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Portfolio Management

 Performance Evaluation

Presented By

T.Ramalingeswararao

Submitted To

Dr.D.H. Malini

Asst. Prof 

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Introductionx Performance evaluation is a critical aspect

of portfolio management

x Proper performance evaluation should

involve a recognition of both the return and

the riskiness of the investment

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Performance Evaluation With

Cash Deposits & Withdrawals

x

Daily valuation methodx Modified Bank Administration Institute

(BAI) Method

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Daily Valuation Methodx The daily valuation method :

• Calculates the exact time-weighted rate of return

• Is bulky because it requires determining a valuefor the portfolio each time any cash flow occurs

 – Might be interest, dividends, or additions and

withdrawals

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Daily Valuation

Method (cont’d)x The daily valuation method solves for  R:

daily

1

1

where

n

i

i

i

i

 R S 

 MVE 

S   MVB

=

= −

=

∏

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Daily Valuation

Method (cont’d)x MVE 

i= market value of the portfolio at the end of 

 period i before any cash flows in period i but

including accrued income for the period

x MVBi= market value of the portfolio at the

 beginning of period i including any cash flows at

the end of the previous sub period and including

accrued income

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Modified BAI Methodx The modified BAI method :

• Approximates the internal rate of return for the

investment over the period in question

• Can be complicated with a large portfolio that

might conceivably have a cash flow every day

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Modified BAI Method (cont’d)x It solves for  R:

1

0

(1 )

where the sum of the cash flows during the period

market value at the end of the period,

including accrued income

market value at the start of the period

to

i

n

w

i

i

i

i

 MVE F R

 F 

 MVE 

 F 

CD DwCD

CD

=

= +

=

=

=

−=

=

∑

tal number of days in the period

number of days since the beginning of the period

in which the cash flow occurred

i D =

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Performance Evaluation

When Options Are Used

x Incremental risk-adjusted return from

optionsx Residual option spread

x Final comments on performance evaluation

with options

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Definitionx The incremental risk-adjusted return

(IRAR) is a single performance measure

indicating the contribution of an options program to overall portfolio performance

• A positive IRAR indicates above-average

 performance• A negative IRAR indicates the portfolio would

have performed better without options

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x The IRAR calculation:

( )

where Sharpe measure of the optioned portfolio

Sharpe measure of the unoptioned portfoliostandard deviation of the optioned portfolio

o u o

o

u

o

 IRAR SH SH 

SH 

SH 

σ  

σ  

= −

=

=

=

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An IRAR Examplex A portfolio manager routinely writes index

call options to take advantage of anticipated

market movementsx Assume:

• The portfolio has an initial value of $200,000

• The stock portfolio has a beta of 1.0• The premiums received from option writing are

invested into more shares of stock 

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IRAR Caveatsx IRAR can be used inappropriately if there is

a floor on the return of the optioned

 portfolio• E.g., a portfolio manager might use puts to

 protect against a large fall in stock price

x

The standard deviation of the optioned portfolio is probably a poor measure of risk 

in these cases

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Residual Option Spreadx The residual option spread (ROS) is an alternative

 performance measure for portfolios containing

optionsx A positive ROS indicates the use of options

resulted in more terminal wealth than only holding

stock 

x A positive ROS does not necessarily mean that theincremental return is appropriate given the risk 

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Residual Option

Spread (cont’d)x The residual option spread (ROS) 

calculation:

1 1

1where /

value of portfolio in Period

n n

ot ut  

t t 

t t t 

t 

 ROS G G

G V V 

V t 

= =

−

= −

=

=

∏ ∏

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Final Commentsx IRAR and ROS both focus on whether an

optioned portfolio outperforms an

unoptioned portfolio• Can overlook subjective considerations such as

 portfolio insurance

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THANK UUUUUUUUUUUUU

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