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Active or Passive? Issues and
Strategies Market Efficiency
Anomalies
Market Timing
A theoretical model of active portfolio
management (Treynor-Black)
Quantitative Investment Management
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Equity Portfolio Management:
Active or Passive?
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Equity Portfolio Management:
Active or Passive? Passive:
LT buy and hold
Indexation
Replication of an index (broad or specialized
Sampling and Tracking Error
= 0Rebalancing
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Indexation
Identify a Benchmark Index
replicate benchmark index performance
a true passive strategy will not attempt tooutperform index
Tracking Error = measure of accuracy
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Tracking Error: Measure 1
TE1 =
where Rpt and Rbt are portfolio and benchmark returns
respectively
n
RRn
t
btpt
1
2)(
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Tracking Error: Measure 1
TE2 = e
This represents the standard deviation of the error terms of
a regression equation explaining returns from the portfolio
with returns from the benchmark.
We will revisit e later
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Rebalancing an Equity Portfolio
Why?
to manage tracking error (if indexing or not)
to maintain a desired set of weights or risk level
client needs change
Market risk level changes
bankruptcies, mergers, IPOs
Why not?
its costly!
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Rebalancing: Example 1
Jan. 1 Price per
Share
Number
of Shares
$ Value % of
Total
Value
Beta
X 20 167 $3340 0.333 1.2
Y 15 222 $3330 0.333 1.6
Z35 95 $3325 0.333 0.8
Total $9995 1.20
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Rebalancing: Example 1
June 1 Price perShare
Numberof Shares
$ Value % ofTotalValue
Beta
down20% X 16 167 $2672 0.256 1.3
up33%
Y 20 222 $4440 0.425 1.7
unch. Z 35 95 $3325 0.319 0.8
Total 10445 1.31
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Rebalancing: Example 1
Portfolio is no longer equally weighted
To rebalance:
Sell Y, buy X and Z
Positions must be reset to $10445/3 = $3482
Sell 4440 - 3482 = $958 of Y (48 shares)
Buy 3482 - 2672 = $810 of X (51 shares)
Buy 3482 - 3325 = $157 of Z (4 shares)
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Rebalancing: Example 1
June 1
Rebal-
anced
Price perShare
Numberof Shares
$ Value % ofTotalValue
Beta
X 16 167 $3488 0.334 1.3
Y 20 222 $3480 0.334 1.7
Z 35 95 $3465 0.332 0.8Total 10433 1.27
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Rebalancing: Example 1
LT effects of this strategy?
Alternatives?
Example 2: Rebalancing to reestablish a
specific level of systematic risk (TargetBeta = 1.2)
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Rebalancing: Example 2
Reestablishing a beta of 1.2:
No unique solution for more than 2 securities
Need to sell high stocks and buy low stocks
For example, sell Y, buy Z, hold X constant
p = (.256)(1.3)+(WY)(1.7)+(1-.256-WY)(.8)
Find Y such that p = 1.2 WY = .302 => WZ = 1-.256-.302 = .442
$3488 in X, $3151 in Y, $4611 in Z
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Active Equity Strategies
Beat the market on a risk adjusted basis!
Need a benchmark
More expensive: turnover, research
Must outperform on a fee-adjusted basis
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Active Management is Forecasting!
The Fundamental Law of Active Management:
(Grinold and Kahn)
IR = IC x (BR)0.5
IR = information ratio
reward-to-risk or /e
IC = information coefficient
correlation between forecast and actual (CORR(E(), )
BR = breadth
# of stocks evaluated per period
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IR = IC x (BR)0.5
Example:
a stockpicker has an IC of .035 and makes 200
bets per quarter (800 per year)IR = (.035)(800)0.5 = .99 (is this good??)
BARRA research indicates that an IR of +1.0 is
in the 90th percentile (-1.0 is in 10th, 0 is in50th)
What if Im an industry picker?
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Using the Fundamental law to forecast alpha
Suppose that there is some indicator or signal that
we use to forecast performance. Call it S. S can
be a single factor (price-to-book) or the result of amultifactor analysis. Standardize S. (e.g., S=+1.0
is 1 s.d. above the mean of 0)
Adapting the fundamental law:
= IC x e x S = Skill x Volatility x Signal
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Using the Fundamental law to forecast alpha
Example:
Your analysis produces a binary buy or sell
recommendation. Your IC = .05 (really good!)
Stock Sigma Buy or Sell Score Alpha
A .15 Buy +1.0 .0075
B .20 Buy +1.0 .01
C .15 Sell -1.0 -.0075D .30 Sell -1.0 -.015
E .25 Sell -1.0 -.0125
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Treynor-Black Model
Suppose you can identify securities that you
expect to outperform (or underperform) on a
risk-adjusted basis
How do you exploit this model?
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Treynor-Black Model: Assumptions
Analysts can only produce quality analysis on a small
number of securities
There is a passive market portfolio (M)
Forecasts of return (E(rM) and risk (s) exist
Determine abnormal return () for analyzed securities
Find optimal weights of analyzed securities to create active
component (A) Combine A, M and risk-free asset to achieve efficiency
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Treynor-Black: Construction
(Step 1) Assume: ri = rf+ i(rM - rf) + ei
For analyzed security k:
rk= rf+ k(rM - rf) + ek+ k=> estimate k, k, s
2(ek)
To construct A:
wk= (k/s2(ek))/(S[i/s2(ei)])=> determine A, A, s
2(eA)
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Treynor-Black: Construction
(Step 2) w0 = (A/s
2(eA))/[(E(rM)-rf)/s2
M]
w* = w0/(1+(1-A)w0)
w0
* is the proportion of A in the new,
enhanced market portfolio (M)
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Active Equity Strategies
Styles:
Sector Rotation: move in/out of sectors as
economy improves/declinesEarnings Momentum: overweight stocks
displaying above average earnings growth
Enhanced Index Fund - majority of funds trackindex, some funds are actively managed
Quantitative Investment Management