Active Portfolio Management
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Theory of Active Portfolio Management
Market timing
portfolio construction
Portfolio Evaluation
Conventional Theory of evaluation
Performance measurement with changing
return characteristics
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
• 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
Market Timing v.s Buy and Hold
• Assume an investor puts $1,000 in a 30-day
CP (riskless instrument) on Jan 1, 1927
and 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
• 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
$1,000
1/1 1978
$67,500
Dec 31, 1978
• 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 !
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
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)
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
TB Portfolio Selection
• For each analyzed security, k, its rate of return can
be written as:
rk -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.
Combining Active Portfolio with
Market Portfolio (passive portfolio)
Return
New CAL
p .
A
CML
M
Risk
rA=aA + rf +bA(rm-rf)
Given:
rp = wrA + (1-w)rm
The optimal weight in the active portfolio is:
w = w0/[1+(1-bA)w0]
where w0=
aA/s2(eA)
(rm-rf)/s2m
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)/sm]2 + [aA/s2(eA)]2
The optimal weights in the active
portfolio for each individual security
will be:
wk =
ak/s2(ek)
a1/s2(e1)+...+an/s2(en)
Illustration of TB Model
• Stock
a
b
s(e)
1
7% 1.6 45%
2
-5
1.0 32
3
3
0.5 26
• rm-rf =0.08; sm=0.2
• Let us construct the optimal active portfolio implied
by the TB model as:
Stock a/s2(e)
Weight (wk)
1
0.07/0.452 = 0.3457
2
-0.05/0.322 = -0.4883
3
0.03/0.262 = 0.4438
Total (T)
0.3012
(1)/T = 1.1417
(2)/T = -1.6212
(3)/T = 1.4735
Composition of active portfolio:
aA = w1a1+w2a2+w3a3
=1.1477(7%)-1.6212(5%)+1.4735(3%)
=20.56%
bA = w1b1+w2b2+w3b3
= 1.1477(1.6)-1.6212(1)+1.4735(0.5)
= 0.9519
s(eA) = [w21s21+w22s22+w23s23]0.5
= [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)
= 0.1506
w = w0 /[1+(1-bA) w0 ]
= 0.1495
Composition of the optimal portfolio:
Stock
Final Position
w (wk)
1
0.1495(1.1477)=0.1716
2
0.1495(-1.6212)=-0.2424
3
0.1495(1.1435)=0.2202
Active portfolio
0.1495
Passive portfolio
0.8505
1.0