Portfolio Performance Evaluation

p
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Risk Adjusted Performance: Treynor
2) Treynor Measure
(rP rf )
P
rp = Average return on the portfolio
rf = Average risk free rate ßp = Weighted average beta for portfolio
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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-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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(rP rf )
P
rp = Average return on the portfolio rf = Average risk free rate = Standard deviation of portfolio return
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24-3
Dollar- and Time-Weighted Returns
Time-weighted returns • The geometric average is a timeweighted average. • Each period’s return has equal weight.
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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.
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24-9
Figure 24.1 Universe Comparison
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Risk AdjusteHale Waihona Puke Baidu Performance: Sharpe
1) Sharpe Index
CHAPTER 24
Portfolio Performance Evaluation
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McGraw-Hill/Irwin Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.
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24-12
Risk Adjusted Performance: Jensen
3) Jensen’s Measure
P rP rf P (rM rf )
p
= Alpha for the portfolio rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Average return on market index portfolio
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24-8
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.
1 rG 1 r1 1 r2 ...1 rn
n
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24-4
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 n 1 r 1 r 1 r
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24-5
Example of Multiperiod Returns
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