Download pdf - Active 3927

7/29/2019 Active 3927

1/23

Active or Passive? Issues and

Strategies Market Efficiency

Anomalies

Market Timing

A theoretical model of active portfolio

management (Treynor-Black)

Quantitative Investment Management

7/29/2019 Active 3927

2/23

Equity Portfolio Management:

Active or Passive?

7/29/2019 Active 3927

3/23

Equity Portfolio Management:

Active or Passive? Passive:

LT buy and hold

Indexation

Replication of an index (broad or specialized

Sampling and Tracking Error

= 0Rebalancing

7/29/2019 Active 3927

4/23

Indexation

Identify a Benchmark Index

replicate benchmark index performance

a true passive strategy will not attempt tooutperform index

Tracking Error = measure of accuracy

7/29/2019 Active 3927

5/23

Tracking Error: Measure 1

TE1 =

where Rpt and Rbt are portfolio and benchmark returns

respectively

n

RRn

t

btpt

1

2)(

7/29/2019 Active 3927

6/23

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

7/29/2019 Active 3927

7/23

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!

7/29/2019 Active 3927

8/23

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

7/29/2019 Active 3927

9/23


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

7/29/2019 Active 3927

10/23


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)

7/29/2019 Active 3927

11/23


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

7/29/2019 Active 3927

12/23


LT effects of this strategy?

Alternatives?

Example 2: Rebalancing to reestablish a

specific level of systematic risk (TargetBeta = 1.2)

7/29/2019 Active 3927

13/23


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

7/29/2019 Active 3927

14/23

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

7/29/2019 Active 3927

15/23

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

7/29/2019 Active 3927

16/23

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?

7/29/2019 Active 3927

17/23

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

7/29/2019 Active 3927

18/23

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

7/29/2019 Active 3927

19/23

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?

7/29/2019 Active 3927

20/23

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

7/29/2019 Active 3927

21/23

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)

7/29/2019 Active 3927

22/23

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)

7/29/2019 Active 3927

23/23

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