INVESTMENT PERFORMANCE INVESTMENT PERFORMANCE EVALUATIONEVALUATION

WEALTH MANAGEMENT CERTIFICATION PROGRAMModule 02: Investment & Portfolio Management

FacilitatorProf. Dr. Sukmawati Sukamulja

Objectives• To outline the issues involved in measuring

portfolio performance, including the problems that remain.

• To present Chartered Financial Analyst (CFA) Institute new presentation standards, and develop well-known measures of return consistent with these standards.

• To develop and illustrate the three composite measures of portfolio performance.

• To consider other important issues, such as performance attribution.

How Should Portfolio Performance Be Evaluated?

• “Bottom line” issue in investing• Is the return after all expenses

adequate compensation for the risk?• What changes should be made if the

compensation is too small?• Performance must be evaluated before

answering these questions

Considerations• Without knowledge of risks taken, little

can be said about performance–Intelligent decisions require an

evaluation of risk and return–Risk-adjusted performance best

• Relative performance comparisons –Benchmark portfolio must be legitimate

alternative that reflects objectives

Considerations• Evaluation of portfolio manager or the

portfolio itself?–Portfolio objectives and investment

policies matter• Constraints on managerial behavior affect performance

• How well-diversified during the evaluation period?–Adequate return for diversifiable risk?

Factors to Consider in Evaluating Portfolio Performance

• Differential Risk Levels– Investing is always a two-dimensional

process with risk and return.– Both should be evaluated to make

intelligent decision.– To evaluate portfolio performance

properly, we must determine whether the returns are high enough given risk involved (risk adjusted).

• Differential Time Periods–The time element must be

adjusted if valid performance of portfolio results is to be obtained.

Factors to Consider in Evaluating Portfolio Performance• Appropriate Benchmarks

– Comparing the returns obtained on the portfolio being evaluated with the returns that could have been obtained form a comparable alternative.

– The benchmark portfolio must be legitimate alternative that accurately reflects the objectives of the portfolio being evaluated.

Factors to Consider in Evaluating Portfolio

Performance• Constraints on Portfolio Managers

–In evaluating portfolio manager rather than the portfolio itself, an investor should consider the objectives set by (or for) the manager and any constrains under which he/she must operate.

–It is imperative to recognize the importance of the investment policy statement pursued by portfolio manager in determining the portfolio result. In many cases, the investment policy determines the return and/or the risk of the portfolio.

Factors to Consider in Evaluating Portfolio Performance

• Other Considerations– It is essential to determine how weal

diversified the portfolio was during the evaluation period, because as we know diversification can reduce portfolio risk.

– New source of information and new techniques to asses the actual performance of portfolio relative to one or more alternatives.

CFA Institute Standards• Minimum standards for reporting

investment performance• Standard objectives:

–Promote full disclosure in reporting–Ensure uniform reporting to enhance

comparability• Requires the use of total return to

calculate performance

CFA Institute Performance Presentation Standards

1. Total return – must be used to calculate performance.

2. Accrual accounting – use accrual, not cash, accounting except for dividends and for periods before 1993.

3. Time-weighted rates of return – to be used on at least a quarterly basis and geometric linking of period returns.

4. Cash and cash equivalents – to be included in composite returns.

5. All portfolio included – all actual discretionary portfolio are to be included in at least one composite.

6. No linked of simulated portfolio with actual performance.

7. Asset-weighting of composites – beginning of period values to be used.

8. Addition of new portfolio – to be added to a composite after the start of the next measurement period.

9. Exclusion of terminated portfolios – excluded from all period after the period in place.

10.No restatement of composite result – after a firm’s reorganization.

11.No portability of portfolio results.12.All cost deducted – subtracted from gross

performance.13.10-year performance record – minimum period

to be presented.14.Recent annual returns for all years.

Return Measures• Change in investor’s total wealth over an

evaluation period(VE - VB) / VB

VE =ending portfolio value

VB =beginning portfolio value• Assumes no funds added or withdrawn

during evaluation period–If not, timing of flows important

Return Measures• Dollar-weighted returns

–Captures cash flows during the evaluation period

–Equivalent to internal rate of return–Equates initial value of portfolio

(investment) with cash inflows or outflows and ending value of portfolio

–Cash flow effects make comparisons to benchmarks inappropriate

Return Measures• Time-weighted returns

– Captures cash flows during the evaluation period and permits comparisons with benchmarks

– Calculate a return relative for each time period defined by a cash inflow or outflow

– Use each return relative to calculate a compound rate of return for the entire period

Which Return Measure Should Be Used?

• Dollar- and Time-weighted Returns can give different results– Dollar-weighted returns appropriate for

portfolio owners– Time-weighted returns appropriate for

portfolio managers• No control over inflows, outflows• Independent of actions of client

• CFA Institute requires time-weighted returns

Time-Weighted Return (TWR) Dollar-Weighted Return / Internal Rate of Return (IRR)

Definition TWR is the return produced over time by a fund independent of contributions or withdrawals.

IRR is the discount rate that equates the cost of an investment with the cash generated by that investment.

Major Differentiator

TWR measures the performance of public fund managers.TWR eliminates the impact of the timing of fund cash flows and isolates the portion of a portfolio’s return that is attributable solely to the manager’s actions.

TWR is used for public fund managers because they normally do not control cash flowing into or out of their funds.

IRR measures the performance of private fund managers.

IRR accounts for the timing and magnitude of fund cash flows.

IRR is used for private fund managers because they typically exercise a degree of control over the amount and timing of fund cash flows.

Formula Annual TWR Formula Given Four Quarterly Returns: [(1+R1)(1+R2)(1+R3)(1+R4)] – 1R = Quarterly Return

2-Step Formula to Calculate Annualized IRR from Four Quarterly Cash Flows:(1) Solve the following equation for “X”

-CF0 + CF1 + CF2 + … CF4 = 0        (1+X)1(1+X)2 (1+X)4

(2) Put “X” in the equation below:    (1+X)4 – 1 = IRR

CF = Quarterly Cash Flows

Risk Measures• Risk differences cause portfolios to

respond differently to market changes• Total risk measured by the standard

deviation of portfolio returns • Nondiversifiable risk measured by a

security’s beta–Estimates may vary, be unstable, and

change over time

Risk-adjusted Performance• In evaluating portfolio performance, investors

should concern on the risk as well as their concern on return of portfolios. Its refer to risk-adjusted performance.

• Three common measurement of risk adjusted performance:1. Sharpe Ratio2. Treynor Ratio 3. Jensen’s Alpha

Portfolio Performance Evaluation: Example 1

Port-folio

Return (%)

Standar Deviation (%)

Beta

ABCD

Market

10.012.512.515.013.0

15.0009.5013.7511.5012.00

0,501,500.750.60 1.00

Question: Using risk free rate = 0.08, evaluate each portfolio assets performance using Sharpe & Treynor ratios and Jensen’s Alpha. Use the market portfolio as a benchmark.

Sharpe Ratio:Reward-to-variability ratio (RVAR)

• Benchmark based on the ex post capital market line

=Average excess return / total risk• Risk premium per unit of risk• The higher, the better the performance• Provides a ranking measure for portfolios• It more suitable for evaluating portfolio rather

than individual assets.

/SDRFTR RVAR pp

Portfolio Performance: Sharpe Ratio

Portfolio Sharpe Ratio(%) DBCA

Pasar

0,610,470,330,130,42

Portfolio Performance: Sharpe Ratio

D

C

Return

B Market

A

15

10

15105 StandardDeviation

RF8

Capital Market Line

Treynor ratio:Reward-to-volatilty ratio (RVOL)

• Distinguishes between total and systematic risk

• Average excess return / market risk• Risk premium per unit of market risk• The higher, the better the performance• Implies a diversified portfolio.• It more flexible for evaluating both portfolio and

individual assets.

/βRFTR RVOL pp

Portfolio Treynor Ratio (%)

DCAB

Market

11.676.004.003.005.00

Portfolio Performance: Treynor Ratio

DC

Return

BMarket

A

15

10

1,510,5 Portfolio’s Beta

RF

8

Security Market Line

Portfolio Performance: Treynor Ratio

RVAR or RVOL?• Depends on the definition of risk

– If total (systematic) risk best, use RVAR (RVOL)

– If portfolios perfectly diversified, rankings based on either RVAR or RVOL are the same

– Differences in diversification cause ranking differences• RVAR captures portfolio diversification

Measuring Diversification• How correlated are portfolio’s returns to market

portfolio?– R2 from estimation of

Rpt - RFt =ap +bp [RMt - RFt] +ept

– R2 is the coefficient of determination– Excess return form of characteristic line– The lower the R2, the greater the diversifiable

risk and the less diversified.

Jensen’s Alpha• The estimated a coefficient in

Rpt - RFt =ap +bp [RMt - RFt] +ept

is a means to identify superior or inferior portfolio performance

–CAPM implies a is zero–Measures contribution of portfolio

manager beyond return attributable to risk

• If a >0 (<0,=0), performance superior (inferior, equals) to market, risk-adjusted.

• For ranking purposes, each asset’s alpha should be divided by its beta coefficient.

• It more flexible for evaluating both portfolio and individual assets.

D`

DC

Return

BMarket

A

15

10

1,510,5 Portfolio’s Beta

RF8

Capital Market Line

Portfolio Performance: Jensen’s Alpha

Portfolio Performance Evaluation: Example 2

Mutual Fund Return

Standard Deviation Alpha Beta

A 0.12 0.06 1.78 0.70B 0.19 0.25 1.01 2.10C 0.14 0.11 1.28 1.10

Question: Using risk free rate = 0.08, rank the three funds performance using Sharpe & Treynor ratios and Jensen’s Alpha.

Mutual Fund

Sharpe Ratio

Treynor Ratio

Jensen’s Alpha Rank

A 0.67 0.057 2.54 1B 0.44 0.052 0.48 3C 0.55 0.055 1.16 2

Mutual Fund Performance: Using Sharpe & Treynor Ratios, and Jensen’s Alpha

Measurement Problems• Performance measures based on CAPM and

its assumptions– Risk less borrowing?– What should market proxy be?

• If not efficient, benchmark error• Global investing increases problem

• How long an evaluation period?– CFA Institute stipulates a 10 year period

Other Evaluation Issues• Performance attribution seeks an

explanation for success or failure– Analysis of investment policy and asset

allocation decision– Analysis of industry and security selection– Benchmark (bogey) selected to measure

passive investment results– Differences due to asset allocation,

market timing, security selection

Thank You..Thank You..