The Portfolio Management Process

1. Policy statement

– specifies investment goals and acceptable risk levels– should be reviewed periodically– guides all investment decisions

2. Study current financial and economic conditions and forecast future trends– determine strategies to meet goals– requires monitoring and updates

3. Construct the portfolio– allocate available funds to meet goals and minimize investor’s risks– Include constraints in the optimization process (e.g., Liquidity needs and

Time horizon)

4. Monitor and update– revise policy statement as needed and modify investment strategy

accordingly– evaluate portfolio performance

Which is about…• Four decisions

– What asset classes to consider for investment– What optimal weights to assign to each eligible

class– The allowable allocation ranges based on policy

weights– What specific securities to purchase for the portfolio

Most (85% to 95%) of the overall investment return is due to the first two decisions, not the

selection of individual investments• FACT: Over long time periods sizable allocation to

equity will improve results

“Adjusting portfolio for up and down movements in the market”

Shift between risky assets and risk-free instruments (CML) Evidence of the importance of Market Timing: Returns from 1987 - 1996 Switch to T-Bills in 87, 90 and 94No negative returns or losses; Average Ret. = 17.44%; S.D. Ret. = 12.38% higher returns, lower risk (downside is partially eliminated)

Example 1: Allocation and Market Timing

Year Lg. Stock Return T-Bill Return87 5.34 5.5088 16.86 6.4489 31.34 8.3290 -3.20 7.8691 30.66 5.6592 7.71 3.5493 9.87 2.9794 1.29 3.9195 37.71 5.5896 23.00 5.20Average 16.06Standard Dev. 14.05

• Ability to catch an EXISTING trend=higher proportions of correct calls:– Bull markets and bear market calls allocation: De-

Emphasize individual security selection and focus on undervalued (promising) asset classes (Efficient Frontier, CML) top-bottom approach

– Undervalued and overvalued securitiesselection: Emphasize on individual security selection and focus on undervalued securities (SML, asset pricing models) bottom-up approach

In Practice:Imperfect Ability to Forecast

3 approaches to portfolio management

• 3 strategies or approaches based on how you will change the weights of your portfolio and select securities:– Passiveselection focus—FIXED PROPORTIONS:

Indexation SML, asset valuation models, fundamental analysis

– Semi-passive some timing, allocation and selection focus—PROPORTIONS CHANGED PERIODICALLY typically, your portfolio is broken down into a passive portion and an active speculative portion.

– Active continuous allocation and selection—PROPORTIONS CHANGED CONTINUOUSLY: recalculate efficient frontier often and/or position the portfolio Beta (look at the CML) for movements in the market :

» Bearishlower ßeta by buying T-bills » Bullishincrease ßeta by selling T-bills

What is Required of a Portfolio Manager?

• Above-average returns within a given risk class.

• Portfolio diversification to eliminate all unsystematic risk.• “above-average” or significant abnormal return?

– Abnormal=Excess performance compared to a benchmark portfolio with the same initial Reward to risk

– Above-average return is a Point estimate– Significant Abnormal (or excess) return refers to statistical inferences

about this point estimate.

• Factors that lead to abnormal performance– Market/asset/sector/industry Allocation

– Security Selection

– Protection

Composite Portfolio Performance Measures

• Treynor Measure SML

• Sharpe Measure CML

• Jensen Measure SML

J=(Rp –Rf) – Bj (Rm – Rf)

Example 2: Differentiate between the three measures

Treynor versus Sharpe Measures• Beta vs. Standard Deviation

– Treynor –> uses SML, thus focus on Beta assumes that portfolio is well diversified.

– Sharpe-> uses the CML, thus focus on standard deviationassumes that portfolio is not well diversified.

• Ranking differences from different diversification levels. (SML vs. CML)R2 will tell you!

• Benchmark choice may affect the R2

Example 3: The Jensen Measure

• Requires use of different RFR, Rm, and Rj, for each period.

• Assumes portfolio is well diversified and only considers systematic risk.

• Provides inferences about abnormal gain/loss

• Regression of (Rj- RFR) and (Rm - RFR).

–R2 can be useful as a measure of diversification.

Example 4: Jensen, Sharpe and Treynor

Portfolio

Jensen

beta R-2

A 0.19 1.05* 0.94

B -0.05 0.66* 0.92

C 0.46* 0.59* 0.69

D 0.36 0.76* 0.64

E 0.30* 0.79* 0.95

Mean (RP)

Sigma

A 1.02% 1.19%

B 0.47% 0.76%

C 0.94% 0.79%

D 0.96% 1.04%

E 0.89% 0.89%

Market 0.9% 1.1%

(Rp-Rf)=Jensen + beta x (Rm-Rf)+e

* Indicates significance at the 95% level

RP is the risk premium: Rp-Rf

ANALYSISTreynor T_rank Sharpe S_rank Jensen J_rank

A 0.0097 4 0.857 4 0.190 4

B 0.0071 6 0.618 6 -0.050 6

C 0.0159 1 1.190 1 0.460* 1

D 0.0126 2 0.923 3 0.360 2

E 0.0113 3 1.000 2 0.300* 3

Market 0.009 5 0.82 5 0 5

• Decomposing overall performance into components

• Components are related to specific elements of performance:– Asset Allocation– Industry/Sector Allocation– Security Choice Selection

• Thus,

Contribution for asset and sector/industry allocation

+ Contribution for security selection

= Total Contribution from asset class

Performance Attribution Analysis

Example 5: BenchmarkBenchmark Component Weight (benchmark) Indexes Return(monthly)

Equity (S&P500) 60.0% 5.81%

Basic material 8.3% 6.40% Business services 4.1% 6.50%

Capital good 7.8% 3.70% Consumer cyclical 12.5% 8.40%

Consumer noncyclical 20.4% 9.40% Credit sensitive 21.8% 4.60%

Energy 14.2% 2.10% Technology 10.9% -0.10%

Bonds(LBI) 30.0% 1.45%

Cash(Money Market) 10.0% 0.48%

Benchmark Return 3.97%

21% treasury; 65% corporate

Example 5: PortfolioPortfolio

Weight (portfolio)

Actual return (monthly)

Indexes Return (monthly)

Equity 70.0% 7.28%

Basic material 2.0% 6.40% Business services 7.8% 6.50%

Capital good 1.9% 3.70% Consumer cyclical 8.5% 8.40%

Consumer noncyclical 40.4% 9.40% Credit sensitive 24.0% 4.60%

Energy 13.5% 2.10% Technology 2.0% -0.10%

Bonds 7.0% 1.89% cash 23.0% 0.48%

Portfolio Return 5.34%

100% corporate

Example 5: So far…

Conclusion, Excess return due to: Formula Partial

Excess return Total

Excess Return Total (equity, bonds and cash) 5.34%-3.97% 1.3700%

Market allocation 0.310% Equity sector allocation 70% x 1.253% 0.877% Bond sector allocation 7% x 0.37% 0.026%

Equity selection 70% x (1.47%-1.253%) 0.152% Bond selection 7% x (0.44%-0.37%) 0.005%

Example 6: Analysis: Weighted excess return due to asset allocation (between

each class)(Actual Weight-Benchmark Weight) x Index Return

Market allocation Actual weight

Benchmark weight

Indexes Return (monthly)

Excess return over the index

Equity 70% 60% 5.81% 0.581% Bond 7% 30% 1.45% -0.334% Cash 23% 10% 0.48% 0.062%

Total excess Return due to

market allocation 0.310%

Example 6: So far…

Conclusion, Excess return due to: Formula Partial

Excess return Total

Excess Return Total (equity, bonds and cash) 5.34%-3.97% 1.3700%

Market allocation 0.310% Equity sector allocation 70% x 1.253% 0.877% Bond sector allocation 7% x 0.37% 0.026%

Equity selection 70% x (1.47%-1.253%) 0.152% Bond selection 7% x (0.44%-0.37%) 0.005%

Example 6: Analysis: Weighted excess return due

to equity sector allocation (between each sector) (Actual Weight-Benchmark Weight) x Index Return

Sector allocation (equity) Actual weight

Benchmark weight

Indexes Return (monthly)

Excess return over the index

Basic material 2.0% 8.3% 6.40% -0.406% Business services 7.8% 4.1% 6.50% 0.243%

Capital good 1.9% 7.8% 3.70% -0.219% Consumer cyclical 8.5% 12.5% 8.40% -0.339%

Consumer noncyclical 40.4% 20.4% 9.40% 1.877% Credit sensitive 24.0% 21.8% 4.60% 0.102%

Energy 13.5% 14.2% 2.10% -0.014% Technology 2.0% 10.9% -0.10% 0.009%

Total excess Return due to

equity sector allocation 1.253%

Weighted excess return due to equity sector allocation=1.253% x 70%=0.877%

Example 6: So far…

Conclusion, Excess return due to: Formula Partial

Excess return Total

Excess Return Total (equity, bonds and cash) 5.34%-3.97% 1.3700%

Market allocation 0.310% Equity sector allocation 70% x 1.253% 0.877% Bond sector allocation 7% x 0.37% 0.026%

Equity selection 70% x (1.47%-1.253%) 0.152% Bond selection 7% x (0.44%-0.37%) 0.005%

Example 6: Analysis: Weighted excess return due to bond family allocation (between each family)

(Actual Weight-Benchmark Weight) x Index Return

Weighted excess return due to bond family allocation=0.37% x 7%=0.026%

Sector allocation (Bond) Actual weight

Benchmark weight

Indexes Return (monthly)

Excess return over the index

Treasury 0% 21% 0.48% -0.102% Corporate 100% 65% 1.69% 0.592%

Others 0% 14% 0.86% -0.120% Total excess Return

due to bond sector allocation 0.370%

Example 6: So far…

Conclusion, Excess return due to: Formula Partial

Excess return Total

Excess Return Total (equity, bonds and cash) 5.34%-3.97% 1.3700%

Market allocation 0.310% Equity sector allocation 70% x 1.253% 0.877% Bond sector allocation 7% x 0.37% 0.026%

Equity selection 70% x (1.47%-1.253%) 0.152% Bond selection 7% x (0.44%-0.37%) 0.005%

Example 6: Analysis: Unweighted excess return due to sector allocation

and security selection (within each class)

Excess return Portfolio R

eturn Benchmark

Return Portfolio

Excess return Equity 7.28% 5.81% 1.47% Bond 1.89% 1.45% 0.44% Cash 0.48% 0.48% 0.00%

Example 6: Conclusion

Conclusion, Excess return due to: Formula Partial

Excess return Total

Excess Return Total (equity, bonds and cash) 5.34%-3.97% 1.3700%

Market allocation 0.310% Equity sector allocation 70% x 1.253% 0.877% Bond sector allocation 7% x 0.37% 0.026%

Equity selection 70% x (1.47%-1.253%) 0.152% Bond selection 7% x (0.44%-0.37%) 0.005%

Total excess return from the equity portion of the portfolio

Total excess return from equity sector allocation

Total excess return from the bond portion of the portfolio

Total excess return from the bond family allocation

You can do it for your portfolio!!!• Go to morningstar.com & do an “X-ray” on your portfolio.

Look at the proportion in Stock/Bond/Cash• For the equity portion: Take note of the weights of your

portfolio and the SP500 in each of the 10 sectors. Get the three-month return for the SP500 and each sector at – http://screen.morningstar.com/index/indexReturns.html?msection=I

dxReturns

– Http://news.morningstar.com/stockReturns/CapWtdSectorReturns.html?msection=SectorReturns

• For the bond portion: Take note of the weights of your portfolio in bonds. Get the three-month return for a bond index (LB) at :– http://screen.morningstar.com/index/indexReturns.html?msection=

IdxReturns

Example 7: Another example of PAA

  Benchmark Manager A Manager B

  Weight Return Weight Return Weight Return

Stock 0.6 -5% 0.5 -4% 0.3 -5%

Bonds 0.3 -3.5 0.2 -2.5 0.4 -3.5

Cash 0.1 0.3 0.3 0.3 0.3 0.3

• Calculate the overall return of each portfolio and comment on whether these managers have under- or over-performed the benchmark fund.• Using attribution analysis, calculate (1) the asset allocation and (2) the sector allocation/stock selection (combined) effects. Combine your findings with those of (a.) and discuss each manager’s skills.

Example 7: Another example of PAA

1. Excess return

R(Benchmark)= weighted average return

=60% x (–5%) +30% x (–3.5%) + 10% x 0.3%

= - 4.02%

R(a)= -2.41%

R(b)= -2.81%

So

Excess return (a)= -2.41%-(-4.02%)= 1.61%

Excess return (b)= -2.81%-(-4.02%)= 1.21%

Example 7: Another example of PAA• Allocation effect:

A W a Wbench R bench Effect

Stock 50 60 -5% 0.5%

Bond 20 30 -3.5% 0.35%

cash 30 10 0.3% 0.06%

Total 0.91%

B W b W bench R bench Effect

Stock 30 60 -5% 1.5%

Bond 40 30 -3.5% -0.35%

cash 30 10 0.3% 0.06%

Total 1.21%

Example 7: Another example of PAA

• Selection Effect: Excess return –Allocation effect

• A: 1.61%-0.91%=0.7%

• B: 1.21%-1.21% =0%

• A is good at allocating and selecting

• B is specialized in allocating among asset classes