Portfolio Performance Evaluation

PORTFOLIO PERFORMANCE EVALUATION 1

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Issues in performance measurement 2 Rules Traditional performance measures Dollar/ Rupee weighted Performance Measures

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MEASURES OF RETURN 

ISSUES IN MEASURES OF RETURN 



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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

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PERFORMANCE MEASURES 

Bank Administrative Institute Report, 1968   

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Performance based on actual returns. Performance based on market value Portfolio manager’s performance should consider risk also Cannot compare among funds operating under different conditions

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2 RULES  

1. Arithmetic Mean is not a useful statistic 2. Rupees are more important than percentages.

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ARITHMETIC V. GEOMETRIC AVERAGES 

GEOMETRIC MEAN FRAMEWORK

GM = (Π HPR)1/N - 1 where Π = the summation of the product of HPR= the holding period returns n= the number of periods

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ARITHMETIC V. GEOMETRIC AVERAGES 

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

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ARITHMETIC V. GEOMETRIC AVERAGES 

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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Why Rupees are more important ?      

2 funds earned 44% and 12% Average rate of return 28% ? 44% return on fund of 2,50,000 12% return on fund of 400,00,000 Average return is (0.9938*12%) + (0.0062*44%) = 12.10%

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Traditional Measures      

NAV change NAV change with index NAV yield Sharpe’s Performance Measure Treynor’s Performance Measure Jensen’s Measure

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NAV Based Measures   

NAV change over the investment period. NAV Yield (NAVt+Dt / NAVt-1 - 1)*100 NAV change with index

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THE USE OF MARKET INDICES 

INDICES 

are used to indicate performance but depend upon  

the securities used to calculate them the calculation weighting measures

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RISK-ADJUSTED MEASURES OF PERFORMANCE 

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THE REWARD TO VOLATILITY RATIO (TREYNOR MEASURE) THE REWARD TO VARIABILITY (SHARPE RATIO) THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE

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TREYNOR MEASURE 

THE REWARD TO VOLATILITY RATIO 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

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TREYNOR MEASURE 

TREYNOR MEASURE 

Formula

RVOL p =

arp − ar f

βp

where arp = the average portfolio return arf = the average risk free rate β p = the slope of the characteristic line during the time period

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TREYNOR MEASURE THE CHARACTERISTIC LINE arp

SML

β

p

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THE SHARPE RATIO 

THE REWARD TO VARIABILITY (SHARPE RATIO) 

measure of risk-adjusted performance that uses a benchmark based on the ex-post capital market line



total risk is measured by

 

σ

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

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THE SHARPE RATIO 

SHARPE RATIO 

formula:

SR p = where

ar p − ar f

σp

SR = the Sharpe ratio

σ

p=

the total risk

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THE SHARPE RATIO

arp

CML

σ

p

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THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE 

BASED ON THE CAPM EQUATION

E (ri ) = RFR + β [ E (rm ) − RFR ] 



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

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THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE 

THE JENSEN MEASURE 

known as the portfolio’s alpha value 

recall the linear regression equation

y=α +β x+e 

alpha is the intercept

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COMPARING MEASURES OF PERFORMANCE 

TREYNOR V. SHARPE  SR measures uses σ as a measure of risk while Treynor uses β  SR evaluates the manager on the basis of both rate of return performance as well as diversification  Sharpe measures is for portfolios only where as Treynor’s measure can be used for portfolios as well as single securities.  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

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MEASURES OF RETURN 

In case of cash with drawls and cash deposits :  Dollar-Weighted Returns  uses discounted cash flow approach  weighted because the period with the greater number of withdrawals or deposits or transaction of shares has a greater influence on the overall average  Also known as IRR

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CALCULATION Value days

return

Annualized return

Rupee Weighted average return

Annualized return = return * 365 / days

Dollar Weighted average return = value * Annualized return / total value

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