Active Portfolio Management

1
Active Portfolio Management

• Theory of Active Portfolio Management
• Market timing
• portfolio construction
• Portfolio Evaluation
• Conventional Theory of evaluation
• Performance measurement with changing return
  characteristics

2
Theory of Portfolio Management- Market Timing

• Most managers will not beat the passive strategy
  (which means investing the market index) but
  exceptional (bright) managers can beat the
  average forecasts of the market
• Some portfolio managers have produced abnornal
  returns that are beyond luck
• Some statistically insignificant return (such 50
  basis point) may be economically significant

3

• According the mean-variance asset pricing
  model, the objective of the portfolio is
  to maximize the excess return over its standard
  deviation(ie., according to the Capital
  Allocation Line (CAL))
• buy and hold?

Return
CAL
SD
4
Market Timing v.s Buy and Hold

• Assume an investor puts 1,000 in a 30-day CP
  (riskless instrument) on Jan 1, 1927and rolls it
  over and holds it until Dec 31, 1978 for 52
  years, the ending value is 3,600

1,000
3,600
52 yrs
5

• An investor buys 1,000 stocks in in NYSE on
  Jan 1, 1978 and reinvests all its
  dividends in that portfolio. The the ending
  value of the portfolio on Dec 31, 1978 would be
  67,500

• Suppose the investor has perfect market timing
  in every month by investing either in CP or
  stocks , whichever yields the highest return, the
  ending value after 52 years is 5.36 billion !

6
Treynor-Black Model

• The Treynor-Black model assumes that the security
  markets are almost efficient
• Active portfolio management is to select the
  mispriced securities which are then added to the
  passive market portfolio whose means and
  variances are estimated by the investment
  management firm unit
• Only a subset of securities are analyzed in the
  active portfolio

7
Steps of Active Portfolio Management

• Estimate the alpha, beta and residual risk of
  each analyzed security. (This can be done via
  the regression analysis.)
• Determine the expected return and abnormal return
  (i.e., alpha)
• Determine the optimal weights of the active
  portfolio according to the estimated alpha, beta
  and residual risk of each security
• Determine the optimal weights of the the entire
  risky portfolio (active portfolio passive
  market portfolio)

8
Advantages of TB model

• TB analysis can add value to portfolio management
  by selecting the mispriced assets
• TB model is easy to implement
• TB model is useful in decentralized organizations

9
TB Portfolio Selection

• For each analyzed security, k, its rate of
  return can be written asrk -rf ak bk(rm-rf)
  ek ak extra expected return (abnormal
  return) bk beta ek residual risk and
  its variance can be estimated as s2(ek)
• Group all securities with nonzero alpha into a
  portfolio called active portfolio. In this
  portfolio, aA, bA and s2(eA) are to be estimated.

10
Combining Active Portfolio with Market Portfolio
(passive portfolio)
Return
New CAL
p
.
A
CML
M
Risk
rAaA rf bA(rm-rf)
11
Given rp wrA (1-w)rmThe optimal weight in
the active portfolio is w w0/1(1-bA)w0
The slope of the CAL (called the Sharpe index)
for the optimal portfolio (consisting of active
and passive portfolio) turns out to include two
components, which are (rm-rf)/sm2
aA/s2(eA)2
aA/s2(eA)(rm-rf)/s2m
where w0
12
The optimal weights in the activeportfolio for
each individual security will be
ak/s2(ek) a1/s2(e1)...an/s2(en)
wk
13
Illustration of TB Model

• Stock a b s(e)1 7 1.6 452 -5 1.0 323 3 0.5
  26
• rm-rf 0.08 sm0.2
• Let us construct the optimal active portfolio
  implied by the TB model asStock a/s2(e)
  Weight (wk)1 0.07/0.452 0.3457
  (1)/T 1.14172 -0.05/0.322 -0.4883
  (2)/T -1.62123 0.03/0.262
  0.4438 (3)/T 1.4735Total (T) 0.3012

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Composition of active portfolio aA
w1a1w2a2w3a3 1.1477(7)-1.6212(5)1.4735(
3) 20.56 bA w1b1w2b2w3b3
1.1477(1.6)-1.6212(1)1.4735(0.5)
0.9519 s(eA) w21s21w22s22w23s230.5
1.14772(0.452)1.62122(0.322)
1.47352(0.262)0.5 0.8262 Composition
of the optimal portfolio w0 (0.2056/0.82622)
/ (0.08/0.22) 0.1506w w0 /1(1-bA) w0
0.1495
15
Composition of the optimal portfolio Stock Fina
l Position w (wk)1 0.1495(1.1477)0.17162 0.
1495(-1.6212)-0.24243 0.1495(1.1435)0.2202Act
ive portfolio 0.1495 Passive portfolio
0.8505 1.0