Portfolio Management

CFA_LV2_PM_F.hwp

 

 

Portfolio Management

 

[ An Introduction To Multi-factor Models ]

 

1. Arbitrage Pricing Theory

- unsystematic risk can be diversified away in a portfolio

- returns are generated using a factor model

- no arbitrage opportunities exist

 

2. Multi-factor Model

1) Macroeconomic factor model

- Ri = E(Ri) + bi1FGDP + bi2FQS + ei

- Ri = return for Asset i

- E(Ri) = expected return for Asset i (in the absence of any surprises)

- FGDP = surprise in GDP

- FQS = surprise in Quality Spread (BB rate bond yield - treasury bond yield)

- sensitivities : regression slope estimates (historical)

2) Fundamental factor model

- Ri = ai + bi1FP/E + bi2FSIZE + ei

- ai = intercept, no economic interpretation

- factor : P/E and size (multiple regression)

- sensitivities : calculated from attribute data

3) statistical factor model

 

3. Active P/F Management & Performance measurement

- active return = RP - RB

- active risk = TE = s(RP - RB)

- information ratio = (RP - RB) / s(RP - RB)

 

4. multi-factor model application

1) return attribution = factor return ＋ security selection return

2) risk attribution = factor risk ＋ security selection risk

3) portfolio construction = passive, active, rules-based or algorithmic active management

4) carhart model

 

 

 

 

 

[ Analysis of Active Portfolio Management ]

 

○ Return

- excess return = Rp - Rf

- active return = Rp - Rb

- Jensen's alpha = Rp - CAPM

- alpha = Rp - βp × RB/M

 

○ Sharpe Ratio and Information Ratio

- SR = (RP - RF) / σP

- IR = (RP - RB) / s(RP - RB)

	SR	IR
± Cash	×	change
± B/M	change	×

- unconstrained active portfolio, optimal active risk σA = ( IR / SRB ) × σP

- active + BM portfolio, optimal active risk

- active + BM portfolio, total risk

- highest IR = highest SR = optimal P/F for all investors regardless of risk tolerance

 

○ Fundamental law of active portfolio management

- information coefficient(IC) = manager's skill = 2 × (%correct) - 1

- transfer coefficient(TC) = correlation between actual active weights and optimal active weights

- breadth(BR) = independent active bets per year = N / 1 + (N-1)r,

N = number of decisions, r = correlation between the decision

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○ Correlation triangle

[ Economics and Investment Markets ]

 

○ Required return

- R = real risk-free discount rate

- π = expected inflation

- θ = uncertainty about inflation

- γ = credit spread

- κ = additional RP relative to risky debt for an investment in equities

- λ = equity risk premium = γ +κ

- φ = risk premium for illiquidity

- Risk premium = depends on asset classes and investor's perception of risk

- nominal RP short term = R ＋ π

- nominal RP long term = R ＋ π ＋ θ

- credit bond = R ＋ π ＋ θ ＋ γ

- equity = R ＋ π ＋ θ ＋ γ ＋ κ

- real estate = R ＋ π ＋ θ ＋ γ ＋ κ ＋ φ

 

○ Inter-temporal rate of substitution

		marginal utility of consuming 1 unit in the future
		marginal utility of current consumption of 1 unit

- investor's trade-off between real consumption now and in the future

 

○ Taylor rule

- r = Rn +π + 0.5(π - π*) + 0.5(y -y*)

- Rn = neural real policy interest rate

- π = current inflation rate

- y = current level of output

 

○ Break-even inflation (BEI)

- BEI = yield on non-inflation indexed bond - yield on inflation indexed bond

- BEI = expected inflation + RP(uncertainty about actual inflation)

 

○ Credit spread

- economic expansion → spread narrow → risky bonds outperform

- economic downturn → spread widen → higher rate bonds outperform

 

 

 

 

 

[ The Portfolio Management Process and the Investment Policy Statement ]

 

○ Objectives

1. return objectives

2. risk objectives

- ability to take risk (portfolio's ability) : above, average, below

- willingness to take risk (investor's behavior) : above, average, below

⇒ ability define the maximum risk tolerance

 

○ Constraints

- time horizon

- taxes

- liquidity : expected cash outflow

- legal & regulatory issue

- unique circumstances