures the
extent to which the portfolio may not have
been completely diversified. Diversification is
measured as:
ifmfm
ifmf RRRRRR FW
W )()(
8/8/2019 Portfolio Performance Measures1
31/53
Portfolio Performance Measures
Famas performance measure
If the portfolio is completely diversified, contains
no unsystematic risk, then diversification measure
would be zero. A positive diversification measureindicates that the portfolio is not completely
diversified; it would contain unsystematic risk.
If the diversification measure is positive, it
represents the extra return t
hat th
e portfolioshould earn for not being completely diversified.
8/8/2019 Portfolio Performance Measures1
32/53
Portfolio Performance Measures
Famas performance measure
Net selectivity = selectivity - diversification
Net selectivity measureshow well t
heportfolio manager did at earning a fair
return for the portfolios systematic risk and
how well the portfolio manager did at
diversifying away unsystematic risk. Positive net selectivity indicates the
portfolio manager did a good job. Negative
net selectivity indicates that the portfolio
manager did a poor job.
8/8/2019 Portfolio Performance Measures1
33/53
The Following Information is available on
performance of the seven portfolio
Portfolio Return SD Beta Correlation
1 15.60 27.00 1.823 0.81
2 11.80 18.00 0.825 0.553 8.30 15.20 0.481 0.38
4 19.00 21.20 1.325 0.75
5 -6.00 4.00 0.150 0.45
6 23.50 19.30 1.013 0.63
7 12.10 8.20 0.670 0.98
Market 13.00 12.00
T Bill 6.00
8/8/2019 Portfolio Performance Measures1
34/53
Measurement of Performance
Rank th
e portfolios based on sh
arpe ratio Rank the portfolios based on treynor ratio
Compare the ratings between sharpe and
treynor and explain th
e reason fordifferences
Rank based on Jensen measure
8/8/2019 Portfolio Performance Measures1
35/53
Sharpe Measure
Port turn ill - f h rp n
. . . .
. . . .
. . . .. . . .
- . - . . - .
. . . .
. . . .
8/8/2019 Portfolio Performance Measures1
36/53
Treynor Measure
Port turn T - f t Tr nyor n
- - -
8/8/2019 Portfolio Performance Measures1
37/53
Reason for Difference
The measure of risk for treynor is Beta ,higher the correlation of the stock with the
market higher the beta and lower the
treynor .
Port Sharpe Rank Trenyor Rank Correlation
1 0. . 0. 1
2 0. 2 5 7.03 4 0.55
3 0.15 6 4.78 6 0.384 0.61 3 9.81 2 0.75
5 -3.00 7 -80.00 7 0.45
6 0.91 1 17.27 1 0.63
7 0.74 2 9.11 3 0.98
8/8/2019 Portfolio Performance Measures1
38/53
8/8/2019 Portfolio Performance Measures1
39/53
Consider the following data
Return of Stock 30% arket Return 18%
SD of Stock 7% SD of arket 5%
Beta of Stock 1.5 Risk free Rate 7%
8/8/2019 Portfolio Performance Measures1
40/53
Using Farma measure calculate
Selectivity
Diversification
Return required Net selectivity
8/8/2019 Portfolio Performance Measures1
41/53
Expected return on systematic risk
E r = Rf + Beta * ( Rm- Rf)
E r = 7 + 1.5 * ( 18 7 )
E r = 23.5%
8/8/2019 Portfolio Performance Measures1
42/53
Return from Selectivity
Return from Selectivity
Return on Stock Expected Return on systematic risk
Return from Selectivity = 30 23.5 = 6.5
8/8/2019 Portfolio Performance Measures1
43/53
Return from Diversification
Return from Diversification
= Rf + SD stock / SD market * ( Rm Rf ) Er
= 7 + 8 / 5 * ( 18 7 ) 23.5
= 24.6 23.5
= 1.1
8/8/2019 Portfolio Performance Measures1
44/53
Return from Net Selectivity
5.4 = 6.5 1.1
Net electivity = electivity iver ific tion
8/8/2019 Portfolio Performance Measures1
45/53
Consider the following information
related to the performance of two
portfolio managers A, B and BenchmarkPortfolio against which their performance
may be measured
Weight Return Weight Return Weight Return
Stock
Bonds
Cash
Benchmark ManagerA Manager B
8/8/2019 Portfolio Performance Measures1
46/53
Based on the information calculate theoverall return for the two managers and
benchmark portfolio against which their
performance may be measured.
Weight eturn W*R
Stock . . .onds . . .
ash . . .
.Return
enchmark
8/8/2019 Portfolio Performance Measures1
47/53
W i t R t r W*R
St 50% -5% -2.50%B 20% -3.50% -0.70%
C 30% 1.30% 0.39%
-2.81%
r
R t r
W i t R t r W*R
St 30% -6% -1.80%
B 40% -4.50% -1.80%C 30% 1.30% 0.39%
-3.21%
rB
R t r
8/8/2019 Portfolio Performance Measures1
48/53
Sharpe measure of Portfolio
Performance is based on
Systematic Risk of Portfolio
Unsystematic Risk of Portfolio Total Risk of Portfolio
Market Risk of the Portfolio
None of the above Ans 3
8/8/2019 Portfolio Performance Measures1
49/53
If the return of a portfolio is 13%
and risk free rate is 7% and beta is1.2 . The Treynor measure for
portfolio is
5 6
6.5
7.5 8
Ans 1
8/8/2019 Portfolio Performance Measures1
50/53
If the return of a portfolio is 15% and
risk free rate is 10% and SD is 25% .
The Sharpe measure for portfolio is
0.15
0.20 0.25
0.35
0.40
Ans 2
8/8/2019 Portfolio Performance Measures1
51/53
If the Jensens alfa is positive it
indicates
Inferior Performance of Portfolio Manager
Superior Performance of Portfolio
Manager Netural Performance of Portfolio Manager
Both 2 and 3
None of th
e above Ans 2
8/8/2019 Portfolio Performance Measures1
52/53
The ranking of the Treynor and Sharpe
measure will be identical when
The funds under consideration areperfectly diversified
The funds under consideration have the
same correlation with the market The funds under consideration have the
same return
The funds under consideration haveperfectly positive correlation
Ans 1
8/8/2019 Portfolio Performance Measures1
53/53
If selectivity is positive and net
selectivity is negative in a portfolio it
implies that
The portfolio has outperformed the market
The portfolio manager could have produced
better returns at lesser risk using market indexportfolio
The portfolio has give returns superior to themarket but at a higer lever of risk
Both
1 and 3 All of the above
Ans 2