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25-1 active equity investing: portfolio construction (4 allocating the…
25-1 active equity investing: portfolio construction
1 introduction
security analysis
the process for ranking the relative attractiveness
predictions about returns and risk are essential
portfolio construction
selecting to be included and percentage
balancing predicted against likelihood derailed or inaccurate
2 buillding blocks of
active equity portfolio
construction
fundamentals of portfolio construction
generate active
returns by
strategically adjusting active weights to create long-term exposure to rewarded risks
tactically adjusting active weights in indentifying mispricing to generate alpha
assuming excessive idiosyncratic risk that result in lucky or unluckly returns
measures
historically, alpha = excess return over benchmark
infor ratio - value-added
today, alternative beta - exposure to rewarded factors
decomposition fo ex post active returns:
R_A = ∑ ( β_pk − β_bk ) × F_k + ( α + ε )
the return of rewarded factor k: F_k
that attributed to specific skills/strateties of manager: α
the idiosyncratic return from random shock: ε
building blocks used
in portfolio construction
three main building blocks +
the fourth critical component
1 rewarded
factors
weightings
to choose, explicitly or implicitly, exposures to rewarded risks
many products allow to directly access such factors as value, size, momentum and quality
market β close to 1, negative exposure to size factor
-has a large-cap tilt
portion not
explained by factors
alpha
incomplete factor model
exposure to idiosyncratic risks
2 alpha
skills
static exposure to known rewarded factor
no longer considered a source of alpha
factor
timing
negative market return, β <1, outperform
also generated from unrewarded factors: regional / sector exposure, price of commodities or security selection
other asset classes ( such as cash)
3 sizing
positions
dramatic impact on idiosyncratic risk
the concentrated portfolio - idiosyncratic risk and impact of luck much greater
active risk / tracking eror: σ_R_A
(σ_R_A)^2 = ∑((R_At)^2) / (T−1)
high confidence in analysis willing to assume high idiosyncratic risk
creating balanced exposures to rewarded factors,
likely to highly diversified portfolio
4 breadth of
expertise
implicit in the fundamental law of active management
the fundamental law, expected active portfolio return:
E(R_A) = IC
√(BR)
(σ_R_A) * TC
IC: expected infor coefficient of the manager
BR: breadth, truly indepent decisions made each year
TC: transfer coefficient or ability to translate without constraint
long-term success not achieved by being right all the time
but by being right often through small vicotories
consistently over long period
the excess return / active return R_A:
R_A = ∑(ΔW_i * R_i)
ΔW_i: active weight, difference between
portfolio and benchmark weights
4 allocating
the risk
budget
absolute
vs relative
measures
of risk
the choice driven by the mandate of the manager and the goals of investor
manager's beliefs about how they add value can influence choice
causes and
sources
of absolute risk
dundamental
principles
add new that higher covariance with the portfolio than most current, total portfolio risk rise
replaces existing that has higher covariance with the portfolio, total portfolio risk rise
total portfolio variance V_P
V_p = ∑∑(x_i
x_j
C_ij)
the contribution of each asset to portfolio variance
CV_i = ∑(x_i
x_j
Cij) = x_i * C_ip
absolute portfolio variance
= variance attributed to factor exposure + variance unexplained
V_p = Var(∑(β_ip × F_i)) + Var(ε_p)
causes and
sources of
relative/active
risk
the variance of the portfolio's active return:
AV_p = ∑∑((x_i − b_i)
(x_j − b_j)
RC_ij )
RC_ij : the covariance of relative returns between
the contribution of each asset to the portfilio active variance:
CAV_i = (x_i − b_i) * RC_ip
manager concerned with active risk not portfolio volatility
cash low correlation with equity benchmark → cash has higher active risk
tin the context of relative measures, what matters is its relative(active) volatility
determining the
appropriate level
of risk three scenarios
implementation constraints
degrade infor ratio if active risk increase beyond specific level
limited diversification
opportunities
the relationship between return and risk is concave
leverage and
implications for risk
in muliti-period setting, leverage reduce expected compounded return
R_g = R_a − (σ^2)/2
geometric/compounded: R_g
arithmetic/periodic: R_a
reasonable leverage can increase expected compounded return
allocating the
risk budget
greater concentration of risk implicity
→ greater sensitivity to unrewarded factors
and idiosyncratic risks
the sector rotator is taking less size bet:
weighted average capitalization
close to index
risk budgeting: a process by which total risk appetite of the portfolio allocated among the various components fo portfolio choice