essentials of investments with s p bind in card phần 10 potx

Our strict definition of a pure passive strategy is one that invests only in index funds and weights those funds by fixed proportions that do not change in response to market condi-tions

where E(r M)
r f is the risk premium on M, andM is the standard deviation of M To make a

rational allocation of funds requires an estimate of M and E(r M), so even a passive investor

needs to do some forecasting

Forecasting E(r M) and M is complicated further because security classes are affected

by different environment factors Long-term bond returns, for example, are driven largely by

changes in the term structure of interest rates, while returns on equity depend also on changes

in the broader economic environment, including macroeconomic factors besides interest rates

Once you begin considering how economic conditions influence separate sorts of investments,

you might as well use a sophisticated asset allocation program to determine the proper mix for

the portfolio It is easy to see how investors get lured away from a purely passive strategy

Even the definition of a “pure” passive strategy is not very clear-cut, as simple strategies

involving only the market index portfolio and risk-free assets now seem to call for market

analysis Our strict definition of a pure passive strategy is one that invests only in index funds

and weights those funds by fixed proportions that do not change in response to market

condi-tions: a portfolio strategy that always places 60% in a stock market index fund, 30% in a bond

index fund, and 10% in a money market fund, regardless of expectations

Active management is attractive because the potential profit is enormous, even though

competition among managers is bound to drive market prices to near-efficient levels For

prices to remain efficient to some degree, decent profits to diligent analysts must be the rule

rather than the exception, although large profits may be difficult to earn Absence of profits

would drive people out of the investment management industry, resulting in prices moving

away from informationally efficient levels

Objectives of Active Portfolios

What does an investor expect from a professional portfolio manager, and how do these

ex-pectations affect the manager’s response? If all clients were risk neutral (indifferent to risk),

the answer would be straightforward: The investment manager should construct a portfolio

with the highest possible expected rate of return, and the manager should then be judged by

the realized average rate of return.

When the client is risk averse, the answer is more difficult Lacking standards to proceed

by, the manager would have to consult with each client before making any portfolio decision

in order to ascertain that the prospective reward (average return) matched the client’s attitude

toward risk Massive, continuous client input would be needed, and the economic value of

professional management would be questionable

Fortunately, the theory of mean-variance efficiency allows us to separate the “product

deci-sion,” which is how to construct a mean-variance efficient risky portfolio, from the

“con-sumption decision,” which describes the investor’s allocation of funds between the efficient

risky portfolio and the safe asset You have learned already that construction of the optimal

risky portfolio is purely a technical problem and that there is a single optimal risky portfolio

appropriate for all investors Investors differ only in how they apportion investment between

that risky portfolio and the safe asset

The mean-variance theory also speaks to performance in offering a criterion for judging

managers on their choice of risky portfolios In Chapter 6, we established that the optimal

risky portfolio is the one that maximizes the reward-to-variability ratio, that is, the expected

excess return divided by the standard deviation A manager who maximizes this ratio will

sat-isfy all clients regardless of risk aversion

Clients can evaluate managers using statistical methods to draw inferences from realized

rates of return about prospective, or ex ante, reward-to-variability ratios The Sharpe measure,

20 Performance Evaluation and Active Portfolio Management 701

or the equivalent M2, is now a widely accepted way to track performance of professionallymanaged portfolios:

S PThe most able manager will be the one who consistently obtains the highest Sharpe meas-ure, implying that the manager has real forecasting ability A client’s judgment of a manager’sability will affect the fraction of investment funds allocated to this manager; the client can in-vest the remainder with competing managers and in a safe fund

If managers’ Sharpe measures were reasonably constant over time, and clients could ably estimate them, allocating funds to managers would be an easy decision

reli-Actually, the use of the Sharpe measure as the prime measure of a manager’s ability quires some qualification We know from the discussion of performance evaluation earlier inthis chapter that the Sharpe ratio is the appropriate measure of performance only when theclient’s entire wealth is managed by the professional investor Moreover, clients may imposeadditional restrictions on portfolio choice that further complicate the performance evaluationproblem

Consider the results of three different investment strategies, as gleaned from Table 5.3:

1 Investor X, who put $1 in 30 day T-bills (or their predecessors) on January 1, 1926, and

always rolled over all proceeds into 30-day T-bills, would have ended on December 31,

2001, 76 years later, with $16.98

2 Investor Y, who put $1 in large stocks (the S&P 500 portfolio) on January 1, 1926,

and reinvested all dividends in that portfolio, would have ended on December 31, 2001,with $1,987.01

3 Suppose we define perfect market timingas the ability to tell with certainty at the

beginning of each year whether stocks will outperform bills Investor Z, the perfect timer,

shifts all funds at the beginning of each year into either bills or stocks, whichever is

going to do better Beginning at the same date, how much would Investor Z have ended

up with 76 years later? Answer: $115,233.89!

3 What are the annually compounded rates of return for the X, Y, and perfect-timing

strategies over the period 1926–2001?

These results have some lessons for us The first has to do with the power of compounding.Its effect is particularly important as more and more of the funds under management representpension savings The horizons of pension investments may not be as long as 76 years, but theyare measured in decades, making compounding a significant factor

The second is a huge difference between the end value of the all-safe asset strategy($16.98) and of the all-equity strategy ($1,987.01) Why would anyone invest in safe assetsgiven this historical record? If you have absorbed all the lessons of this book, you know thereason: risk The averages of the annual rates of return and the standard deviations on the all-bills and all-equity strategies were

Arithmetic Mean Standard Deviation

The significantly higher standard deviation of the rate of return on the equity portfolio is

commensurate with its significantly higher average return The higher average return reflects

the risk premium

Is the return premium on the perfect-timing strategy a risk premium? Because the perfect

timer never does worse than either bills or the market, the extra return cannot be

compensa-tion for the possibility of poor returns; instead it is attributable to superior analysis The value

of superior information is reflected in the tremendous ending value of the portfolio This value

does not reflect compensation for risk

To see why, consider how you might choose between two hypothetical strategies

Strat-egy 1 offers a sure rate of return of 5%; stratStrat-egy 2 offers an uncertain return that is given by

5% plus a random number that is zero with a probability of 0.5 and 5% with a probability of

0.5 The results for each strategy are

Clearly, strategy 2 dominates strategy 1, as its rate of return is at least equal to that of

egy 1 and sometimes greater No matter how risk averse you are, you will always prefer

strat-egy 2 to stratstrat-egy 1, even though stratstrat-egy 2 has a significant standard deviation Compared to

strategy 1, strategy 2 provides only good surprises, so the standard deviation in this case

can-not be a measure of risk

You can look at these strategies as analogous to the case of the perfect timer compared with

either an all-equity or all-bills strategy In every period, the perfect timer obtains at least as

good a return, in some cases better Therefore, the timer’s standard deviation is a misleading

measure of risk when you compare perfect timing to an all-equity or all-bills strategy

Valuing Market Timing as an Option

Merton (1981) shows that the key to analyzing the pattern of returns of a perfect market timer

is to compare the returns of a perfect foresight investor with those of another investor who

holds a call option on the equity portfolio Investing 100% in bills plus holding a call option

on the equity portfolio will yield returns identical to those of the portfolio of the perfect timer

who invests 100% in either the safe asset or the equity portfolio, whichever will yield the

higher return The perfect timer’s return is shown in Figure 20.5 The rate of return is bounded

from below by the risk-free rate, r f

To see how the value of information can be treated as an option, suppose the market index

currently is at S0and a call option on the index has exercise price of X  S0(1 r f) If the

market outperforms bills over the coming period, S T will exceed X; it will be less than X

other-wise Now look at the payoff to a portfolio consisting of this option and S0dollars invested

in bills

Payoff to Portfolio Outcome: S T X S T  X

The portfolio returns the risk-free rate when the market is bearish (that is, when the marketreturn is less than the risk-free rate) and pays the market return when the market is bullish andbeats bills This represents perfect market timing Consequently, the value of perfect timingability is equivalent to the value of the call option, for a call enables the investor to earn the

market return only when it exceeds r f.Valuation of the call option embedded in market timing is relatively straightforward using

the Black-Scholes formula Set S $1 (to find the value of the call per dollar invested in the

market), use an exercise price of X  (1  r f) (the current risk-free rate is about 3%), and

a volatility of   203 (the historical volatility of the S&P 500) For a once-a-year timer,

T 1 year According to the Black-Scholes formula, the call option conveyed by market ing ability is worth about 8.1% of assets, and this is the annual fee one could presumablycharge for such services More frequent timing would be worth more If one could time

tim-the market on a monthly basis, tim-then T1⁄12and the value of perfect timing would be 2.3%

per month.

The Value of Imperfect Forecasting

But managers are not perfect forecasters While managers who are right most of the time

presumably do very well, “right most of the time” does not mean merely the percentage of the time a manager is right For example, a Tucson, Arizona, weather forecaster who always

predicts “no rain” may be right 90% of the time, but this “stopped clock” strategy does notrequire any forecasting ability

Neither is the overall proportion of correct forecasts an appropriate measure of marketforecasting ability If the market is up two days out of three, and a forecaster always predicts

a market advance, the two-thirds success rate is not a measure of forecasting ability We need

to examine the proportion of bull markets (r M  r f ) correctly forecast and the proportion of bear markets (r M f) correctly forecast

If we call P1 the proportion of the correct forecasts of bull markets and P2the proportion

for bear markets, then P1  P2
1 is the correct measure of timing ability For example, a

forecaster who always guesses correctly will have P1  P2 1 and will show ability of 1(100%) An analyst who always bets on a bear market will mispredict all bull markets

(P1  0), will correctly “predict” all bear markets (P2  1), and will end up with timing

ability of P1  P2
1  0 If C denotes the (call option) value of a perfect market timer, then (P1  P2
1)C measures the value of imperfect forecasting ability.

704 Part SIX Active Investment Management

The incredible potential payoff to accurate timing versus the relative scarcity of billionaires

should suggest to you that market timing is far from a trivial exercise and that very imperfect

timing is the most that we can hope for

4 What is the market timing score of someone who flips a fair coin to predict the

market?

Measurement of Market Timing Performance

In its pure form, market timing involves shifting funds between a market index portfolio and

a safe asset, such as T-bills or a money market fund, depending on whether the market as a

whole is expected to outperform the safe asset In practice, most managers do not shift fully

between bills and the market How might we measure partial shifts into the market when it is

expected to perform well?

To simplify, suppose the investor holds only the market index portfolio and T-bills If the

weight on the market were constant, say 0.6, then the portfolio beta would also be constant,

and the portfolio characteristic line would plot as a straight line with a slope 0.6, as in Figure

20.6A If, however, the investor could correctly time the market and shift funds into it in

peri-ods when the market does well, the characteristic line would plot as in Figure 20.6B The idea

is that if the timer can predict bull and bear markets, more will be shifted into the market when

the market is about to go up The portfolio beta and the slope of the characteristic line will be

higher when r Mis higher, resulting in the curved line that appears in 20.6B

Treynor and Mazuy (1966) tested to see whether portfolio betas did in fact increase prior

to market advances, but they found little evidence of timing ability A similar test was

imple-mented by Henriksson (1984) His examination of market timing ability for 116 funds in

20 Performance Evaluation and Active Portfolio Management 705

Concept

CHECK

<

F I G U R E 20.6Characteristic lines A: No market timing, beta is constant B: Market timing, beta increases with expected market excess return

Steadily increasing slope

A No Market Timing, Beta Is Constant

B Market Timing, Beta Increases with Expected Market Excess Return

1968–1980 found that, on average, portfolio betas actually fell slightly during the market

ad-vances, although in most cases the response of portfolio betas to the market was not cally significant Eleven funds had statistically positive values of market timing, while eighthad significantly negative values Overall, 62% of the funds had negative point estimates oftiming ability

statisti-In sum, empirical tests to date show little evidence of market timing ability Perhaps thisshould be expected; given the tremendous values to be reaped by a successful market timer, itwould be surprising to uncover clear-cut evidence of such skills in nearly efficient markets

as much as 97% of fund returns can be explained by asset allocation alone

Sharpe considered 12 asset class (style) portfolios His idea was to regress fund returns onindexes representing a range of asset classes The regression coefficient on each index wouldthen measure the implicit allocation to that “style.” Because funds are barred from short posi-tions, the regression coefficients are constrained to be either zero or positive and to sum to

100%, so as to represent a complete asset allocation The R-square of the regression would

then measure the percentage of return variability attributed to the effects of security selection

To illustrate the approach, consider Sharpe’s study of the monthly returns on Fidelity’sMagellan Fund over the period January 1985 through December 1989, shown in Table 20.7

706 Part SIX Active Investment Management

TA B L E 20.7

Sharpe’s style portfolios for the Magellan fund

Regression Coefficient*

Intermediate bonds 0 Long-term bonds 0 Corporate bonds 0

*Regressions are constrained to have nonnegative coefficients and to have coefficients that sum to 100%.

Source: William F Sharpe, “Asset Allocation: Management Style and Performance

Evaluation,” Journal of Portfolio Management, Winter 1992, pp 7–19.

3William F Sharpe, “Asset Allocation: Management Style and Performance Evaluation,” Journal of Portfolio

Man-agement, Winter 1992, pp 7–19.

4Gary Brinson, Brian Singer, and Gilbert Beebower, “Determinants of Portfolio Performance,” Financial Analysts

Journal, May/June 1991.

While there are 12 asset classes, each one represented by a stock index, the regression

coefficients are positive for only 4 of them We can conclude that the fund returns are well

explained by only four style portfolios Moreover, these three style portfolios alone explain

97.3% of returns

The proportion of return variability not explained by asset allocation can be attributed to

security selection within asset classes For Magellan, this was 100
97.3  2.7% To

evalu-ate the average contribution of stock selection to fund performance we track the residuals from

the regression, displayed in Figure 20.7 The figure plots the cumulative effect of these

resid-uals; the steady upward trend confirms Magellan’s success at stock selection in this period

Notice that the plot in Figure 20.7 is far smoother than the plot in Figure 20.8, which shows

Magellan’s performance compared to a standard benchmark, the S&P 500 This reflects the

fact that the regression-weighted index portfolio tracks Magellan’s overall style much better

than the S&P 500 The performance spread is much noisier using the S&P as the benchmark

Of course, Magellan’s consistently positive residual returns (reflected in the steadily

increasing plot of cumulative return difference) is hardly common Figure 20.9 shows the

20 Performance Evaluation and Active Portfolio Management 707

F I G U R E 20.7Fidelity Magellan Fund cumulative return difference: fund versus style benchmark Source: William F Sharpe,

“Asset Allocation: Management Style and Performance Evaluation,”

Journal of Portfolio Management, Winter 1992,

“Asset Allocation: Management Style and Performance Evaluation,”

Journal of Portfolio Management, Winter 1992,

frequency distribution of average residuals across 636 mutual funds The distribution has thefamiliar bell shape with a slightly negative mean of
.074% per month.

Style analysis has become very popular in the investment management industry and hasspawned quite a few variations on Sharpe’s methodology Many portfolio managers utilizewebsites that help investors identify their style and stock selection performance

The commercial success of Morningstar, Inc., the premier source of information on mutual

funds, has made its Risk Adjusted Rating (RAR) among the most widely used performance

measures The Morningstar five-star rating is coveted by the managers of the thousands offunds covered by the service

Morningstar calculates a number of RAR performance measures that are similar, althoughnot identical, to the standard mean-variance measures The most distinct measure, the Morn-ingstar Star Rating, is based on comparison of each fund to a peer group The peer group foreach fund is selected on the basis of the fund’s investment universe (e.g., international, growthversus value, fixed-income, and so on) as well as portfolio characteristics such as averageprice-to-book value, price-earnings ratio, and market capitalization

Morningstar computes fund returns (adjusted for loads) as well as a risk measure based onfund performance in its worst years The risk-adjusted performance is ranked across funds in

a style group and stars are awarded based on the following table:

Average tracking error (%/month)

The Morningstar RAR method produces results that are similar but not identical to that of

the mean/variance-based Sharpe ratios Figure 20.10 demonstrates the fit between ranking by

RAR and by Sharpe ratios from the performance of 1,286 diversified equity funds over the

pe-riod 1994–1996 Sharpe notes that this pepe-riod is characterized by high returns that contribute

to a good fit

THE TREYNOR-BL ACK MODEL

Overview of the Treynor-Black Model

Security analysis is the other dimension of active investment besides timing the overall

mar-ket and asset allocation Suppose you are an analyst studying individual securities Quite

likely, you will turn up several securities that appear to be mispriced and offer positive alphas

But how do you exploit your analysis? Concentrating a portfolio on these securities entails a

cost, namely, the firm-specific risk you could shed by more fully diversifying As an active

manager, you must strike a balance between aggressive exploitation of security mispricing and

diversification considerations that dictate against concentrating a portfolio in a few stocks

Jack Treynor and Fischer Black (1973) developed a portfolio construction model for

man-agers who use security analysis It assumes security markets are nearly efficient The essence

of the model is this:

1 Security analysts in an active investment management organization can analyze in depth

only a relatively small number of stocks out of the entire universe of securities The

securities not analyzed are assumed to be fairly priced

2 For the purpose of efficient diversification, the market index portfolio is the baseline

portfolio, which is treated as the passive portfolio

3 The macro forecasting unit of the investment management firm provides forecasts of

the expected rate of return and variance of the passive (market index) portfolio

4 The objective of security analysis is to form an active portfolio of a necessarily limited

number of securities Perceived mispricing of the analyzed securities is what determines

the composition of this active portfolio

20 Performance Evaluation and Active Portfolio Management 709

F I G U R E 20.10Rankings based on Morningstar’s category RARs and excess return

Sharpe ratios Source: William F Sharpe,

“Morningstar Performance Measures,” www.wsharpe.com.

5 Analysts follow several steps to make up the active portfolio and forecast itsperformance:

a Estimate the characteristic line of each analyzed security and obtain its beta and residual variance From the beta and the macro forecast, E(r M)
r f, determine

the required rate of return of the security.

b Determine the expected return Subtracting the required return yields the expected abnormal return (alpha) of the security.

c Use the estimates for the values of alpha, beta, and residual risk to determine the

optimal weight of each security in the active portfolio

d Estimate the alpha, beta, and residual variance for the active portfolio according to

the weights of the securities in the portfolio

6 The macroeconomic forecasts for the passive index portfolio and the composite forecastfor the active portfolio are used to determine the optimal risky portfolio, which will be

a combination of the passive and active portfolios

Although some sophisticated investment managers use the Treynor-Black model,it hasnot taken the industry by storm This is unfortunate for several reasons:

1 Just as even imperfect market-timing ability has enormous value, security analysis of thesort Treynor and Black propose has similar potential value Even with far-from-perfectsecurity analysis, active management can add value

2 The Treynor-Black model is easy to implement Moreover, it is useful even relaxingsome of its simplifying assumptions

3 The model lends itself to use with decentralized decision making, which is essential toefficiency in complex organizations

Portfolio Construction

Assuming all securities are fairly priced and using the index model as a guideline for the rate

of return on securities, the rate of return on security i is given by

r i  r f i (r M
r f) e i (20.1)

where e iis the zero mean, firm-specific (nonsystematic) component

Absent security analysis, Treynor and Black take Equation 20.1 to represent the rate of

re-turn on all securities and assume the index portfolio (M) is efficient For simplicity, they also assume the nonsystematic components of returns, e i, are independent across securities Mar-

ket timing is incorporated in the terms r MandM, representing index portfolio forecasts Theoverall investment in the risky portfolio will be affected by the optimism or pessimism re-flected in these numbers

Assume a team of security analysts investigates a subset of the universe of available rities, with the objective of forming an active portfolio That portfolio will then be mixed with

secu-the index portfolio to improve diversification For each security, k, that is researched, we write

the rate of return as

model for portfolio

managers who use

security analysis in a

nearly efficient

market.

possibility In general, there will be a significant number of nonzero values, some positive

and some negative

Consider first how you would use the active portfolio once you found it Suppose the

active portfolio(A) has been constructed and has the parameters

A,A,2(e A)The total variance of the active portfolio is the sum of its systematic variance, 2

A2

M, plus thenonsystematic variance, 2(e A) These three parameters, plus the mean and variance of the

index portfolio, are sufficient to identify the opportunity set generated by the active and

pas-sive portfolios

Figure 20.11 shows the optimization process with active and passive portfolios The dashed

efficient frontier line represents the universe of all securities, assuming they are all fairly

priced, that is, that all alphas are zero By definition, the market index (M) is on this efficient

frontier and is tangent to the (dashed) capital market line (CML) In practice, our analysts do

not need to (indeed cannot) know this frontier, but they need to forecast the index portfolio

and construct the optimal risky portfolio using the index and active (A) portfolios The

opti-mal portfolio (P) will lie on the capital allocation line (CAL) that lies above the CML.

From the viewpoint of an investor with superior analysis, the index portfolio will be

in-efficient; that is, the active portfolio (A) constructed from mispriced securities will lie above

the CML

The optimal combination of the active portfolio with the passive portfolio takes off from

the construction of an optimal risky portfolio from two risky assets that we first encountered

in Chapter 6 As the active portfolio is not perfectly correlated with the index, further

diversi-fication—that is, mixing it with the index—is likely to be beneficial

We can judge the success of active management, and the contribution of the active portfolio

(A), by the Sharpe measure (ratio of reward to variability) of the resultant risky portfolio (P),

compared with that of the index portfolio (M).

20 Performance Evaluation and Active Portfolio Management 711

active portfolio

In the context of the Treynor-Black model, the portfolio formed

by mixing analyzed stocks with perceived nonzero alpha values This portfolio is ultimately mixed with the passive market index portfolio.

E(r)

E(r A)

A P

M

σ σA

CAL CML

F I G U R E 20.11The optimization process with active and passive portfolios

The mathematics of the efficient frontier reveal that the Sharpe measure of the risky folio is

appraisal ratio.

The contribution of individual securities (say, k) to the active portfolio (A) is analogous to that of the active portfolio to the risky portfolio (P) It is measured by the appraisal ratio,

k/(e k)

712 Part SIX Active Investment Management

measure is most appropriate when the portfolio represents the entire investment fund.The Treynor measure or Jensen measure is appropriate when the portfolio is to be mixedwith several other assets, allowing for diversification of firm-specific risk outside of eachportfolio

• The shifting mean and variance of actively managed portfolios make it harder to assessperformance A typical example is the attempt of portfolio managers to time the market,resulting in ever-changing portfolio betas and standard deviations

• Common attribution procedures partition performance improvements to asset allocation,sector selection, and security selection Performance is assessed by calculating departures

of portfolio composition from a benchmark or neutral portfolio

• Active portfolio managers attempt to construct a risky portfolio that improves on thereward-to-variability (Sharpe) ratio of a passive strategy

• Active management has two components: market timing (or, more generally, assetallocation) and security analysis

• The value of perfect market-timing ability is enormous The rate of return to a perfectmarket timer will be uncertain, but the risk cannot be measured by standard deviation,because perfect timing dominates a passive strategy, providing only “good” surprises

• Perfect-timing ability is equivalent to having a call option on the market portfolio Thevalue of that option can be determined using valuation techniques such as the Black-Scholes formula

• The value of imperfect market timing depends on the sum of the probabilities of the true outcome conditional on the forecast: P1  P2
1 If perfect timing is equivalent to call

option C, then imperfect timing can be valued by: (P1  P2
1)C.

• The Treynor-Black model is based on an index model that takes market-timing forecasts

as given The investment manager uses security analysis to construct an active portfolio.The active portfolio is mixed with the index portfolio to maximize the Sharpe measure

of the optimal risky portfolio

• In the Treynor-Black model, the weight of each analyzed security is proportional tothe ratio of its alpha to its residual variance

20 Performance Evaluation and Active Portfolio Management 713

KEY TERMS

active portfolio, 711

bogey, 694

comparison universe, 684

Jensen measure, 686market timing, 702Sharpe measure, 686

Treynor-Black model, 710Treynor measure, 686

PROBLEM SETS

Questions 1–3 appeared in past CFA examinations.

1 A plan sponsor with a portfolio manager who invests in small-capitalization, high-growth

stocks should have the plan sponsor’s performance measured against which one of the

2 Assume you purchased a rental property for $50,000 and sold it one year later for

$55,000 (there was no mortgage on the property) At the time of the sale, you paid $2,000

in commissions and $600 in taxes If you received $6,000 in rental income (all of it

received at the end of the year), what annual rate of return did you earn?

a 15.3%

b 15.9%

c 16.8%

d 17.1%

3 A two-year investment of $2,000 results in a return of $150 at the end of the first year

and a return of $150 at the end of the second year, in addition to the return of the original

investment The internal rate of return on the investment is:

a 6.4%

b 7.5%

c 15.0%

d None of the above

4 Based on current dividend yields and expected capital gains, the expected rates of return

on portfolios A and B are 11% and 14%, respectively The beta of A is 0.8 while that of B

is 1.5 The T-bill rate is currently 6%, while the expected rate of return of the S&P 500

index is 12% The standard deviation of portfolio A is 10% annually, while that of B is

31%, and that of the index is 20%

a If you currently hold a market index portfolio, would you choose to add either of these

portfolios to your holdings? Explain

b If instead you could invest only in bills and one of these portfolios, which would you

choose?

5 Evaluate the timing and selection abilities of four managers whose performances are

plotted in the following four scatter diagrams

714 Part SIX Active Investment Management

6 Consider the following information regarding the performance of a money manager

in a recent month The table presents the actual return of each sector of the manager’sportfolio in column (1), the fraction of the portfolio allocated to each sector incolumn (2), the benchmark or neutral sector allocations in column (3), andthe returns of sector indexes in column (4)

Actual Actual Benchmark Index

b What was the contribution of security selection to relative performance?

c What was the contribution of asset allocation to relative performance? Confirm that

the sum of selection and allocation contributions equals her total “excess” returnrelative to the bogey

7 Conventional wisdom says one should measure a manager’s investment performanceover an entire market cycle What arguments support this contention? What argumentscontradict it?

8 Does the use of universes of managers with similar investment styles to evaluate relativeinvestment performance overcome the statistical problems associated with instability ofbeta or total variability?

9 During a particular year, the T-bill rate was 6%, the market return was 14%, and aportfolio manager with beta of 0.5 realized a return of 10% Evaluate the manager based

on the portfolio alpha

10 The chairman provides you with the following data, covering one year, concerning the

portfolios of two of the fund’s equity managers (manager A and manager B) Although

the portfolios consist primarily of common stocks, cash reserves are included in the

calculation of both portfolio betas and performance By way of perspective, selected

data for the financial markets are included in the following table

Total Return Beta

a Calculate and compare the risk-adjusted performance of the two managers relative to

each other and to the S&P 500

b Explain two reasons the conclusions drawn from this calculation may be misleading.

11 Carl Karl, a portfolio manager for the Alpine Trust Company, has been responsible since

1990 for the City of Alpine’s Employee Retirement Plan, a municipal pension fund

Alpine is a growing community, and city services and employee payrolls have expanded

in each of the past 10 years Contributions to the plan in fiscal 1995 exceeded benefit

payments by a three-to-one ratio

The plan’s Board of Trustees directed Karl five years ago to invest for total return

over the long term However, as trustees of this highly visible public fund, they

cautioned him that volatile or erratic results could cause them embarrassment They also

noted a state statute that mandated that not more than 25% of the plan’s assets (at cost)

be invested in common stocks

At the annual meeting of the trustees in November 1995, Karl presented the

following portfolio and performance report to the Board

ALPINE EMPLOYEE RETIREMENT PLAN

5 Years 1 Year Total Alpine Fund:

20 Performance Evaluation and Active Portfolio Management 715

U.S Treasury bills 7.5% 11.3%

Large sample of pension funds (average 60% equities, 40% fixed income) 10.1% 14.3%

Average portfolio beta coefficient 0.90 0.89 Standard & Poor’s 500 stock index 13.8% 21.1%

Fixed-income securities—Alpine Fund 6.7% 1.0%

Karl was proud of his performance and was chagrined when a trustee made thefollowing critical observations:

a “Our one-year results were terrible, and it’s what you’ve done for us lately that

counts most.”

b “Our total fund performance was clearly inferior compared to the large sample of

other pension funds for the last five years What else could this reflect except poormanagement judgment?”

c “Our common stock performance was especially poor for the five-year period.”

d “Why bother to compare your returns to the return from Treasury bills and the

actuarial assumption rate? What your competition could have earned for us or how

we would have fared if invested in a passive index (which doesn’t charge a fee) arethe only relevant measures of performance.”

e “Who cares about time-weighted return? If it can’t pay pensions, what good is it!”

Appraise the merits of each of these statements and give counterarguments that Mr Karlcan use

12 Historical data suggest the standard deviation of an all-equity strategy is about 5.5% permonth Suppose the risk-free rate is now 1% per month and market volatility is at itshistorical level What would be a fair monthly fee to a perfect market timer, according

to the Black-Scholes formula?

13 A fund manager scrutinizing the record of two market timers comes up with thisinformation:

Number of months that rM  rf 135 Correctly predicted by timer A 78

Correctly predicted by timer B 86

Number of months that rM f 92 Correctly predicted by timer A 57

Correctly predicted by timer B 50

a What are the conditional probabilities, P1and P2, and the total ability parameters fortimers A and B?

b Using the historical data of problem 12, what is a fair monthly fee for the two

a Calculate expected excess returns, alpha values, and residual variances for these

stocks

b Construct the optimal risky portfolio.

c What is Sharpe’s measure for the optimal portfolio and how much of it is contributed

by the active portfolio? What is the M2?

20 Performance Evaluation and Active Portfolio Management 717

W E B M A S T E R

Analyzing Performance

Go to http://www.morningstar.com/Cover/Funds.html to access the Morningstar Fund

Quick Rank program.

Using this screening program, get a listing of funds that are ranked the highest in

both 5- and 10-year returns From those lists, select the highest-ranking fund that

ap-pears on both lists Once you have identified the fund, click on its ticker to get a

Morn-ingstar Quicktake report Using that report, answer the following questions:

1 What is the fund’s Sharpe ratio?

2 What are the beta and alpha coefficients for both the S&P 500 and the Russell

718 Part SIX Active Investment Management

2 Performance attribution First compute the new bogey performance as (0.70  5.81)  (0.25  1.45)  (0.05  0.48)  4.45%

a Contribution of asset allocation to performance

b Contribution of selection to total performance

16.98 Strategy  Bills only

F1 c 1,987.01 Strategy  Market only 115,233.89 Strategy  Perfect timing

Number of periods: N 76 years Annual compounded rate:

(1 r A)N

r A ¢ ≤

1/N

1 3.80% Strategy  Bills only

r A c10.51% Strategy  Market only 16.57% Strategy  Perfect timing

4 The timer will guess bear or bull markets randomly One-half of all bull markets will be preceded

by a correct forecast, and similarly, one-half of all bear markets will be preceded by a correct

Understand international investment strategies.

Decompose investment returns into contributing factorssuch as country, currency, and stock selection

INTERNATIONAL INVESTING

>

>

>

>

http://www.imf.org This site provides information on international economics and performance in regions.

http://www.ishares.com This site offers information on international index securities that can be used to secure portfolio diversification.

Although we in the United States customarily treat the S&P 500 as the market

index portfolio, this practice is increasingly inappropriate Equities representless than 25% of total U.S wealth and a much smaller proportion than that ofworld wealth In this chapter, we look beyond domestic markets to survey issues of ex-tended diversification

In one sense, international investing may be viewed as no more than a forward generalization of our earlier treatment of portfolio selection with a largermenu of assets from which to construct a portfolio One faces similar issues of diver-sification, security analysis, security selection, and asset allocation On the otherhand, international investments pose some problems not encountered in domesticmarkets Among these are the presence of exchange rate risk, restrictions on capitalflows across national boundaries, an added dimension of political risk and country-specific regulations, and differing accounting practices in different countries

straight-We begin by looking at market capitalization of stock exchanges around theworld and its relation to the home country GDP Next, we examine exchange rate riskand how such risk can be mitigated by using foreign exchange futures and forwardcontracts We also introduce political and country-specific risk that must be consid-ered in the overall risk assessment of international investments We then examine cor-relation across country portfolios with and without hedging foreign exchange risk.Based on these insights, we assess the efficacy of investing globally in the context ofequilibrium in international capital markets Finally, we show how performance attri-bution procedures can be adapted to an international setting

21.1 GLOBAL MARKETS FOR EQUITIES Developed Countries

To appreciate the myopia of an exclusive investment focus on U.S stocks and bonds, considerthe data in Table 21.1 Developed (high-income) countries are defined as those with per capitaincome exceeding $9,300 (in 2000), and their broad stock indexes are generally less risky thanthose of emerging markets The World Bank listed 52 developed countries in 2000, many ofthem with very small exchanges Our list includes 25 countries with the largest equity capi-talization, the smallest of which is New Zealand with a capitalization of $19 billion in 2001.These countries made up 79% of the World gross domestic product in 2001

The first five columns of Table 21.1 show market capitalization over the years 1996–2001.The first line shows capitalization for all world exchanges, showing total capitalization of cor-porate equity in 2001 as $25.7 trillion, of which U.S stock exchanges made up $13.2 trillion(49%) The figures in these columns demonstrate the volatility of these markets; indeed, worldcapitalization in 2001 was less than it was two years earlier and in the entire Pacific Basin itwas less than it was in 1996!

The next three columns of Table 21.1 show country equity capitalization as a percentage ofthe world’s in 2001 and 1996 and the growth in capitalization over the five years 1996–2001.The large volatility of country stock indexes resulted in significant changes in relative size Forexample, U.S weight in the world equity portfolio increased from 37% in 1996 to 49% in 2001,while that of Japan decreased from 24% to 11% The weights of the five largest countriesbehind the U.S (Japan, U.K., France, Germany, and Switzerland) added up to 39.2% in 2001,

so that in the universe of these six countries alone, the weight of the U.S was only 62%[49/(49⫹ 39.2)] Clearly, U.S stocks may not comprise an adequately diversified portfolio

of equities

Unlike the 1980s and early 1990s, the period 1996–2001 saw a decline in the value of ties of the Pacific Basin (growth of ⫺4%), but a resurgence in North America (growth of136%) and Europe (104%) These numbers show that economic position of countries is just asprecarious as the stock prices that capitalize the future value of the particular corporate sectors

equi-of these economies

The last tree columns of Table 21.1 show GDP, per capita GDP, and the equity tion as a percentage of GDP for the year 2001 As we would expect, per capital GDP in de-veloped countries is not as variable across countries as total GDP, which is determined in part

capitaliza-by total population But market capitalization as a percentage of GDP is quite variable, gesting widespread differences in economic structure even across developed countries We re-turn to this issue in the next section

sug-Emerging Markets

For a passive strategy one could argue that a portfolio of equities of just the six countries withthe largest capitalization would make up 79.2% (in 2001) of the world portfolio and may besufficiently diversified This argument will not hold for active portfolios that seek to tilt in-vestments toward promising assets Active portfolios will naturally include many stocks oreven indexes of emerging markets

Table 21.2 makes the point Surely, active portfolio managers must prudently scour stocks

in markets such as China, Brazil, or Korea Table 21.2 shows data from the 20 largest ing markets, the most notable of which is China with equity capitalization of $170 billion(0.66% of world capitalization) in 2001, and growth of 651% over the five years 1966–2001.But managers also would not want to have missed a market like Poland (0.09% of world capi-talization) with a growth of 287% over the same years

emerg-722 Part SIX Active Investment Management

These 20 emerging markets make up 16% of the world GDP and, together with the 25

de-veloped markets in Table 21.1, make up 95% of the world GDP Per capita GDP in these

coun-tries in 2001 was quite variable, ranging from $470 (India) to $8,870 (Korea); still, no active

manager would want to ignore India in an international portfolio Market capitalization as a

percent of GDP, which ranges from 3% (Venezuela) to 90% (South Africa), suggests that these

markets are expected to show significant growth over the coming years, even absent

spectac-ular growth in GDP

The growth of capitalization in emerging markets over 1966–2001 was much more volatile

than growth in developed countries (as disastrous as ⫺71% for Thailand), suggesting that both

risk and rewards in this segment of the globe may be substantial

Market Capitalization and GDP

The contemporary view of economic development (rigorously stated in deSoto 2000) holds

that a major requirement for economic advancement is a developed code of business laws,

in-stitutions, and regulation that allows citizens to legally own, capitalize, and trade capital

as-sets As a corollary, we expect that development of equity markets will serve as catalysts for

enrichment of the population, that is, that countries with larger relative capitalization of

equi-ties will tend to be richer

Figure 21.1 is a simple (perhaps simplistic since other relevant explanatory variables are

omitted) rendition of the argument that a developed market for corporate equity contributes

to the enrichment of the population The R-square of the regression line shown in Figure

21.1 is 35% and the regression coefficient is 73, suggesting that an increase of 1% in the

ratio of market capitalization to GDP is associated with an increase in per capita GDP of

0.73% It is remarkable that not one of the 25 developed countries is below the regression

line; only low-income emerging markets lie below the line Countries like Venezuela and

Norway that lie above the line, that is, exhibit higher per capita GDP than predicted by the

regression, enjoy oil wealth that contributes to population income Countries below the line,

such as Indonesia, South Africa, Philippines, and India, suffered from deterioration of

the business environment due to political strife and/or government policies that restricted

F I G U R E 21.1Per capita GDP tends

to be higher when market capitalization

as a percentage of GDP is higher (log scale)

the private sector China’s policies of freeing up economic activities contributed to the markable growth in market capitalization over 1996–2001 The expected continuation ofthis process will likely move China toward the predicted relationship in coming years.

re-Home-Country Bias

One would expect that most investors, particularly institutional and professional investors,would be aware of the opportunities offered by international investing Yet in practice, in-vestor portfolios notoriously overweight home-country stocks compared to a neutral indexingstrategy and underweight, or even completely ignore, foreign equities This has come to be

known as the home-country bias Despite a continuous increase in cross-border investing,

home-country bias still dominates investor portfolios

Opportunities in international investments do not come free of risk or of the cost of ized analysis The risk factors that are unique to international investments are exchange raterisk and country-specific risk, discussed in the next two sections

special-Exchange Rate Risk

It is best to begin with a simple example

We can generalize from Example 21.1 The $20,000 is exchanged for $20,000/E0pounds,

where E0 denotes the original exchange rate ($2/£) The U.K investment grows to

(20,000/E0)[1 ⫹ r f (UK)] British pounds, where r f(UK) is the risk-free rate in the United dom The pound proceeds ultimately are converted back to dollars at the subsequent exchange

King-rate E1, for total dollar proceeds of 20,000(E1/E0)[1 ⫹ r f(UK)] The dollar-denominated return

on the investment in British bills, therefore, is

We see in Equation 21.1 that the dollar-denominated return for a U.S investor equals thepound-denominated return times the exchange rate “return.” For a U.S investor, the invest-ment in British bills is a combination of a safe investment in the United Kingdom and a riskyinvestment in the performance of the pound relative to the dollar Here, the pound faredpoorly, falling from a value of $2.00 to only $1.80 The loss on the pound more than offsetsthe earnings on the British bill

726 Part SIX Active Investment Management

£10,000 and invested at a riskless 10% rate in the United Kingdom to provide £11,000 in one year.

What happens if the dollar–pound exchange rate varies over the year? Say that during the year, the pound depreciates relative to the dollar, so that by year-end only $1.80 is required

to purchase £1 The £11,000 can be exchanged at the year-end exchange rate for only

$19,800 ( ⫽ £11,000 ⫻ $1.80/£), resulting in a loss of $200 relative to the initial $20,000 investment Despite the positive 10% pound-denominated return, the dollar-denominated re- turn is a negative 1%.

Figure 21.2 illustrates this point It presents rates of returns on stock market indexes in

several countries for 2001 The dark boxes depict returns in local currencies, while the light

boxes depict returns in dollars, adjusted for exchange rate movements It’s clear that

ex-change rate fluctuations over this period had large effects on dollar-denominated returns in

several countries

1 Using the data in Example 21.1, calculate the rate of return in dollars to a U.S

in-vestor holding the British bill if the year-end exchange rate is: (a) E1⫽ $2.00/£; (b)

E1⫽ $2.20/£

Pureexchange rate riskis the risk borne by investments in foreign safe assets The investor

in U.K bills of Example 21.1 bears only the risk of the U.K./ U.S exchange rate We can

assess the magnitude of exchange rate risk by examination of historical rates of change in

vari-ous exchange rates and their correlations

Table 21.3A shows historical exchange rate risk measured from monthly percent changes

in the exchange rates of major currencies over the period 1997–2001 The data shows that

cur-rency risk is quite high The annualized standard deviation of the percent changes in the

ex-change rate ranged from 5.01% (Canadian dollar) to 14.18% (Japanese yen) The standard

deviation of monthly returns on U.S large stocks for the same period was 18.81% Hence,

major currency exchange risk alone would amount to between 27% (5.01/18.81) and 75%

(14.18/18.81) of the risk on stocks Clearly, an active investor who believes that Japanese

stocks are underpriced, but has no information about any mispricing of the Japanese yen,

F I G U R E 21.2Stock market returns

in dollars and local currencies for 2001 Source: Datastream.

8.7 15.5 10.7

would be advised to hedge the yen risk exposure when tilting the portfolio toward Japanesestocks Exchange rate risk of the major currencies is quite stable over time For example, astudy by Solnik (1999) for the period 1971–1998 finds similar standard deviations, rangingfrom 4.8% (Canadian dollar) to 12.0% (Japanese yen).

In the context of international portfolios, exchange rate risk may be mostly diversifiable.This is evident from the low correlation coefficients in Table 21.3B (This observation will bereinforced when we compare the risk of hedged and unhedged country portfolios in a later sec-tion.) Thus, passive investors with well-diversified international portfolios need not be con-cerned with hedging exposure to foreign currencies

The annualized average monthly increase in the value of the U.S dollar against the majorcurrencies over the five-year period and dollar returns on foreign bills (cash investments) ap-pear in Table 21.3C The table shows that the value of the U.S dollar consistently increased inthis particular period For example, the total increase against the Japanese yen over the fiveyears was 18% and against the Australian dollar, 57% This currency appreciation of the U.S

728 Part SIX Active Investment Management

TA B L E 21.3

Rates of change in the value of the U.S dollar against major world currencies, 1997–2001 (monthly data)

A Standard Deviation (annualized)

dollar was not offset by higher interest rates available in other countries Had an investor been

able to forecast the large exchange rate movements, it would have been a source of great

profit The currency market thus provided attractive opportunities for investors with superior

information or analytical ability

The investor in Example 21.1 could have hedged the exchange rate risk using a forward or

futures contract in foreign exchange Recall that a forward or futures contract on foreign

ex-change calls for delivery or acceptance of one currency for another at a stipulated exex-change

rate Here, the U.S investor would agree to deliver pounds for dollars at a fixed exchange rate,

thereby eliminating the future risk involved with conversion of the pound investment back

into dollars

You may recall that the futures hedge in Example 21.2 is the same type of hedging strategy

at the heart of the spot-futures parity relationship discussed in Chapter 16 In both instances,

futures markets are used to eliminate the risk of holding another asset The U.S investor can

lock in a riskless dollar-denominated return either by investing in the United Kingdom and

hedging exchange rate risk or by investing in riskless U.S assets Because the returns on two

riskless strategies must provide equal returns, we conclude

This relationship is called the interest rate parity relationshiporcovered interest arbitrage

relationship.

Consider the intuition behind this result If r f (US) is greater than r f(UK), money invested in

the United States will grow at a faster rate than money invested in the United Kingdom If this

is so, why wouldn’t all investors decide to invest their money in the United States? One

im-portant reason is that the dollar may be depreciating relative to the pound Although dollar

in-vestments in the United States grow faster than pound inin-vestments in the United Kingdom,

each dollar is worth progressively fewer pounds as time passes Such an effect will exactly

offset the advantage of the higher U.S interest rate

If the futures exchange rate had been F0 ⫽ $1.93/£ when the investment was made, the

U.S investor could have assured a riskless dollar-denominated return by locking in the

year-end exchange rate at $1.93/£ In this case, the riskless U.S return would have been 6.15%:

[1⫹ rf(UK)]F0/E0

⫽ (1.10)1.93/2.00

⫽ 1.0615

Here are the steps to lock in the dollar-denominated returns The futures contract entered

in the second step exactly offsets the exchange rate risk incurred in step 1.

Initial Transaction End-of-Year Proceeds in Dollars

Exchange $20,000 for £10,000 and invest at

Enter a contract to deliver £11,000 for dollars at

the (forward) exchange rate $1.93/£ £11,000(1.93 ⫺ E1 )

interest rateparityrelationship,

or coveredinterest arbitragerelationshipThe spot-futures exchange rate relationship that precludes arbitrage opportunities.

To complete the argument, we need only determine how a depreciating dollar will affectEquation 21.2 If the dollar is depreciating, meaning that progressively more dollars are re-

quired to purchase each pound, then the forward exchange rate, F0(which equals the dollars

required to purchase one pound for delivery in the future), must exceed E0, the current

ex-change rate

That is exactly what Equation 21.2 tells us: When r f (US) exceeds r f (UK), F0must exceed

E0 The depreciation of the dollar embodied in the ratio of F0 to E0exactly compensates forthe difference in interest rates available in the two countries Of course, the argument also

works in reverse: If r f (US) is less than r f (UK), then F0 will be less than E0.

2 What are the arbitrage strategy and associated profits if the initial future price is

Ample empirical evidence bears out this theoretical relationship For example, on January

25, 2000, the interest rate on U.S Treasury securities with maturity of one-half year was5.84%, while the comparable rate in the United Kingdom was 5.88% The spot exchange ratewas $1.6450/£ Substituting these values into Equation 21.2, we find that interest rate parityimplies that the forward exchange rate for delivery in one-half year should have been 1.6450

⫻ (1.0584/1.0588)1/2⫽ $1.6447/£ The actual forward rate was $1.644/£, which was so close

to the parity value that transaction costs would have prevented arbitrageurs from profitingfrom the discrepancy

Unfortunately, such perfect exchange rate hedging usually is not so easy In our example,

we knew exactly how many pounds to sell in the forward or futures market because the

730 Part SIX Active Investment Management

Initial Cash Flow Cash Flow in One Year

1 Borrow 1 UK pound in

2 Convert the pound to $2 and

3 Enter a contract to purchase 1.10 pounds at a (futures) price

In step 1, you borrow one pound in the United Kingdom (worth $2 at the current change rate) and, after one year, repay the pound borrowed with interest Because the loan

ex-is made in the United Kingdom at the U.K interest rate, you would repay 1.10 pounds,

which would be worth E1 (1.10) dollars The U.S loan in step 2 is made at the U.S interest rate of 6.15% The futures position in step 3 results in receipt of 1.10 pounds, for which you

would first pay F0(i.e., 1.90) dollars each and then convert into dollars at exchange rate E1 The exchange rate risk here is exactly offset between the pound obligation in step 1 and the futures position in step 3 The profit from the strategy is, therefore, riskless and requires

no net investment This is an arbitrage opportunity.

pound-denominated proceeds in the United Kingdom were riskless If the U.K investment

had not been in bills, but instead had been in risky U.K equity, we would know neither the

ul-timate value in pounds of our U.K investment nor how many pounds to sell forward That is,

the hedging opportunity offered by foreign exchange forward contracts would be imperfect

To summarize, the generalization of Equation 21.1 is that

where r (foreign) is the possibly risky return earned in the currency of the foreign investment.

You can set up a perfect hedge only in the special case that r (foreign) is itself a known number.

In that case, you know you must sell in the forward or futures market an amount of foreign

cur-rency equal to [1 ⫹ r(foreign)] for each unit of that currency you purchase today.

3 How many pounds would the investor in Example 21.2 need to sell forward to

hedge exchange rate risk if: (a) r(UK) ⫽ 20%; and (b) r(UK) ⫽ 30%?

Country-Specific Risk

In principle, security analysis at the macroeconomic, industry, and firm-specific level is

simi-lar in all countries Such analysis aims to provide estimates of expected returns and risk of

individual assets and portfolios To achieve the same quality of information about assets in a

foreign country is by nature more difficult and hence more expensive Moreover, the risk of

coming by false or misleading information is greater

Consider two investors: an American wishing to invest in Indonesian stocks and an

In-donesian wishing to invest in U.S stocks While each would have to consider macroeconomic

analysis of the foreign country, the task would be much more difficult for the American

in-vestor The reason is not that investment in Indonesia is necessarily riskier than investment in

the U.S You can easily find many U.S stocks that are, in the final analysis, riskier than a

num-ber of Indonesian stocks The difference lies in the fact that the U.S investment environment

is more predictable than that of Indonesia

In the past, when international investing was novel, the added risk was referred to as political

riskand its assessment was an art As cross-border investment has increased and more resources

have been utilized, the quality of related analysis has improved A leading organization in the

field (which is quite competitive) is the PRS Group (Political Risk Services) and the

presenta-tion here follows the PRS methodology.1

PRS’s country risk analysis results in a country composite risk rating on a scale of 0 (most

risky) to 100 (least risky) Countries are then ranked by composite risk measure and divided

into five categories: very low risk (100–80), low risk (79.9–70), moderate risk (69.9–60), high

risk (59.9–50), and very high risk (less than 50) To illustrate, Table 21.4 shows the placement

of five countries in the September 2001 issue of the PRS International Country Risk Guide.

The countries shown are the two largest capitalization countries (U.S and Japan) and the three

most populous emerging markets (China, India, and Indonesia) Surprisingly, Table 21.4

shows that the U.S ranked only 20th in September of 2001, having deteriorated from the 11th

rank in the previous year Japan actually ranked higher at 13 Both these developed countries

placed in the “very low risk” category Of the three emerging markets, it is not surprising to

see Indonesia ranked 115th of 140 countries, placing it in the “high risk” category, while

China ranked 60th, in the “low risk” category, and India ranked 92nd, in the “moderate risk”

category

The composite risk rating is an average of three measures: political risk, financial risk,

and economic risk Political risk is measured on a scale of 100–0, while financial and

eco-nomic risk are measured on a scale of 50–0 The three measures are added and divided by

political riskPossibility of expropriation of assets, changes in tax policy, restrictions on the exchange of foreign currency for domestic currency, or other changes in the business climate of a

two to obtain the composite rating This amounts to a weighted average of the three sures with a weight of 5 on political risk and 25 each on financial and economic risk Thevariables used by PRS to determine the composite risk rating of the three measured areshown in Table 21.5.

mea-Table 21.6 shows the three risk measures for the five countries in mea-Table 21.4, in order of theSeptember 2001 ranking of the composite risk ratings The table shows that by political risk,the five countries ranked in the same order But in the financial risk measure, the U.S rankedbelow China and India (!), and by the economic risk measure, the U.S ranked above Japan, andIndia ranked below Indonesia More interesting are the ratings forecasts for one and five years.These forecasts are quite pessimistic about the U.S., whose composite rating is expected to con-tinue to deteriorate over the years 2002–2006 (This may have been prescient, since it appearsthis report was prepared prior to the September 11, 2001, attacks.) At the same time, the ratings

of three of the other four countries were expected to improve over the next five years

The country risk is captured in greater depth by scenario analysis for the composite sure and each of its components Table 21.7 (A and B) shows one- and five-year worst caseand best case scenarios for the composite ratings and for the political risk measure Risk sta-bility is defined as the difference in the rating between the best and worst case scenarios and

mea-is quite large in most cases The worst case scenario mea-is in some cases sufficient to move a

732 Part SIX Active Investment Management

TA B L E 21.4

Composite risk ratings for October 2000 and September 2001

Sept 2001 Country Rating, Sept 2001 Rating, Oct 2000 Oct 2000 Rating Oct 2000

Very low risk

Political Risk Variables Financial Risk Variables Economic Risk Variables

Government stability Foreign debt (% of GDP) GDP per capita Socioeconomic conditions Foreign debt service Real annual GDP growth Investment profile (% of GDP) Annual inflation rate Internal conflicts Current account Budget balance (% of GDP) External conflicts (% of exports) Current account balance (% GDP) Corruption Net liquidity in months

Military in politics of imports Religious tensions Exchange rate stability Law and order

Ethnic tensions Democratic accountability Bureaucracy quality

country to a higher risk category Table 21.7B shows that U.S political risk was forecast to

deteriorate in five years (2006) to the level of Japan

Finally, Table 21.8 shows ratings of political risk by each of its 12 components Corruption

(variable F) in China is rated worse than in India and equal to that of Indonesia In democratic

accountability (variable K), China ranked worst and India best, while Indonesia ranked better

than both in external conflict (variable E)

TA B L E 21.6

Current risk ratings and composite risk forecasts

Political Risk, Financial Risk, Economic Risk, Year Ago, Current, One-Year Five-Year Country Sept 2001 Sept 2001 Sept 2001 Oct 2000 Sept 2001 Forecast Forecast

Composite and political risk forecasts

A Composite Risk Forecasts

Rating Case Probable Case Stability Case Probable Case Stability

B Political Risk Forecasts

Rating Case Probable Case Stability Case Probable Case Stability

Each monthly issue of the International Country Risk Guide of the PRS Group includes

great detail and holds some 250 pages Other organizations compete in supplying such tions The result is that today’s investor can become well equipped to properly assess the riskinvolved in international investing

AND BENEFITS FROM DIVERSIFICATION

U.S investors have several avenues through which they can invest internationally The mostobvious method, which is available in practice primarily to larger institutional investors, is topurchase securities directly in the capital markets of other countries However, even small in-vestors now can take advantage of several investment vehicles with an international focus.Shares of several foreign firms are traded in U.S markets in the form of American deposi-tory receipts, or ADRs A U.S financial institution such as a bank will purchase shares of aforeign firm in that firm’s country, then issue claims to those shares in the United States EachADR is then a claim on a given number of the shares of stock held by the bank In this way,the stock of foreign companies can be traded on U.S stock exchanges Trading foreign stockswith ADRs has become increasingly easy

There is also a wide array of mutual funds with an international focus Single-country fundsare mutual funds that invest in the shares of only one country These tend to be closed-endfunds, as the listing of these funds in Table 21.9 indicates In addition to single-country funds,there are several open-end mutual funds with an international focus For example, Fidelity of-fers funds with investments concentrated overseas, generally in Europe, in the Pacific Basin,and in developing economies in an emerging opportunities fund Vanguard, consistent with itsindexing philosophy, offers separate index funds for Europe, the Pacific Basin, and emergingmarkets The nearby box discusses a wide range of single-country index funds

734 Part SIX Active Investment Management

TA B L E 21.8

Political risk points by component, September 2001

This table lists the total points for each of the following political risk components out of the maximum points indicated The symbol ↑ indicates a rise in the points awarded to that specific risk component from the previous month (an improving risk), while the symbol ↓ indicates a decrease (deteriorating risk) The final columns in the table show the overall political risk rating (the sum of the points awarded to each component) and the change from the preceding month.

A Government stability 12 E External conflict 12 J Ethnic tensions 6

B Socioeconomic conditions 12 F Corruption 6 K Democratic accountability 6

C Investment profile 12 H Religious tensions 6 L Bureaucracy quality 4

D Internal conflict 12 I Law and order 6

U.S investors also can trade derivative securities based on prices in foreign security

mar-kets For example, they can trade options and futures on the Nikkei stock index of 225 stocks

traded on the Tokyo stock exchange, or on FTSE (Financial Times Share Exchange) indexes

of U.K and European stocks

Risk and Return: Summary Statistics

Table 21.10 presents annualized average returns and standard deviations in U.S dollars and in

local currency from monthly returns over the period 1997–2001 Developed countries appear

in panel A and emerging markets in panel B We use this table to develop insights into the risk

and reward in international investing The equity markets in both panels of Table 21.10 are

ordered by standard deviation

Are Investments in Emerging Markets Riskier?

In Figure 21.3, developed countries and emerging markets are ordered from low to high

stan-dard deviation The stanstan-dard deviations of investments in emerging markets are charted over

those in developed countries The graphs clearly show that investment in emerging markets is

largely riskier than in developed countries, at least as measured by total volatility of returns

Still, you can find emerging markets that appear safer than some developed countries

Europe/Middle East Pacific/Asia

Turkish Inv TKF Jardine Fleming China JFC

Asia Pacific APB Emerging Markets Tele ETF

First Philippine FPF Templeton Emerging EMF

Open-End Funds

Merrill Latin Amer Developing Cap 130

Source: The Wall Street Journal, July 5, 2002.

736 Part SIX Active Investment Management

TA B L E 21.10

Risk and return

across the globe,

1997–2001

% Per Annum in

% Per Annum in U.S Dollars Local Currency

New Funds that Track Foreign Markets

LOW-COST FOREIGN INDEX FUNDS

CALLED WEBS ELIMINATE SOME OF THE

GUESSWORK AND COSTS OF INVESTING

ABROAD

With foreign markets generally stronger this year, a new

way to invest abroad has appeared at a good time.

WEBS, an acronym for World Equity Benchmark Shares,

represents an investment in a portfolio of publicly traded

foreign stocks in a selected country Each WEBS Index

Series seeks to generate investment results that

gener-ally correspond to the price and yield performance of a

specific Morgan Stanley Capital International (MSCI)

index.

You sell these shares rather than redeeming them,

but there the similarity to closed-end country funds

ends WEBS are equity securities, not mutual funds.

WEBS shares trade continuously on a secondary

mar-ket, the Amex, during regular Amex trading hours, like

any other publicly traded U.S stock listed on the

ex-change In contrast, mutual fund shares do not trade

in the secondary market, and are normally bought and

sold from the issuing mutual fund at prices determined

only at the end of the day The new funds create and

redeem shares in large blocks as needed, thus

pre-venting the big premiums or discounts to net asset

value typical of closed-end country funds As index

portfolios, WEBS are passively managed, so their

ex-penses run much lower than for current open- or

closed-end country funds.

WEBS shares offer U.S investors portfolio exposure

to country-specific equity markets, in a single, listed

se-curity you can easily buy, sell, or short on the Amex.

Unlike American Depository Receipts (ADRs) that give

you an investment in just one company, WEBS shares

enable you to gain exposure to a broad portfolio of a

desired foreign country’s stocks You gain broad

expo-sure in the country or countries of your choice without the complications usually associated with buying, own- ing, or monitoring direct investments in foreign coun- tries You also have the conveniences of trading on a major U.S exchange and dealing in U.S dollars.

Some investors may prefer the active management, diversity, and flexibility of open-end international equity index funds as a way to limit currency and political risks of investing in foreign markets As conventional open-end funds, however, the international funds are sometimes forced by net redemptions to sell stocks at inopportune times, which can be a particular problem

in foreign markets with highly volatile stocks.

You pay brokerage commissions on the purchase and sale of WEBS, but since their portfolios are pas- sively managed, their management and administrative fees are relatively low and they eliminate most of the transaction charges typical of managed funds.

Foreign Index Baskets

SOURCES: Modified from The Outlook, May 22, 1996, and Amex

website, www.amex.com/indexshares/index_shares_webs.stm, February 2000.

F I G U R E 21.3Annualized standard deviation of investments across the globe, 1997–2001.

100 90 80 70 60 50 40 30 20 10 0

Are Average Returns in Emerging Markets Greater?

Figure 21.4 repeats the previous exercise for average returns The graphs show that investing inemerging markets generally provided lower returns than investing in developed countries Ofcourse these data are far from conclusive since five-year averages are still subject to consider-able imprecision The fact that a number of markets averaged a negative rate of return is proofpositive that expectations were not realized over the period and hence these data are inadequatefor risk-return analysis But regardless of these qualifications, we should not even expect anyclear relationship since the higher standard deviation of emerging market equities is not anadequate measure of risk In the context of a diversified international portfolio, the risk ofany single market is measured by its covariance with the overall portfolio Assessment of theproportion of systematic risk in country portfolios can be gleaned from the correlation matrixthat we will examine shortly First, we inquire about the role of exchange rate risk in overallcountry risk

Is Exchange Rate Risk Important in International Portfolios?

Table 21.3 revealed that changes in exchange rates are not highly correlated across countries.This feature suggests that when international portfolios are well diversified, the exchange ratecomponent of overall risk will be effectively diminished Another feature that would renderexchange rate risk diversifiable is low correlation between changes in exchange rates andcountry stock returns in local currencies

In Figure 21.5, all 45 stock markets are ordered from low to high standard deviation of turns in U.S dollars The figure contrasts the graph of standard deviation of returns in localcurrency with that of returns in U.S dollars The graphs are quite close in most cases, rein-forcing the notion that hedging exchange rate risk is not crucial in well-diversified interna-tional portfolios

re-Benefits from International Diversification

Table 21.11 presents correlations between returns on stock and long-term bond portfolios invarious countries Panel A shows correlation of returns in U.S dollars, that is, returns to a U.S.investor when currency risk is not hedged Panel B shows correlation of returns in local cur-rencies, that is, returns to a U.S investor when the exchange risk is hedged As noted earlier,the correlation coefficients of the hedged (local currency) and unhedged (U.S dollars) returnsare very similar, confirming that hedging currencies is not a significant issue in diversifyinginternationally

738 Part SIX Active Investment Management

⫺10

⫺20

⫺30

Emerging markets Developed countries

Developed countries and emerging markets are ranked from low to high standard deviation

The correlation coefficients between a stock index of one country and bond portfolios of

another are very low, suggesting that income portfolios that are balanced between stocks and

bonds would greatly benefit from international diversification The correlation among

unhedged stock portfolios of the countries in Table 21.11A is much larger, in the range of 45

(Japan–Germany) to 89 (France–Germany) These correlation coefficients are much larger

than conventional wisdom; they suggest that cross-border correlation of stock indexes has

been increasing For another, independent example, Table 21.12 shows the correlation of

various country indexes with U.S stocks using monthly excess returns over the period

1970–1989, next to the same coefficients estimated over 1996–2001 The marked increase in

correlation with 17 stock indexes and the world portfolio is uniform

These results raise the question of whether the increase in correlation is an artifact of the

sample period or a result of globalization and increased capital market integration that would

be expected to increase cross-border correlation While there is no question that a five-year

sample period is quite short and limits precision, the fact that we find the increase in

correla-tion across the board suggests that globalizacorrela-tion and market integracorrela-tion are the more plausible

cause, as discussed in the nearby box

The observed high correlation across markets brings into question the conventional wisdom

of large diversification benefits from international investing This conventional wisdom is

de-picted in Figure 21.6, which is based on data for the period 1961–1975 Figure 21.6 suggests

that international diversification can reduce the standard deviation of a domestic portfolio by as

much as half (from about 27% to about 12%) This improvement may well be exaggerated if

correlation across markets has markedly increased as data from recent years suggest Still,

ben-efits from international diversification are significant, as we will show shortly But first it is

well to dispose of a misleading, yet widespread, representation of benefits from diversification

Misleading Representation of Diversification Benefits

The baseline technique for constructing efficient portfolios is the efficient frontier A useful

ef-ficient frontier is constructed from expected returns and an estimate of the covariance matrix of

returns This frontier, combined with cash assets generates the capital allocation line, the set of

efficient complete portfolios, as elaborated in Chapter 6 and the first section of Chapter 7 The

benefit from this efficient diversification is reflected in the curvature of the efficient frontier

Other things equal, the lower the covariance across stocks, the greater the curvature of the

effi-cient frontier and the greater the risk reduction for any desired expected return So far, so good.

F I G U R E 21.5Standard deviation of investments across the globe in U.S dollars vs local currency, 1997–2001.

But suppose we replace expected returns with realized average returns from a sample period to

construct an efficient frontier; what is the possible use of this graph?

The ex post efficient frontier (derived from realized returns) describes the portfolio of only

one investor—the clairvoyant who actually expected the precise averages of realized returns

on all assets and estimated a covariance matrix that materialized, precisely, in the actual

real-izations of the sample period returns on all assets Obviously, we are talking about a slim to

of the average standard deviation of

a one-stock portfolio Source: B Solnik, “Why Not Diversify Internationally Rather Than

U.S stocks Global stocks

Number of stocks