0 Portfolio Management 3-228-07 Albert Lee Chun Evaluation of Portfolio Performance Lecture 11 2 Dec...

Portfolio ManagementPortfolio Management3-228-073-228-07

Albert Lee ChunAlbert Lee Chun

Evaluation of Portfolio Evaluation of Portfolio PerformancePerformance

Lecture 11Lecture 11

2 Dec 2008

2Albert Lee Chun Portfolio Management

IntroductionIntroduction

As portfolio managers, how can we evaluate the As portfolio managers, how can we evaluate the performance of our portfolio? performance of our portfolio?

We know that there are 2 major requirements of a We know that there are 2 major requirements of a portfolio manager’s performance:portfolio manager’s performance:1.1. The ability to derive above-average returns The ability to derive above-average returns conditioned on risk taken, either through conditioned on risk taken, either through superior superior market timing market timing oror superior security selection. superior security selection.2.2. The ability to diversify the portfolio and eliminate The ability to diversify the portfolio and eliminate non-systematic risk, relative to a benchmark non-systematic risk, relative to a benchmark portfolio.portfolio.

TodayToday

Performance Measurement Performance Measurement Risk Adjusted Performance MeasuresRisk Adjusted Performance MeasuresMeasures of Sharpe, Treynor and JensenMeasures of Sharpe, Treynor and JensenMeasures of Skill and Timing Measures of Skill and Timing

Attribution de performanceAttribution de performance

Concept de mesures ajustées pour le risqueConcept de mesures ajustées pour le risque

Mesures de Sharpe, Treynor et JensenMesures de Sharpe, Treynor et Jensen

Mesure des habilités de Mesure des habilités de timingtiming

Averaging ReturnsAveraging Returns

Arithmetic Mean:

Geometric Mean:

1)1(/1

Example:

(.10 + .0566) / 2 = 7.83%

[ (1.1) (1.0566) ]1/2 - 1

= 7.808%

Example:

TheThe arithmetic average arithmetic average provides unbiased estimates of the expected provides unbiased estimates of the expected return of the stock. Use this to forecast returns in the next period.return of the stock. Use this to forecast returns in the next period.

The fixed rate of return over the sample period that would yield the The fixed rate of return over the sample period that would yield the terminal value is know as the terminal value is know as the geometric averagegeometric average..

The geometric average is less than the arithmetic average and this The geometric average is less than the arithmetic average and this difference increases with the volatility of returns.difference increases with the volatility of returns.

The geometric average is also called the The geometric average is also called the time-weighted average time-weighted average (as (as opposed to theopposed to the dollar weighted average dollar weighted average), because it puts equal ), because it puts equal weights on each return.weights on each return.

Geometric AverageGeometric Average

Dollar-weighted returnsDollar-weighted returns Internal rate of return.Internal rate of return. Returns are weighted by the amount invested in each Returns are weighted by the amount invested in each

stock.stock.

Time-weighted returnsTime-weighted returns Not weighted by investment amount.Not weighted by investment amount. Equal weighting Equal weighting Geometric averageGeometric average

Dollar- and Time-Weighted ReturnsDollar- and Time-Weighted Returns

Example: Multiperiod ReturnsExample: Multiperiod Returns

PeriodPeriod ActionAction

00 Purchase 1 share of Eggbert’s Egg Co. at $50Purchase 1 share of Eggbert’s Egg Co. at $50

11 Purchase 1 share of Eggbert’s Egg Co. at $53Purchase 1 share of Eggbert’s Egg Co. at $53

Eggbert pays a dividend of $2 per shareEggbert pays a dividend of $2 per share

22 Eggbert pays a dividend of $2 per shareEggbert pays a dividend of $2 per share

Sell both shares for $108Sell both shares for $108

Period Cash Flow

0 -50 share purchase

1 +2 dividend -53 share purchase

2 +4 dividend + 108 shares sold

%117.7

rrInternal Rate of Return:

Dollar-Weighted ReturnDollar-Weighted Return

Dollar Weighted: The stocks performance in the second year, when we own 2 shares, has a greater influence on the overall return.

Time-Weighted ReturnTime-Weighted Return

%66.553

[ (1.1) (1.0566) ]1/2 - 1= 7.808%

Time Weighted: Each return has equal weight in the geometric average.

Geometric Mean:

Performance MeasurementPerformance Measurement

Early Performance Measure TechniquesEarly Performance Measure Techniques

Portfolio evaluation before 1960Portfolio evaluation before 1960 Once upon a time, investors evaluated a portfolio’s

performance based purely on the basis of the rate of return.

Research in the 1960’s showed investors how to quantify and measure risk.

Grouped portfolios into similar risk classes and compared rates of return within risk classes.

Peer Group ComparisonsPeer Group Comparisons

This is the most common manner of evaluating This is the most common manner of evaluating portfolio managers. portfolio managers.

Collects returns of a representative universe of Collects returns of a representative universe of investors over a period of time and displays them in a investors over a period of time and displays them in a box plot format.box plot format.

Example: “US Equity with Cash” relative to peer Example: “US Equity with Cash” relative to peer universe of US domestic equity managers.universe of US domestic equity managers.

Issue:Issue: There is no explicit adjustment for risk. Risk is There is no explicit adjustment for risk. Risk is only considered implicitly. only considered implicitly.

Treynor Portfolio Performance MeasureTreynor Portfolio Performance Measure

Treynor (1965)Treynor (1965)

Treynor (1965) developed the first composite measure of Treynor (1965) developed the first composite measure of portfolio performance that portfolio performance that included riskincluded risk..

He introduced the He introduced the portfolio characteristic lineportfolio characteristic line, which , which defines a relation between the rate of return on a specific defines a relation between the rate of return on a specific portfolio and the rate of return on the market portfolio.portfolio and the rate of return on the market portfolio.

The beta is the slope that measures the volatility of the The beta is the slope that measures the volatility of the portfolio’s returns relative to the market.portfolio’s returns relative to the market.

Alpha represents Alpha represents uniqueunique returns for the portfolio. returns for the portfolio. As the portfolio becomes diversified, unique risk As the portfolio becomes diversified, unique risk

diminishes.diminishes.

tppp ,tM,tp, RR

A risk-adjusted measure of return that divides a portfolio'sA risk-adjusted measure of return that divides a portfolio'sexcess return by its beta.excess return by its beta.

The The Treynor MeasureTreynor Measure is given by is given by

Treynor MeasureTreynor Measure

The Treynor Measure is defined using the average rate of return The Treynor Measure is defined using the average rate of return for portfolio p and the risk-free asset.for portfolio p and the risk-free asset.

A larger Tp is better for all investors, regardless of their risk A larger Tp is better for all investors, regardless of their risk preferences. preferences.

Because it adjusts returns based on systematic risk, it is the Because it adjusts returns based on systematic risk, it is the relevant performance measure when evaluating diversified relevant performance measure when evaluating diversified portfolios held in portfolios held in separatelyseparately or in or in combination with other combination with other portfoliosportfolios..

Beta measures systematic risk, yet if the portfolio is not fully Beta measures systematic risk, yet if the portfolio is not fully diversified then this measure is not a complete characterization diversified then this measure is not a complete characterization of the portfolio risk.of the portfolio risk.

Hence, it implicitly assumes a completely diversified portfolio.Hence, it implicitly assumes a completely diversified portfolio. Portfolios with identical systematic risk, but different total risk, Portfolios with identical systematic risk, but different total risk,

will have the same Treynor ratio!will have the same Treynor ratio! Higher idiosyncratic risk should not matter in a diversified Higher idiosyncratic risk should not matter in a diversified

portfolio and hence is not reflected in the Treynor measure. portfolio and hence is not reflected in the Treynor measure. A portfolio negative Beta will have a negative Treynor measure.A portfolio negative Beta will have a negative Treynor measure. Also known as the Also known as the Treynor RatioTreynor Ratio..

T-Lines T-Lines

Q has higher alpha, but P has steeper T-line.

P is the better portfolio.

Sharpe Portfolio Performance MeasureSharpe Portfolio Performance Measure

Similar to the Treynor measure, but uses the Similar to the Treynor measure, but uses the total risktotal risk of the of the portfolio, not just the systematic risk. portfolio, not just the systematic risk.

The The Sharpe RatioSharpe Ratio is given by is given by

The larger the measure the better, as the portfolio earned a The larger the measure the better, as the portfolio earned a higher excess return per unit of higher excess return per unit of total risktotal risk. .

Sharpe MeasureSharpe Measure

r R =S

Sharpe MeasureSharpe Measure

It adjusts returns for total portfolio risk, as opposed to only It adjusts returns for total portfolio risk, as opposed to only systematic risk as in the Treynor Measure.systematic risk as in the Treynor Measure.

Thus, an implicit assumption of the Sharpe ratio is that the Thus, an implicit assumption of the Sharpe ratio is that the portfolio is not fully diversified, nor will it be combined with portfolio is not fully diversified, nor will it be combined with other diversified portfolios. other diversified portfolios.

It is relevant for performance evaluation when comparing It is relevant for performance evaluation when comparing mutually exclusive portfolios. mutually exclusive portfolios.

Sharpe originally called it the Sharpe originally called it the "reward-to-variability" ratio, "reward-to-variability" ratio, before others startedbefore others started calling it the calling it the Sharpe RatioSharpe Ratio..

SML vs. CMLSML vs. CML

Treynor’sTreynor’s measure uses measure uses BetaBeta and hence examines portfolio and hence examines portfolio return performance in relation to the return performance in relation to the SMLSML..

Sharpe’sSharpe’s measure uses measure uses total risktotal risk and hence examines portfolio and hence examines portfolio return performance in relation to the return performance in relation to the CMLCML..

For a totally diversified portfolio, both measures give equal For a totally diversified portfolio, both measures give equal rankings.rankings.

If it is not a diversified portfolio, the Sharpe measure could If it is not a diversified portfolio, the Sharpe measure could give lower rankings than the Treynor measure. give lower rankings than the Treynor measure.

Thus, the Sharpe measure evaluates the portfolio manager in Thus, the Sharpe measure evaluates the portfolio manager in terms of terms of bothboth return performance and diversification. return performance and diversification.

Price of RiskPrice of Risk

Both the Treynor and Sharp measures, indicate the risk Both the Treynor and Sharp measures, indicate the risk premium per unit of risk, either systematic risk (Treynor) or premium per unit of risk, either systematic risk (Treynor) or total risk (Sharpe). total risk (Sharpe).

They measure the They measure the price of riskprice of risk in units of in units of excess returnsexcess returns per per each unit of riskeach unit of risk (measured either by beta or the standard (measured either by beta or the standard deviation of the portfolio).deviation of the portfolio).

T =rR ppfp ppfp Sr R

Jensen Portfolio Performance MeasureJensen Portfolio Performance Measure

Alpha is a risk-adjusted measure of superior performanceAlpha is a risk-adjusted measure of superior performance

This measure adjusts for the systematic risk of the portfolio. This measure adjusts for the systematic risk of the portfolio. Positive alpha signals superior risk-adjusted returns, and that the Positive alpha signals superior risk-adjusted returns, and that the

manager is good at selecting stocks or predicting market turning manager is good at selecting stocks or predicting market turning points.points.

Unlike the Sharpe Ratio, Jensen’s method does not consider the Unlike the Sharpe Ratio, Jensen’s method does not consider the ability of the manager to diversify, as it is only accounts for ability of the manager to diversify, as it is only accounts for systematic risk.systematic risk.

Jensen’s AlphaJensen’s Alpha

tptfpp r ,,tM,tf,tp, RrR

Multifactor Jensen’s MeasureMultifactor Jensen’s Measure

Measure can be extended to a multi-factor setting, for example:Measure can be extended to a multi-factor setting, for example:

tppptfpp HMLSMLr ,32

tf,tp, RrR

Information RatioInformation Ratio

Information Ratio 1Information Ratio 1

Using a historical regression, the IR takes on the formUsing a historical regression, the IR takes on the form

where the numerator is Jensen’s alpha and the denominator is the where the numerator is Jensen’s alpha and the denominator is the standard error of the regression. Recalling thatstandard error of the regression. Recalling that

tptfpp r ,,tM,tf,tp, RrR

Note that the risk here is nonsystematic risk, that could, in theory,

be eliminated by diversification.

Information Ratio 2Information Ratio 2

R R =IR

Measures excess returns relative to a benchmark portfolio.

Sharpe Ratio is the special case where the benchmark equals the risk-free asset.

Risk is measured as the standard deviation of the excess return (Recall that this is the Tracking Error)

For an actively managed portfolio, we may want to maximize the excess return per unit of nonsystematic risk we are bearing.

Portfolio Tracking ErrorPortfolio Tracking Error

Excess Return relative Excess Return relative

to benchmark portfolio b to benchmark portfolio b

Average Excess ReturnAverage Excess Return

Variance in Excess DifferenceVariance in Excess Difference

Tracking ErrorTracking Error

tbtpt RRER ,,

ttER ERER

Information RatioInformation Ratio

Excess return represents manager’s ability to use Excess return represents manager’s ability to use informationinformation and talent to generate excess returns. and talent to generate excess returns.

Fluctuations in excess returns represent random Fluctuations in excess returns represent random noisenoise that is that is interpreted as unsystematic risk.interpreted as unsystematic risk.

InformationInformation to to noisenoise ratio. ratio. Annualized IR Annualized IR

R R =IR

pp IR T =IR

Information RatiosInformation Ratios

MM2 2 MeasureMeasure

Developed by Leah and her grandfather Franco Modigliani.Developed by Leah and her grandfather Franco Modigliani.

MM2 2 = r= rp*p*- r- rmm

rrp*p* is return of the adjusted portfolio that matches the volatility of the is return of the adjusted portfolio that matches the volatility of the

market index market index rrmm.. It is mixed with a position in T-bills. It is mixed with a position in T-bills.

If the risk of the portfolio is lower than that of the market, one has to If the risk of the portfolio is lower than that of the market, one has to increase the volatility by using leverage.increase the volatility by using leverage.

Because the market index and the adjusted portfolio have the same Because the market index and the adjusted portfolio have the same standard deviation, we may compare their performances by standard deviation, we may compare their performances by comparing returns.comparing returns.

MM2 2 Measure: ExampleMeasure: Example

Managed Portfolio: return = 35% st dev = 42%

Market Portfolio: return = 28% st dev = 30%

T-bill return = 6%

Hypothetical Portfolio:

30/42 = .714 in P (1-.714) or .286 in T-bills

Return = (.714) (.35) + (.286) (.06) = 26.7%

Since the return of the portfolio is less than the market, MM22 is negative, and the managed portfolio underperformed the market.

MM22 of Portfolio P of Portfolio P

Excess Returns for Portfolios P and Q and Excess Returns for Portfolios P and Q and the Benchmark Mthe Benchmark M

Performance StatisticsPerformance Statistics

Which Portfolio is Best?Which Portfolio is Best?

It depends.It depends. If P or Q represent the entire portfolio, Q would be If P or Q represent the entire portfolio, Q would be

preferable based on having higher sharp ratio and a preferable based on having higher sharp ratio and a better Mbetter M22..

If P or Q represents a sub-portfolio, the Q would be If P or Q represents a sub-portfolio, the Q would be preferable because it has a higher Treynor ratio.preferable because it has a higher Treynor ratio.

For an actively managed portfolio, P may be For an actively managed portfolio, P may be preferred because it’s information ratio is larger (that preferred because it’s information ratio is larger (that is it maximizes return relative to nonsystematic risk, is it maximizes return relative to nonsystematic risk, or the tracking error).or the tracking error).

Style AnalysisStyle Analysis

Introduced by William SharpeIntroduced by William Sharpe

1992 study of mutual fund performance1992 study of mutual fund performance 91.5% of variation in return could be explained

by the funds’ allocations to bills, bonds and stocks

Later studies show that 97% of the variation in return Later studies show that 97% of the variation in return could be explained by the funds’ allocation to set of could be explained by the funds’ allocation to set of different asset classes.different asset classes.

Sharpe’s Style Portfolios for the Magellan FundSharpe’s Style Portfolios for the Magellan Fund

Monthly returns on Magellan Fund over five year period.

Regression coefficient only positive for 3.

They explain 97.5% of Magellan’s returns.

2.5 percent attributed to security selection within asset classes.

Fidelity Magellan Fund Returns vs BenchmarksFidelity Magellan Fund Returns vs Benchmarks

Fund vs Style and Fund vs SMLFund vs Style and Fund vs SML

Impact of positive alpha on abnormal

returns.

19.19%

Average Tracking Error for 636 Mutual FundsAverage Tracking Error for 636 Mutual Funds

Bell shaped

Market TimingMarket Timing

Perfect Market TimingPerfect Market Timing

A manager with perfect market timing, that shifts assets A manager with perfect market timing, that shifts assets efficiently across stocks, bonds and cash would have a return efficiently across stocks, bonds and cash would have a return equal toequal to

0,,max tbttsttpt RFRRRFRRRFRR

Returns from 1990 - 1999Returns from 1990 - 1999YearYear Lg StocksLg Stocks T-BillsT-Bills

19901990 -3.20-3.20 7.867.86

19911991 30.6630.66 5.655.65

19921992 7.717.71 3.543.54

19931993 9.879.87 2.972.97

19941994 1.291.29 3.913.91

19951995 37.7137.71 5.585.58

19961996 23.0723.07 5.585.58

19981998 28.5828.58 5.115.11

19991999 21.0421.04 4.804.80

Switch to T-Bills in 90 and 94Switch to T-Bills in 90 and 94 Mean = 18.94%, Standard Deviation = 12.04%

Invested in large stocks for the entire period:Invested in large stocks for the entire period: Mean = 17.41% Standard Deviation = 14.11

With Perfect Forecasting AbilityWith Perfect Forecasting Ability

Performance of Bills, Equities and TimersPerformance of Bills, Equities and TimersBeginning with $1 dollar in 1926, and ending in 2005....

Value of Imperfect ForecastingValue of Imperfect Forecasting

Suppose you are forecasting rain in Seattle. If you predict rain, Suppose you are forecasting rain in Seattle. If you predict rain, you would be correct most of the time.you would be correct most of the time.

Does this make you a good forecaster? Certainly not.Does this make you a good forecaster? Certainly not. We need to examine the proportion of correct forecasts for We need to examine the proportion of correct forecasts for

rain (rain (P1P1) and the proportion of correct forecasts for sun () and the proportion of correct forecasts for sun (P2P2).). The correct measure of timing ability isThe correct measure of timing ability is

PP = = P1P1 + + P2P2 – 1 – 1

An forecaster who always guesses correctly will show An forecaster who always guesses correctly will show P1P1 = = P2P2 = = PP =1, whereas on who always predicts rain will have =1, whereas on who always predicts rain will have P1P1 = 1, = 1, P2P2 = = PP = 0. = 0.

If an investor holds only the market and the risk free security, and If an investor holds only the market and the risk free security, and the weights remained constant, the portfolio characteristic line the weights remained constant, the portfolio characteristic line would be a straight line. would be a straight line.

Adjusting portfolio weights for up and down movements in Adjusting portfolio weights for up and down movements in market returns, we would have:market returns, we would have:

Low Market Return - low weight on the market - Low Market Return - low weight on the market - low ßetalow ßeta High Market Return – high weight on the market - High Market Return – high weight on the market - high ßetahigh ßeta

Identifying Market TimingIdentifying Market Timing

Henriksson (1984) showed little evidence of market timing. Evidence of market efficiency.

Characteristic Lines: Market TimingCharacteristic Lines: Market Timing

No Market TimingNo Market Timing

Beta Increases with ReturnBeta Increases with Return Two Values of BetaTwo Values of Beta

Testing Market TimingTesting Market Timing

The following regression equation, controls for the movements The following regression equation, controls for the movements in bond and stock markets, and captures the superior market in bond and stock markets, and captures the superior market timing of managerstiming of managers

Gamma was found to be equal to .3 and statistically significant, Gamma was found to be equal to .3 and statistically significant, suggesting that TAA managers were able to time the markets. suggesting that TAA managers were able to time the markets.

However, the study also found a negative alpha of -.5.However, the study also found a negative alpha of -.5.

ttbttst

ststbtbtpt

RFRRRFRR

RFRRRFRRRFRR

0,,max

Performance Attribution AnalysisPerformance Attribution Analysis

SelectivitySelectivity

The basic premise of the Fama method is that overall The basic premise of the Fama method is that overall performance of a portfolio can be decomposed into a performance of a portfolio can be decomposed into a portfolio risk premium component and a selectivity portfolio risk premium component and a selectivity component.component.

SelectivitySelectivity is the portion of excess returns that is the portion of excess returns that exceeds that which can be attained by an unmanaged exceeds that which can be attained by an unmanaged benchmark portfolio.benchmark portfolio.

Overall performanceOverall performance = = Portfolio Risk PremiumPortfolio Risk Premium + + SelectivitySelectivity

Overall performanceOverall performance = = Portfolio Risk Portfolio Risk PremiumPremium+ + SelectivitySelectivity

)(R-RR )(R = R xpfxf pppR Overall

PerformancePortfolio Risk

PremiumSelectivity

Selectivity measures the distance between the return on portfolio p and the return on a

benchmark portfolio with beta equal to the beta of portfolio p.

Attribution AnalysisAttribution Analysis

Portfolio managers add value to their investors by Portfolio managers add value to their investors by 1)1) selecting superior securities selecting superior securities2)2) demonstrating superior market timing skills by demonstrating superior market timing skills by allocating funds to different asset classes or market allocating funds to different asset classes or market segments.segments.

Attribution analysisAttribution analysis attempts to distinguish is the source attempts to distinguish is the source of the portfolio’s overall performance.of the portfolio’s overall performance.

Total value added performance is the sum of selection Total value added performance is the sum of selection and allocation effects.and allocation effects.

ipipiBp

ipipip

iBiBiB

rwrwrr

rwrrwr

Where B is the bogey portfolio and p is the managed portfolio.

Formula for AttributionFormula for Attribution

Set up a ‘Benchmark’ or ‘Bogey’ portfolio

Allocation EffectAllocation Effect

Asset Allocation EffectAsset Allocation Effect

Captures the manager’s decision to over or Captures the manager’s decision to over or underweight a particular market segment underweight a particular market segment ii..

Overweighting a segment Overweighting a segment ii when the benchmark yield when the benchmark yield is high is rewarded.is high is rewarded.

BiBiPii rww

Selection EffectSelection Effect

Security Selection EffectSecurity Selection Effect

Captures the stock picking ability of the manager, and Captures the stock picking ability of the manager, and rewards the ability to form specific market segment rewards the ability to form specific market segment portfolios. Rewards the manger for placing larger weights portfolios. Rewards the manger for placing larger weights on those segments where his portfolio outperforms the on those segments where his portfolio outperforms the benchmark portfolio in that particular segmentbenchmark portfolio in that particular segment . .

BiPiPii rrw

Performance of the Managed PortfolioPerformance of the Managed Portfolio

Performance AttributionPerformance Attribution

Sector Selection within the Equity MarketSector Selection within the Equity Market

Portfolio Attribution: Summary Portfolio Attribution: Summary

Global Benchmark ProblemGlobal Benchmark Problem(Optional)(Optional)

Benchmark ErrorBenchmark Error

Market portfolio is difficult to approximateMarket portfolio is difficult to approximate Benchmark errorBenchmark error

can effect slope of SML can effect calculation of Beta greater concern with global investing problem is one of measurement

Note:Note: Sharpe measure not as dependent on market Sharpe measure not as dependent on market portfolio as the Treynor measure and others relying portfolio as the Treynor measure and others relying on Beta.on Beta.

Differences in Betas Differences in Betas

Two major differences in the various beta statistics:Two major differences in the various beta statistics: For any particular stock, the beta estimates change

a great deal over time. There are substantial differences in betas estimated

for the same stock over the same time period when two different definitions of the benchmark portfolio are employed.

Global Benchmark Problem - SMLGlobal Benchmark Problem - SML

Bond Portfolio Performance MeasuresBond Portfolio Performance Measures(Optional)(Optional)

Bond Portfolio MeasuresBond Portfolio Measures

Returns-Based Bond Performance MeasurementReturns-Based Bond Performance Measurement Early attempts to analyze fixed-income performance

involved peer group comparisons Peer group comparisons are potentially flawed because

they do not account for investment risk directly. How did the performance levels of portfolio managers How did the performance levels of portfolio managers

compare to the overall bond market?compare to the overall bond market? What factors lead to superior or inferior bond-portfolio What factors lead to superior or inferior bond-portfolio

performance?performance?

Fama-French MeasureFama-French Measure

Fama and French extended their 3-factor equity pricing Fama and French extended their 3-factor equity pricing model with 2 additional factors to account for the return model with 2 additional factors to account for the return characteristics of bondscharacteristics of bonds

TERM – captures the term premium in the slope of the yield TERM – captures the term premium in the slope of the yield curve.curve.

DEF – captures the default premium in the credit spread DEF – captures the default premium in the credit spread between corporate bonds and treasuries.between corporate bonds and treasuries.

These two bond factors are the dominate drivers of bond These two bond factors are the dominate drivers of bond portfolio returns.portfolio returns.

jt t j j1 mt t j2 t j3 t j4 t j4 t jtR - RFR = α + b R - RFR + b SMB + b HML + b TERM + b DEF + e

Seven Bond PortfoliosSeven Bond Portfolios

Bond Performance AttributionBond Performance Attribution

A Bond Market Line A Bond Market Line Need a measure of risk such as beta coefficient for

equities Difficult to achieve due to bond maturity and

coupon effect on volatility of prices Composite risk measure is the bond’s duration Duration replaces beta as risk measure in a bond

market line

Bond Market LineBond Market Line

That’s all for today!That’s all for today!

0 Portfolio Management 3-228-07 Albert Lee Chun Evaluation of Portfolio Performance Lecture 11 2 Dec...

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