portfolio performance measures1

8/8/2019 Portfolio Performance Measures1

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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.


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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


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Factors for Portfolio Performance

Risk

Variance

Standard Deviation Beta

Correlation Coefficient

Covariance


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Return

Expected Rate of Return

Require Rate of Return Risk Free Rate of Return

Market Return


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Risk Return relationship

Coefficient of variation

Sharpe measure Treynors measure

Jensens Alpha

Benchmark


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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


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Trade offs

debt vs. equity

domestic vs. international

growth vs. safety Sector Specific vs Market

Mid Cap vs Large Cap

etc


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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


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Portfolio Performance

Measurement Benchmarking

Gives us a reference point for comparison

Comparison of return and risk


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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


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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


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Treynors measure

i

fi

i

RR

T F

!


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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.


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Tryenors measure

Benchmark comparison

fmm

fm

m RR

RR

T !

! F


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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.


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Sharpe performance measure

i

fi

iSW

!


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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

!


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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).


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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.


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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


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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


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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


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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.


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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.


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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.


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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.


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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.


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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


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(+) 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.


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Diversification: Diversification measures the

extent to which the portfolio may not have

been completely diversified. Diversification is

measured as:

ifmfm

ifmf RRRRRR FW

W )()(


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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.


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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.


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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


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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


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Sharpe Measure

Port turn ill - f h rp n

. . . .

. . . .

. . . .. . . .

- . - . . - .

. . . .

. . . .


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Treynor Measure

Port turn T - f t Tr nyor n

- - -


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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


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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%


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Using Farma measure calculate

Selectivity

Diversification

Return required Net selectivity


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Expected return on systematic risk

E r = Rf + Beta * ( Rm- Rf)

E r = 7 + 1.5 * ( 18 7 )

E r = 23.5%


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Return from Selectivity

Return from Selectivity

Return on Stock Expected Return on systematic risk

Return from Selectivity = 30 23.5 = 6.5


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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


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Return from Net Selectivity

5.4 = 6.5 1.1

Net electivity = electivity iver ific tion


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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


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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


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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


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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


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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


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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


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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


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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


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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

portfolio performance measures1

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