Zeus Asset Management

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Business and Economics

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Business and Economics

Funds Management Performance

(BKM Ch 24)

Introduction
§  Investment Performance is a complicated subject §  Theoretically correct measures are difficult to construct §  Different statistics or measures are appropriate for different types of investment decisions or portfolios §  Many industry and academic measures are different §  The nature of active management leads to measurement problems

Introduction
§  Two common ways to measure average portfolio return:

1.  Time-weighted returns 2.  Dollar-weighted returns
§  Returns must be adjusted for risk.

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Dollar- and Time-Weighted Returns
Time-weighted returns §  The geometric average is a time-weighted average. §  Each period’s return has equal weight.

(1 + rG ) = (1 + r1 )(1 + r2 )...(1 + rn )
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n

Dollar- and Time-Weighted Returns
Dollar-weighted returns
§  Internal rate of return considering the cash flow from or to investment §  Returns are weighted by the amount invested in each period:

Cn C1 C2 PV = + + ... 1 2 (1 + r ) (1 + r ) (1 + r )n

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Example of Multiperiod Returns

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Dollar-Weighted Return
$2 $4+$108

-

$50

-

$53

Dollar-weighted Return (IRR):

− 51 112 − 50 = + 1 (1 + r ) (1 + r ) 2 r = 7.117%
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Time-Weighted Return
53 − 50 + 2 r1 = = 10% 50 54 − 53 + 2 r2 = = 5.66% 53
rG = [ (1.1) (1.0566) ]1/2 – 1 = 7.81% The dollar-weighted average is less than the time-weighted average in this example because more money is invested in year two, when the return was lower. AFF5300 Case Studies in Finance 9

Adjusting Returns for Risk
§  The simplest and most popular way to adjust returns for risk is to compare the portfolio’s return with the returns on a comparison universe. §  The comparison universe is a benchmark composed of a group of funds or portfolios with similar risk characteristics, such as growth stock funds or high-yield bond funds.

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Universe Comparison

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Risk Adjusted Performance: Sharpe
1) Sharpe Index

(rP − rf )

σP
rp = Average return on the portfolio rf = Average risk free rate

σ = Standard deviation of portfolio return p
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Risk Adjusted Performance: Treynor
(rP − rf )

βP

rp =
 Average
 return
 on
 the
 por/olio
 
 

 
 
  rf
 =
 Average
 risk
 free
 rate
 
  ßp
 =
 Weighted
 average
 beta
 for
 por/olio
 
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Risk Adjusted Performance: Jensen’s Alpha
! p = rp ! "r f + bp (rm ! rf )$ # %

α

p

= Alpha for the portfolio

rp = Average
 return
 on
 the
 por/olio
  ßp
 =
 
 Weighted
 average
 Beta
  rf
 
 =
 
 Average
 risk
 free
 rate
  rm
 =
 
 Average
 return
 on
 market
 index
 por/olio
 
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Information Ratio
Information Ratio = αp / σ(ep)
The information ratio divides the alpha of the portfolio by the nonsystematic risk. Nonsystematic risk could, in theory, be eliminated by diversification.

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M2 Measure
§  Developed by Modigliani and Modigliani §  Create an adjusted portfolio (P*)that has the same standard deviation as the market index. §  Because the market index and P* have the same standard deviation, their returns are comparable:

M = rP* − rM

2

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M Measure: Example
Managed Portfolio: return = 35% standard deviation = 42% Market Portfolio: return = 28% T-bill return = 6% P* Portfolio: 30/42 = .714 in P and (1-.714) or .286 in T-bills The return on...
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