finance

PREPARED BY:PIYUESH PANDEY (B52)

AMAN SINGHAL(B35)JYOTI PRAKASH ROUT (B27)

ZAIN UL ABDEEN (B61)SAMIR CHAWLA (B31)

1

PORTFOLIO PERFORMANCE

EVALUATION - TREYNOR & JENSEN’S MEASURE

MEASURES OF RETURN2

MEASURES OF RETURN complicated by addition or withdrawal of money by

the investor percentage change is not reliable when the base

amount may be changing timing of additions or withdrawals is important to

measurement

MAKING RELEVANT COMPARISONS3

PERFORMANCE should be evaluated on the basis of a relative and not

an absolute basis this is done by use of a benchmark portfolio

BENCHMARK PORTFOLIO should be relevant and feasible reflects objectives of the fund reflects return as well as risk

ARITHMETIC V. GEOMETRIC AVERAGES

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GEOMETRIC MEAN FRAMEWORK

GM = ( HPR)1/N – 1


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GEOMETRIC MEAN FRAMEWORK measures past performance well represents exactly the constant rate of return needed

to earn in each year to match some historical performance


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ARITHMETIC MEAN FRAMEWORK provides a good indication of the expected rate of

return for an investment during a future individual year

it is biased upward if you attempt to measure an asset’s long-run performance

RISK-ADJUSTED MEASURES OF PERFORMANCE

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THE REWARD TO VOLATILITY RATIO (TREYNOR MEASURE) There are two components of risk

risk associated with market fluctuations risk associated with the stock

Characteristic Line (ex post security line) defines the relationship between historical portfolio

returns and the market portfolio

TREYNOR MEASURE8

TREYNOR MEASURE Formula

where arp = the average portfolio returnarf = the average risk free ratep= the slope of the characteristic

line during the time period

p

fpp

ararRVOL

TREYNOR MEASURE9

THE CHARACTERISTIC LINE

arp

p

SML

TREYNOR MEASURE10

CHARACTERISTIC LINE slope of CL

measures the relative volatility of portfolio returns in relation to returns for the aggregate market, i.e. the portfolio’s beta

the higher the slope, the more sensitive is the portfolio to the market

TREYNOR MEASURE11

THE CHARACTERISTIC LINE

arp

p

SML

THE SHARPE RATIO12

THE REWARD TO VARIABILITY (SHARPE RATIO) measure of risk-adjusted performance that uses a

benchmark based on the ex-post security market line

total risk is measured by p

THE SHARPE RATIO13

SHARPE RATIO formula:

where SR = the Sharpe ratio

p = the total risk

p

fpp

ararSR

THE SHARPE RATIO14

SHARPE RATIO indicates the risk premium per unit of total risk uses the Capital Market Line in its analysis

THE SHARPE RATIO15

arp

p

CML

THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE

16

BASED ON THE CAPM EQUATION

measures the average return on the portfolio over and above that predicted by the CAPM

given the portfolio’s beta and the average market return

])([)( RFRrERFRrE mi


17

THE JENSEN MEASURE known as the portfolio’s alpha value

recall the linear regression equation

y = + x + e alpha is the intercept


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DERIVATION OF ALPHA Let the expectations formula in terms of realized rates

of return be written

subtracting RFR from both sides jttmtjtjt uRFRRRFRR

jttmtjtjt uRFRRRFRR


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DERIVATION OF ALPHA in this form an intercept value for the regression is

not expected if all assets are in equilibrium in words, the risk premium earned on the jth portfolio

is equal to j times a market risk premium plus a random error term


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DERIVATION OF ALPHA to measure superior portfolio performance, you must

allow for an intercept a superior manager has a significant and positive

alpha because of constant positive random errors

COMPARING MEASURES OF PERFORMANCE

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TREYNOR V. SHARPE SR measures uses as a measure of risk while

Treynor uses SR evaluates the manager on the basis of both rate of

return performance as well as diversification

COMPARING MEASURES OF PERFORMANCE

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for a completely diversified portfolio SR and Treynor give identical rankings because total risk

is really systematic variance any difference in ranking comes directly from a

difference in diversification

CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES23

Use of a market surrogate Roll: criticized any measure that attempted to model the

market portfolio with a surrogate such as the S&P500 it is almost impossible to form a portfolio whose

returns replicate those over time making slight changes in the surrogate may completely

change performance rankings

CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES

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measuring the risk free rate using T-bills gives too low of a return making it easier for

a portfolio to show superior performance borrowing a T-bill rate is unrealistically low and produces

too high a rate of return making it more difficult to show superior performance

25

Thank you

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