Capital Market Assumptions

Global Investment SolutionsCapital Market Assumptions

February 2005

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Contents

1. Introduction 2

2. Risk Estimates 2

2.1 Assumptions 2

2.2 Historical Data 3

2.2.1 Historical Volatility as a Proxy for Future Risk 3

2.2.2 Degree of Freedom Problem 3

2.3 Consistency 3

2.4 Factor Approach 4

2.4.1 Two-Layer Approach 4

2.4.2 Multi-Layer Approach 5

2.5 Qualitative Judgment vs. Quantitative Inputs 7

2.6 About Alternative Assets 7

3. Returns 9

3.1 Introduction 9

3.2 Integration/Segmentation Approach 9

3.3 Illiquidity 9

3.3.1 Issue 9

3.3.2 Sharpe Ratio Approach 10

3.3.3 Improved Put Option Approach 10

3.3.4 Results 10

3.4 Return Summary 11

References 12

© 2005 UBS Global Asset Management (Americas) Inc., a member of UBS AG - All rights reserved. 1

February 2005 Capital Market Assumptions

1. Introduction

One of the most important decisions investors need tomake is determining their asset allocation. This sets theportfolio composition in terms of asset classes, such as USstocks, European stocks, US bonds, etc., for reasons ofachieving the best risk-return ratio. Further, it includes boththe long-term average or so-called "normal" allocation, andthe size and duration of temporary deviations.

First of all, we need to define the relevant investment uni-verse. In their seminal article, Brinson, Diermeier andSchlarbaum formulate "admission" criteria to the universeof investable assets.1 The criteria are:

Based on these criteria, e.g., it would not make sense toinvest in a market that provides economic value, but has noviable legal system to protect ownership of this value.Brinson, Diermeier and Schlarbaum considered over 80 assetclasses and subclasses for inclusion in their Multiple MarketsIndex (MMI). They describe the investable capital market as"primary wealth generating assets where sufficient marketshave developed and legal hurdles do not prohibit meaning-ful investment by tax-exempt investors".2

This definition then led to the inclusion of five asset classes:equity, venture capital, fixed income, real estate, and cash;more recently, we added high yield bonds, emerging mar-kets bonds, and emerging markets equity. Given the rele-vance of what has become a $800 billion industry, weshould include hedge funds as well. But for reasons of dou-ble-counting assets, we exclude these from the universe.3 Asof 2003, this implies the following investable capital market,as shown in the right-hand column.

Once the universe is identified, both the derivation of theaverage long-term portfolio—i.e., the policy or "normal"portfolio—the valuation of the individual markets requirethe long-term rates of return as an input. These in turndepend on their risks and correlations.

That is, first we estimate the average risks and correlations.Thereafter, the returns are estimated as a function of therisk structure. On the other hand, as we do not live in anentirely efficient world, we must allow for return-generatingfactors other than risk and correlation.

The two other main return-generating sources are thedegree of segmentation and illiquidity. Segmentation statesthe extent to which a market's capital in- and outflows arehampered by legal and practical barriers; illiquidity describeslock-in periods for investors, constraining their investmentflexibility. In a rational context, investors expect to be com-pensated for segmentation and illiquidity.

It is the objective of this paper to explain how we estimateour long-term policy covariance matrix, which is an instru-mental input for

The long-term return estimates; and

The construction of the normal allocation.

In turn, we receive the derivation of the long-term averagerates of return that are essential for the

Construction of a normal allocation; and

Valuation.

2. Risk Estimates

2.1 Assumptions

We assume implicitly that risk is measured in terms of stan-dard deviation. We are aware of the fact that risk is oneword,4 but not one number. That is, risk has various facetssuch as return span, downside risk, kurtosis, skewness,changing states, etc. But as there is justification for thesevarious measures in specific contexts, we do not think theyare overly relevant in the classical top-down world of asset

2 © 2005 UBS Global Asset Management (Americas) Inc., a member of UBS AG - All rights reserved.

Capital Market Assumptions February 2005

All Other Equities15.6%

Emerging Mkt Equities0.9%

US Equity17.2%

Cash Equiv.5.2%

US Real Estate5.7%

High Yield Bonds1.1%

Dollar Bonds27.8%

All Other Bonds24.2%

Emerging Mkt Debt2.1%

Private Markets0.2%

Analytical

Adequate Control and Regulation

Marketability and Liquidity

Meaningful Impact

Nonredundant

Manageable Estimation Risk

Legal

Talent Availability

1 [2] Brinson, Diermeier and Schlarbaum (1986), p.17.2 [2] Brinson, Diermeier and Schlarbaum (1986), p.17.3 Theoretically, hedge funds are strategies rather than an asset class. That is, they are built on the basis of already existing asset classes.4 Quote of Harry M. Kat, Q-group conference, Scottsdale, AZ, 2003.

allocation. In the following sections, we describe ourprocess for:

Modeling the policy covariance matrix;

Modeling the long-term sustainable returns; and

Discussing the main issues in this process.

2.2 Historical Data

2.2.1 Historical Volatility as a Proxy for Future Risk

In practice, there is usually a historical investigation at thebeginning of every risk analysis. Too often, unfortunately,this simply means that the analyst in charge extends thepast into the future without much further reflection.

Hasty shortcuts like this are not necessarily justified, as it iseasily possible, for instance, that some market provided ahigh average return at a low volatility over some examina-tion period, while another market produced little or even anegative return at a high volatility. That is, the ex-postobservation is not necessarily consistent with the accordingex-ante expectation that ultimately determines pricing.Rather, observed volatility may turn out significantly differ-ent from expected risk.

This does not mean that historical estimates per se are inap-propriate proxies for future expectations. But instead ofserving as a proxy in the first place, they should be consid-ered as a starting point for a discussion. If we find no justifi-cation for a change going forward, it is fine to project thehistorical estimates into the future.

2.2.2 Degree of Freedom Problem

The estimation of historical correlations requires the numberof observations to be larger than the number of variables.Assume the simplest case to be where you observe twomarkets twice. Every market is represented by an axis in aplane, and the observations are marked by dots. Since astraight line is defined by two (different) dots, there isalways a perfect regression line in the case of two observa-tions and two markets only, hence, implying—technically—aperfect correlation.

As a result, we estimate a correlation of 1, even if the mar-kets are uncorrelated. Hence, there is no correlation infor-mation in two observations only. A more formal explanationis the observation that a straight line is a 1D subspace of a2D plane. Hence, we need at least three observations.

In the case of three observed markets, this means that weneed at least four observations, as three observations onlyare located in a plane, i.e., a 2D subspace of the 3D space.However, the degree of insufficiency could even be worse, ifall dots lined up perfectly, in which case they would belocated in a one-dimensional subspace.

On the other hand, nothing prevents us from calculatingpairwise correlations, but in case of insufficient observa-tions, the resulting correlation matrix is of limited use, evenif not immediately evident.5

As we may deal with many variables in practice, the degree-of-freedom problem often requires long data series.However, this may turn into another problem:

Most likely, long data series cover various regimes.

Time series of the required length may not be available.

In order to get a data series of the required length, theanalyst may be tempted to increase the frequency (week-ly or even daily).

Data of higher frequency are more sensitive to asynchro-nism. As a result, high-frequency data tend to producelower correlation estimates.

2.3 Consistency

Another important question is whether to set the correla-tion matrix directly or by some methodology. In the case ofa small matrix, it is no challenge to set the correlationsdirectly. But we should not underestimate the consistencyproblem. Assume the following correlation matrix:

7© 2005 UBS Global Asset Management (Americas) Inc., a member of UBS AG - All rights reserved. 3


Market 1

Market 2

Observation 1

Observation 2

Regression LineMarket 1

Market 2

Observation 1

Observation 2


Market 2

Observation 1

Observation 2


Market 2

Observation 1

Observation 2

Regression Line

5 In this case, a row of the matrix is a linear combination of other rows. Technically, this is revealed through the so-called eigenvalues of the matrix. For the theory ofeigenvalues, see [6] Hamilton, pp. 729-732.

Market 1 Market 2 Market 3

Market 1 1 -1 -1

Market 2 -1 1 -1

Market 3 -1 -1 1

However, mutual correlations of -1 between all three mar-kets are not possible. Namely, if market A and B are diamet-rical and market B and C are diametrical, then Market Aand C are identical. Hence, the above matrix reflects anunfeasible correlation pattern. It is an inconsistent matrix.

There are, thus, constraints. What may look like a real corre-lation matrix at first inspection is not necessarily feasible inreality. But while the above example is intuitive, there areless obvious border cases in practice. Are, for instance,mutual correlations of -0.51 feasible? No. Mutual correla-tions of -0.50, on the other hand, are feasible.

While dealing with three markets means dealing with threerelations only, we are able to set a consistent correlationstructure without theory. But as the number of marketsincreases, the number of relations explodes at some point,and, hence, it becomes impossible to set a consistent matrixdirectly. For a large matrix, it may be still possible, if all cor-relations are fairly high and of similar size, but this does notapply to a market covariance matrix.

Clearly, we need a methodology for setting a consistentmatrix.

2.4 Factor Approach

2.4.1 Two-Layer Approach

Our methodology separates the generation process into sev-eral manageable steps and ensures consistency. It is a so-called factor approach. In order to understand it, we offerthe following example:

Assume that the risks of the investable universe are drivenby two factors only, global equity and global bonds. In thiscase, we start the modeling process with a 2 x 2 covariancematrix, F, between global equity and global bonds.Assuming a 14% risk for global equity and 4% for globalbonds, and a correlation of 0.30 between them, this impliesthe following covariance matrix.

This is a factor covariance matrix, as it contains the drivingfactors only. Next, in order to derive the market covariancematrix, we need to know how the markets respond to fac-tor movements. These responses are reflected by the so-called sensitivity or 'loadings' matrix, L. Essentially, L con-tains the betas of the modeled markets with regard to thefactors. If market A moves by 110 basis points in response

to a 100 basis point move of global equity, the correspon-ding position in the loadings matrix is 110%. In addition,every market has usually some risk that is not explained bythe factors. It is called idiosyncratic or residual risk.

Here is a hypothetical example consisting of five marketsonly:

Apparently, market A is an equity market, as it only loads onglobal equity. On the other hand, a zero sensitivity versusglobal bonds does not necessarily mean it is uncorrelatedwith global bonds. Rather, it only claims that global bonds isnot one of A's drivers. Through the positive correlationbetween global equity and global bonds, market A is stillpositively correlated with global bonds, albeit very moder-ately.

Ultimately, the market covariance, M, is calculated as fol-lows:6

M = LFL' + diag (R2) (1)

The first term captures the systematic risk contribution tothe covariance matrix, and the second term the nonsystem-atic risk contribution. Further, as usual, risks are added geo-metrically.

An invaluable advantage of the factor-approach is the factthat M is consistent as long as F is consistent, no matterhow the sensitivities and residual risks are set. Namely, everymarket is—technically—absolutely free in terms of itsresponses to factor movements and its independent moves.On the other hand, consistency of F is no challenge, as it isa 2 x 2 matrix only.

To sum up, we have presented so far a two-layer approachwith the factors on the first layer and the markets to bemodeled on the second layer.6



6 Diag (R2) means a squared matrix with R2 in the diagonal and zeros elsewhere.7 The two-layer concept goes back to [5] Grinold and Kahn (1995) who employ it for stock modeling. For more detail, see p. 58f.

Global Equity Global Bonds

Global Equity 0.0196 0.0017

Global Bonds 0.0017 0.0016

Global Equity Global Bonds Residual Risk

Market A 110% 0% 10.0%

Market B 105 0 8.0

Market C 90 0 7.0

Market D 0 103 1.2

Market E 0 99 0.9

Layer 2: MarketsMarkets A, B, C, D and E

Layer 1: FactorsGlobal EquityGlobal Bonds

2.4.2 Multi-Layer Approach

In practice, a two-layer approach is not sufficient. Assume,for instance, you model various real estate sectors such asapartment, industry, office, and retail. These are highlymutually correlated, but they only have moderate correla-tions with all other markets. In order to differentiate themsufficiently from the other markets, we need to add sub-stantial residual risk to them. On the other hand, muchresidual risk differentiates them among themselves. As aresult, the mutual correlations between the real estate sec-tors turn out low. This is not what we want to achieve.

In short, the challenge of modeling this particular constella-tion cannot be mastered by a two-layer approach. The pointis that at one end of the spectrum there are very broad fac-tors, and at the other end there is much fine-tuning.Ultimately, the world is driven by more than just two fac-tors, but the perception of "factor" depends on the layerwe are looking from.

Two factors may be sufficient, but only for modeling thenext level of granularity after global equity and globalbonds, which is still very broad. Global equity is sufficient tomodel global sectors, but not individual stocks. Clearly, wecannot go all the way from the broadest aggregates to allthe fine-tuning with one step only. Rather, we have to gothrough several layers.

Hence, while modeling European equity and US early-stageventure capital on the same layer does not seem appropri-ate from a practical perspective, this is not even feasiblefrom a theoretical point of view.

For these reasons we need to replace the two-layerapproach by a multi-layer approach. Technically, it isstraightforward: The covariance matrix, M, as derived on thebasis of F, L and R, is considered the input matrix for gener-ating the third layer. Then we define new matrices L and Rthat contain the sensitivities and residual risks of the nextlayer aggregates. Finally, we calculate equation (1) with thenew set of input variables F, L, and R; as a new output, weget layer 3.

This scheme allows modeling through as many layers asneeded. The process resembles the organic growth of a treefrom the very root all the way up to its leaves.

Assigning aggregates to selected layers is trickier than itmay seem at first inspection, as it leaves much room forinterpretation, and, hence, requires judgment. On the otherhand, there are clear constraints. As a national real estatemarket, for instance, is driven (to some extent) by its nation-al stock market, it must be modeled on a consecutive layer.

Actually, our covariance matrix is based on a six-layerapproach, involving the following aggregates:

Again, the resulting covariance matrix is on a market level.The risks and betas on the market level are revealed in thereturn table in section 3. Ultimately, through aggregation,we get the covariance matrix on an asset class level, asshown on page 5.8



8 The covariance matrix on a market level has a dimension greater than 200 x 200, and is, hence, too large to be presented in this paper.

Layer# of

AggregatesAggregates

6 66 National early stage venture capital markets

National late stage venture capital markets

National LBO markets

National mezzanine markets

National distressed debt markets

U.S. hedge fund strategies

U.S. private real estate sectors

U.S. REITs sectors

5 22 National corporate bond markets

National inflation protected bond markets

National real estate markets

Regional timber factors

Regional farmland factors

4 82 National equity markets

National bond markets

National cash markets

National currency markets

3 25 10 equity sectors

Regional currency factors

Country factors

2 13 Broad regional bond factors

Broad equity sectors

Global currency factors

Global real estate factor

Global timber factor

Global farmland factor

1 5 Global equity factor

Global bond factor

Broad regional factors

Layer 6

Layer 5

Layer 4

Layer 3

Layer 2

Layer 1

Market Covariance Matrix Aggregated to Asset ClassesThe risks and betas on the market level are revealed in thereturn table in section 3. This table is the result of aggregat-ing the market covariance matrix.



Risk

GIM (Hedged)

GSMI

BVG *)

CAPS **)

US Equity

US Bonds

ex-US Equity (Hedged)

ex-US Bonds (Hedged)

Emerging Markets Equity

Emerging Markets Bonds

US High Yield Bonds

US Private Equity

UK Private Equity

US REITS

US Real Estate

US Timber

US Farmland

US Hedge Funds

ex-US Real Estate

Return

GIM

(Hed

ged)

6.44

%1.

000.

910.

920.

670.

840.

660.

820.

610.

650.

450.

570.

790.

640.

470.

430.

350.

260.

240.

396.

67%

GSM

I10

.41%

0.91

1.00

0.99

0.81

0.93

0.41

0.86

0.32

0.71

0.41

0.53

0.85

0.74

0.45

0.36

0.35

0.26

0.28

0.49

7.41

%

BVG

*)10

.20%

0.92

0.99

1.00

0.78

0.93

0.41

0.86

0.30

0.71

0.41

0.53

0.89

0.73

0.52

0.44

0.38

0.27

0.29

0.47

7.81

%

CAPS

**)

14.4

1%0.

670.

810.

781.

000.

640.

210.

790.

220.

580.

260.

350.

600.

880.

330.

260.

250.

160.

190.

687.

56%

US E

quity

15.0

0%0.

840.

930.

930.

641.

000.

300.

790.

170.

650.

350.

480.

870.

620.

460.

340.

350.

270.

300.

308.

13%

US B

onds

5.68

%0.

660.

410.

410.

210.

301.

000.

200.

730.

280.

450.

470.

310.

170.

170.

270.

220.

200.

060.

165.

78%

ex-U

S Eq

uity

(Hed

ged)

13.8

9%0.

820.

860.

860.

790.

790.

201.

000.

270.

680.

300.

410.

750.

780.

400.

300.

310.

190.

240.

378.

08%

ex-U

S Bo

nds

(Hed

ged)

4.77

%0.

610.

320.

300.

220.

170.

730.

271.

000.

150.

270.

330.

160.

190.

080.

160.

090.

050.

030.

235.

60%

Emer

ging

Mar

kets

Equ

ity21

.91%

0.65

0.71

0.71

0.58

0.65

0.28

0.68

0.15

1.00

0.31

0.37

0.63

0.54

0.34

0.28

0.29

0.21

0.19

0.29

10.0

0%

Emer

ging

Mar

kets

Bon

ds12

.00%

0.45

0.41

0.41

0.26

0.35

0.45

0.30

0.27

0.31

1.00

0.30

0.35

0.25

0.19

0.20

0.19

0.16

0.10

0.14

7.09

%

US H

igh

Yie

ld B

onds

9.00

%0.

570.

530.

530.

350.

480.

470.

410.

330.

370.

301.

000.

450.

330.

240.

230.

210.

170.

140.

186.

63%

US P

rivat

e Eq

uity

26.1

2%0.

790.

850.

890.

600.

870.

310.

750.

160.

630.

350.

451.

000.

600.

430.

330.

330.

250.

260.

2815

.04%

UK P

rivat

e Eq

uity

28.9

1%0.

640.

740.

730.

880.

620.

170.

780.

190.

540.

250.

330.

601.

000.

320.

240.

250.

160.

190.

5114

.71%

US R

EITS

12.1

6%0.

470.

450.

520.

330.

460.

170.

400.

080.

340.

190.

240.

430.

321.

000.

850.

190.

150.

140.

297.

01%

US R

eal E

stat

e9.

99%

0.43

0.36

0.44

0.26

0.34

0.27

0.30

0.16

0.28

0.20

0.23

0.33

0.24

0.85

1.00

0.17

0.14

0.10

0.28

6.67

%

US T

imbe

r13

.70%

0.35

0.35

0.38

0.25

0.35

0.22

0.31

0.09

0.29

0.19

0.21

0.33

0.25

0.19

0.17

1.00

0.14

0.10

0.12

8.23

%

US F

arm

land

13.5

0%0.

260.

260.

270.

160.

270.

200.

190.

050.

210.

160.

170.

250.

160.

150.

140.

141.

000.

080.

087.

67%

US H

edge

Fun

ds5.

67%

0.24

0.28

0.29

0.19

0.30

0.06

0.24

0.03

0.19

0.10

0.14

0.26

0.19

0.14

0.10

0.10

0.08

1.00

0.09

7.04

%

ex-U

S Re

al E

stat

e12

.67%

0.39

0.49

0.47

0.68

0.30

0.16

0.37

0.23

0.29

0.14

0.18

0.28

0.51

0.29

0.28

0.12

0.08

0.09

1.00

7.25

%

* Ri

sk fr

om C

HF p

ersp

ectiv

e: 6

.1%

** R

isk

from

GBP

per

spec

tive:

12.

2%

2.5 Qualitative Judgment vs. Quantitative Inputs

Although sounding fairly mechanical, our modeling processis just the framework that ensures a consistent covariancematrix. Consistency, however, only means free of internalcontradictions, but not necessarily accuracy.

In the end, setting concrete numbers is a decision. Numbersmust be deliberated.

In spite of implying objectiveness and precision, numbersare based on judgment, no matter whether explicit orimplicit. Consider, for instance, rolling volatility estimates ofthe S&P 500 Index, based on monthly or quarterly returns:

Now, if we conclude that historical estimates are a reason-able proxy for future expectations, who tells us in the endwhat frequency and observation span we should use?Again, historical estimates are an accurate starting point fora discussion, but accepting them as a forward-lookingexpectation is a decision. It cannot be delegated andrequires qualitative judgment.

A good example of qualitative judgment is the correlationbetween US equity and US bonds. Based on data betweenthe mid 1970s and 1998, we estimate a correlation of morethan 0.40. But since inflation is one common factor of stockand bond returns, and we may not feel that inflation shockssimilar to the 1970s will happen again in the medium term,we think a realistic forward looking correlation will be small-er than 0.40. We set it to 0.30.

2.6 About Alternative Assets

The perception of alternatives is quite often that they notonly yield high returns and low risk, but that they also hard-ly correlate with traditional asset classes. This perception isdue to the fact that the according data show little volatilityand correlation. The reason is that alternative assets are nottraded on stock exchanges, and continuously observablemarket data are thus not available.

Consider the following analogy: A bat is flying through adark tunnel. While it is in the tunnel, you cannot see it.

But the fact that you cannot see it, does not mean that itdoes not move up and down on its flight through the tunnel.

The time in the tunnel corresponds to the illiquidity span ofthe alternative asset. The price at which the asset would betraded goes up and down. You just cannot see it, because itis not traded. The point of time when the asset becomesliquid corresponds to the end of the tunnel. Then you seethe true price, as you can see the bat's true position. In thecontext of venture capital, for instance, the end of the tun-nel can be the IPO.

The reason for the inaccuracy of data for alternative assetsis the fact that they are appraisal-based, which is tricky, asappraisals tend to be overly smooth. Indices for real estate,private equity and natural resources were created for meas-uring return rather than risk.

Once alternative investments are involved in risk estimates,the consequences of historical estimates are intensified. Foralternatives, the main issue is not whether the past is agood indicator for the future; rather, the problem is that thepast is not even correctly recorded.

As an illustration, between 1981 and 2004, we calculatevolatilities of 16.3% for the S&P 500 and 15.0% for venturecapital. Meanwhile, the average annual returns for the sameperiod are 12.8% and 15.8%, respectively.



0%

10%

20%

30%

Dec-72 Dec-77 Dec-82 Dec-87 Dec-92 Dec-97 Dec-02

Monthly Data Quarterly Data

Rolling 3-Year Volatility of the S&P 500

TunnelTunnel

Source: Standard & Poor’s

Such numbers suggest a free lunch for venture capital:More return for less risk. Hence, we should not trust them,and we need to find other approaches for estimating therisks and correlations of alternative investments. In order totriangulate the "true" risks, we apply several heuristicapproaches. The following documents one of them:

The S&P 500 provided the following quarterly returnsbetween 1981 and 2004, wherein the crash of 1987 standsout:

We count 26 negative quarters. On the other hand, basedon Venture Economics data, the index-based quarterly ven-ture capital returns over the same period are considerablysmoother. Venture capital also seems unaffected by thecrash, according to a reported return of -0.2% in the fourthquarter of 1987:

Overall, only 17 negative quarters are reported, and we esti-mate an annual volatility of 15% and a correlation with theS&P 500 of 0.41.

As rational investors are compensated for taking more risk,the risk of the better-performing venture asset class shouldbe greater. Specifically, the fourth quarter return of 1987demonstrates how the strongly lagged appraisals reducevolatility. We would expect the opposite, i.e., substantiallyhigher venture capital returns as a compensation for theburden of higher risk.

The idea of this heuristic approach is to rescale the reportedventure capital return data such that their dispersion isincreased, but the mean is unchanged. The point is that thelarger the rescaling, the larger the number of negative quar-terly returns. The next figure shows the same returns butrescaled by a factor of 2.

The data series manipulated like this provides 38 negativequarters. Overall, we find:

This experiment suggests that venture capital's risk is proba-bly a multiple of index-based volatility estimates, given thatventure capital is subject to more shortfalls than the S&P500.

In the end, we propose risks of 43% for early-stage venturecapital, 34% for late-stage venture capital, 29% for LBOs,20.5% for distressed debt, and 18% for mezzanine invest-ments.



-30%

-20%

-10%

0%

10%

20%

30%

Mar-81 Mar-84 Mar-87 Mar-90 Mar-93 Mar-96 Mar-99 Mar-02

Quarterly S&P 500 Returns between 1981 and 2004

-30%

-20%

-10%

0%

10%

20%

30%


Quarterly US Venture Capital Returns between 1981 and 2004

Rescaling Factor

Shortfalls Risk

S&P 500 1.0 26 16.3%

1.0 17 15.0%

1.5 33 22.5%

2.0 38 30.1%

2.5 42 37.6%

3.0 44 45.1%

Venture Capital

-30%

-20%

-10%

0%

10%

20%

30%


Quarterly US Venture Capital Returns between 1981 and 2004 Rescaled

Source: Standard & Poor’s

Source: Venture Economics

Source: Venture Economics

The key is to model the risks of alternative investments as ifthey were liquid—that is, through their exposure. Thismeans that the price of alternatives moves in the samemanner as does the price of constantly traded assets.

The fact that an investor needs to hold on with the expo-sure to the risks of alternative assets means that he faces awider price distribution once the asset can be liquidated(i.e., at the end of the "tunnel"). The wider distribution isthe result of compounded instantaneous risks. In a rationalworld, we expect this to be compensated.

3. Returns

3.1 Introduction

As mentioned previously, returns must be estimated afterthe risks and correlations, as returns depend on them. Ourmain approach for return modeling is the integration/seg-mentation approach. Further, in the case of alternativeassets, we need to compensate illiquidity. As the literaturedoes not provide ready-to-go approaches, we derive twoproprietary approaches, which can be combined with theintegration/segmentation approach.

3.2 Integration/Segmentation Approach9

A cornerstone in finance, and generally accepted as anequilibrium model, the Capital Asset Pricing Model (CAPM)is usually the approach of choice for estimating risk premia.It claims that every asset is rewarded by a risk premium pro-portional to its beta versus the entire market plus a risk-freereturn, that is:

Based on the criteria of Brinson, Diermeier and Schlarbaum,10

we define the Global Investable Market (GIM). In contrast toa common US-biased global balanced portfolio, GIM hasless exposure to US assets (particularly US equity). On theother hand, GIM contains alternative assets, which aremainly, but not exclusively, represented by US real estate.

The CAPM, however, assumes perfect markets, and is thusnot an appropriate representation of the real world. Whilethe US equity market approaches a state of high integra-tion, it does not meet it perfectly. Barriers to internationalcapital flows have come down, but they still exist to someextent, and many asset markets are still significantly seg-mented by national borders.

These barriers are not necessarily erected by law; rather,they may reflect investor preference. Such restrictions oncapital in- and outflows tend to create markets that aredominated by local investors, and, in the most extreme case,i.e., if a market is completely segmented, its own riskbecomes its compensation reference, because there are nosubstitution opportunities. That means that the market'sabsolute rather than systematic risk is compensated:

Of course, complete segmentation is as fictitious as perfectintegration. Therefore, in practice, it is important to esti-mate a market's degree of integration. The according returnis considered a weighted average of perfect integration andabsolute segmentation. That is:

where the two weights sum up to 100%.

Both approaches require the global price of risk as an input.Singer and Terhaar12 have spent a considerable amount oftime for estimating it. While they recommend a price of0.30% return per 1% of (compensated) risk, we adopted0.25%. A few years later, Goodall, Manzini, and Rose13

revisited this issue on the basis of different macro modelsand recommended a price of 0.28% return per 1% risk,which was never approved. However, given the large errormargins of macro models, this is not significantly differentfrom what we have in place.

While we set a degree of segmentation as low as 20% fordeveloped equity and bond markets, we think it is relativelyhigh for less developed and alternative markets. As of now,the most extreme degree of segmentation is set to 60% forLatin American timber. Probably more important than theabsolute values of the degrees of segmentation, however,are their relative values. According misrankings would mostlikely cause serious policy misallocations.

3.3 Illiquidity

3.3.1 Issue

The integration/segmentation approach characterizes liquidassets fairly well, but for alternative investments, we needto model illiquidity compensation as well. There are differentperceptions about illiquidity. Illiquidity as relevant to ourcase does not mean that assets can only be traded at thecost of significant bid-ask spreads. Rather, it applies to



ffMM

σ i

i R)R(RR +−=σ

(3)ffMM

σ i

i R)R(RR +−=σ

(3)

segi,seginti,intweightedi, RwRwR += segi,seginti,intweightedi, RwRwR += (4)

ffMMi,i RRRR +−⋅= )(β (2)ffMMi,i RRRR +−⋅= )(β (2)

9 This approach is documented at length in [7] Singer and Karnosky (1993).

10 [2] Brinson, Diermeier and Schlarbaum (1986), p.17.

11 Where i indicates an individual market and M the entire market. Rf is the risk-free rate of return

12 [8] Singer and Terhaar (1997), pp. 44-52.

13 [4] Goodall, Manzini, and Rose (1999), pp. 4-10.

11

assets that cannot be traded at all for quite some time, asthey are completely locked up.

Traditional finance does not provide answers with regard toilliquidity compensation: The CAPM assumes perfect mar-kets and, hence, ignores the "real world issue" of illiquidity.Hence, we derive two proprietary methods.14

3.3.2 Sharpe Ratio Approach

The key point of this approach is the fact that a one-periodSharpe Ratio is an inappropriate measure of the compensa-tion for risk when assets cannot be liquidated after one peri-od. Consequently, the liquidity premium should be derived inthe context of an asset's time horizon, and it can be shownthat its multiperiod Sharpe Ratio (MPSR)—that is, the asset'smulti-period wealth in excess of the wealth generated by therisk-free investment (i.e., compounded return over com-pounded cash return)—is a nonlinear function of time.

Investing in liquid assets, the investor has the option of fre-quent rebalancing. On the other hand, with illiquid invest-ments, the investor is "locked in," and, as a consequence,instantaneous rebalancing between the traded-asset marketportfolio and the alternative assets is not possible. We thinkthere is no incentive to invest in the illiquid alternativeinvestments unless the MPSR - the risk-adjusted wealth - forits horizon is as high as the MPSR for the reference market,which is the entire market.

In the above graphs, SR1 is the MPSR of the reference port-folio, and SR2 is the MPSR of the alternative asset in thecase. While in the first graph, SR2 is not adjusted for illiq-uidity, it is adjusted in the second graph. Overall, through anincrease in the liquidity premium, SR2 is lifted. We lift itsuch that the resulting total return of the illiquid assetequals the total return of the reference market for the givenlock-up span (in our example about 5 years).

3.3.3 Improved Put Option Approach

Considering the value of a risky asset with all dividends rein-vested, the difference between the asset's expected valueand median value increases with an increasing horizon. Wecall the difference the holding effect; it applies to both liq-uid and illiquid assets. The Put Option Approach15 claimsthat free insurance of the expected value versus the medianvalue—i.e., the average portion gained through holding—isa fair compensation for the commitment to stay exposed tothis asymmetric return pattern.16 In contrast to the SharpeRatio Approach, the Put Option Approach only relates tothe asset's own risk and return properties.

3.3.4 Results

While the risk estimates are determined by the underlyingcovariance structure and the capitalization weights, thedetermination of the illiquidity horizon is more challenging.For venture capital, for instance, the illiquidity span in aduration-sense is much shorter, as not all capital is investedat the very beginning and the investment starts to generatecash flows after a few years.

Based on both approaches, we find that the larger the riskand illiquidity horizon, the larger the return and the steeperthe return function. Ultimately, both can be translated intoour standard framework of integration/segmentation for liq-uid assets, in that we calculate them with both total andsystematic risk and take the weighted mean.

While illiquidity compensation turns out to be substantial forassets with long illiquidity spans at high risk, low-risk assetsonly get moderate liquidity premia, no matter how long thelock-up period. Venture capital clearly gets the highest com-pensation due to its high risk, combined with a significantlock-up time. Further, the low illiquidity premia for real estateand timber are due to low total and systematic risk.



0.00

0.40

0.80

1.20

0 5 10 15 20 25 30 35 40 45 50

Illiquidity Horizon (Years)

SR1

SR2

Sharpe Ratio

0.00

0.40

0.80

1.20

0 5 10 15 20 25 30 35 40 45 50

Illiquidity Horizon (Years)

SR1

SR2

Sharpe Ratio

14 These are documented at length in [9] Staub and Diermeier (2003).15 The Put Option Approach is our response to other put option approaches that are—in our opinion—too generous or not generous enough, depending on the length of

the lock-up.16 "Commitment to stay exposed" is just a more technical definition of investing in an illiquid asset.

However, real estate and natural resource investments aremainly driven by diversification purposes and their capabilityto hedge against inflation rather than for boosting return.

3.4 Return Summary

A high segmentation premium is due to the combination ofa high risk and a low degree of integration. Hence, emerg-ing markets equity and venture capital provide by far thehighest compensation for segmentation.

The most outstanding return numbers are probably thereturns for early-stage venture capital. However, note that'early-stage' is a relatively short period with a—nonetheless—long lock-up and a very high risk; therefore, the high illiq-uidity compensation.

Hedge funds do not seem to achieve particularly high riskand illiquidity premia. The reason is that we model, conse-quently, on a passive basis in order to put everything on anequal footing; and we do not expect hedge funds to pro-vide a significant illiquidity compensation as their lock-up isshort.

Finally, both the risk premium and illiquidity premium forreal estate are moderate, since real estate's risk and correla-tion are moderate. Again, the prime motivation to invest inreal estate is diversification.

Note, never compare absolute asset returns per se. Youshould always put returns in relation to their beta and lock-up, since the 'competitiveness' of returns is clearly a relativeissue.

Conclusion

In a first step, we identified the investable capital market.This universe forms the market aggregate from which wederive long-term rates of return for each asset class, consis-tent with their risks relative to, and correlations with, theglobal market.

We model risks on the basis of both historical observationand qualitative assessment. We employ a multi-layerapproach which starts with very broad aggregates and tran-sitions to increasingly detailed markets. This approachreduces complexity as much as possible and ensures consis-tency of the matrix. In fact, the factor approach is a nicereconciliation between a quantitative method and qualita-tive input.

The resulting correlation matrix reflects our general beliefs:There are no negative correlations, as markets are consid-ered (to some extent) investment substitutes; in fact, a 0.40correlation of any market with the entire market is at thelower end of what can be expected. Balanced portfolios arehighly correlated with equity markets and also show consid-erable correlation with bond markets. The lower correlations

of markets such as REITs, natural resources and farmlandwith the overall market are a result of higher idiosyncraticrisk in these markets. Further, alternative assets have variousspecific characteristics: Real estate, e.g., is a low-risk / low-correlation market. On the other hand, private equity is ahigh-risk / high-correlation market.

Since selected global capital markets may not be entirelyefficient, our approach also allows for return-generating fac-tors other than risk and correlation: the degree of marketsegmentation, i.e. the extent to which a market’s capital in-and outflows are hampered by legal and practical barriers;and illiquidity, which describes the constraint to investorflexibility imposed by lock-in periods.

It turns out that markets with higher risk receive more com-pensation for the same degree of segmentation through thedirect impact of total risk. Apart from an already significantcompensation for segmentation, private equity is substan-tially compensated for illiquidity due to a relatively longlock-up period combined with a high level of risk. On theother hand, real estate only gets a moderate compensationfor illiquidity. However, real estate provides further diversifi-cation and return in the form of yield.

Our long-term global market covariance matrix is not onlyused in estimating long-term returns; it is also critical forsetting appropriate asset allocation policies, and for derivingdiscount rates for use in cash flow-driven valuation models.In practice, these estimates of asset class and market returnsand risks are reviewed and revised regularly, to ensure accu-rate inputs for our valuation models.





Markets of the UBS Global Asset Management Covariance Matrix

Equity Australia 80% 0 20.0% 1.69 2.73% 5.00% 3.18% 0.00% 8.03%Equity Austria 80 0 22.5 1.85 2.98 5.63 3.51 0.00 8.37Equity Belgium 80 0 17.5 1.70 2.74 4.38 3.07 0.00 7.91Equity Canada 80 0 16.0 1.66 2.68 4.00 2.94 0.00 7.78Equity Denmark 80 0 18.5 1.66 2.67 4.63 3.06 0.00 7.91Equity Germany 80 0 18.0 1.82 2.93 4.51 3.24 0.00 8.10Equity Greece 80 0 25.0 1.89 3.04 6.26 3.68 0.00 8.56Equity Finland 80 0 30.0 2.12 3.43 7.51 4.24 0.00 9.14Equity France 80 0 20.0 1.85 2.98 5.00 3.39 0.00 8.25Equity Hong Kong 80 0 32.0 1.67 2.70 8.01 3.76 0.00 8.64Equity Ireland 80 0 18.5 1.83 2.95 4.63 3.29 0.00 8.14Equity Italy 80 0 25.0 1.88 3.02 6.26 3.67 0.00 8.54Equity Japan 80 0 20.0 1.86 3.00 5.00 3.40 0.00 8.26Equity Netherlands 80 0 16.5 1.71 2.76 4.13 3.03 0.00 7.87Equity New Zealand 80 0 24.0 1.66 2.68 6.01 3.35 0.00 8.20Equity Norway 80 0 27.0 1.60 2.58 6.76 3.41 0.00 8.27Equity Portugal 80 0 22.0 1.82 2.93 5.50 3.45 0.00 8.31Equity Singapore 80 0 25.0 1.74 2.81 6.26 3.50 0.00 8.36Equity Spain 80 0 22.0 1.79 2.89 5.51 3.41 0.00 8.27Equity Sweden 80 0 25.0 1.78 2.87 6.26 3.55 0.00 8.41Equity Switzerland 80 0 18.5 1.71 2.76 4.63 3.13 0.00 7.98Equity UK 80 0 16.0 1.66 2.68 4.00 2.95 0.00 7.79Equity US (Wilshire 5000) 80 0 15.7 2.06 3.33 3.94 3.45 0.00 8.31Equity US (S&P 500) 80 0 15.0 1.96 3.15 3.75 3.27 0.00 8.13Equity US (MSCI) 80 0 15.2 1.99 3.21 3.80 3.33 0.00 8.19Equity Brazil 65 0 36.0 2.53 4.08 9.01 5.80 0.00 10.78Equity Chile 65 0 32.0 2.52 4.06 8.01 5.44 0.00 10.40Equity China 55 0 34.0 1.86 2.99 8.51 5.48 0.00 10.43Equity Hungary 70 0 34.0 2.08 3.35 8.51 4.90 0.00 9.83Equity India 55 0 34.0 1.86 3.00 8.51 5.48 0.00 10.44Equity Korea 70 0 34.0 2.06 3.31 8.51 4.87 0.00 9.80Equity Malaysia 70 0 28.0 1.83 2.95 7.01 4.17 0.00 9.06Equity Mexico 70 0 30.0 2.48 4.00 7.51 5.05 0.00 9.99Equity Russia 60 0 38.0 2.30 3.70 9.51 6.02 0.00 11.01Equity South Africa 75 0 34.0 2.59 4.18 8.51 5.26 0.00 10.21Equity Taiwan 80 0 34.0 2.10 3.39 8.51 4.41 0.00 9.32Equity Thailand 65 0 34.0 1.86 3.00 8.51 4.93 0.00 9.86Equity Emerging Markets 65 0 21.3 2.19 3.53 5.33 4.16 0.00 9.0610y Treasury Australia 80 0 8.0 0.67 1.08 2.00 1.27 0.00 6.0310y Treasury Canada 80 0 7.2 0.62 0.99 1.80 1.16 0.00 5.9110y Treasury Denmark 80 0 7.2 0.54 0.87 1.80 1.06 0.00 5.8110y Treasury EMU 80 0 7.2 0.64 1.03 1.80 1.18 0.00 5.9410y Treasury Japan 80 0 7.2 0.46 0.74 1.80 0.96 0.00 5.7010y Treasury Sweden 80 0 7.2 0.52 0.83 1.80 1.03 0.00 5.7710y Treasury Switzerland 80 0 6.0 0.44 0.71 1.50 0.87 0.00 5.6110y Treasury UK 80 0 7.2 0.62 1.01 1.80 1.17 0.00 5.9210y Treasury US 80 0 7.2 0.73 1.17 1.80 1.30 0.00 6.06Bonds Australia 80 0 4.5 0.38 0.62 1.12 0.72 0.00 5.45Bonds Canada 80 0 6.4 0.56 0.90 1.60 1.04 0.00 5.78

Integrated SegmentedLock-up Risk Risk Risk Liquitidy Total

Integration time Risk Beta Premia Premia Premia Premia Return



Markets of the UBS Global Asset Management Covariance Matrix (Continued)

Bonds Denmark 80% 0 4.8% 0.37 0.59% 1.20% 0.71% 0.00% 5.45%Bonds EMU 80 0 5.6 0.51 0.82 1.41 0.93 0.00 5.68Bonds Japan 80 0 5.2 0.34 0.55 1.31 0.70 0.00 5.43Bonds Sweden 80 0 4.4 0.32 0.51 1.09 0.63 0.00 5.36Bonds Switzerland 80 0 6.1 0.45 0.73 1.52 0.89 0.00 5.63Bonds Switz. SBI Dom 80 0 4.5 0.34 0.54 1.13 0.66 0.00 5.39Bonds Switz. SBI For 80 0 3.4 0.26 0.41 0.86 0.50 0.00 5.23Bonds Switz. SBI Dom 3-5y 80 0 3.2 0.24 0.38 0.80 0.47 0.00 5.19Bonds Switz. SBI D/For 1-3y 80 0 2.0 0.15 0.24 0.50 0.29 0.00 5.00Bonds UK 80 0 7.3 0.64 1.02 1.82 1.18 0.00 5.94Bonds USA 80 0 5.7 0.58 0.94 1.42 1.03 0.00 5.78Bonds USA (SBBIG) 80 0 5.1 0.53 0.86 1.28 0.94 0.00 5.69Corporate Bonds Australia 80 0 3.5 0.33 0.54 0.87 0.60 0.00 5.33Corporate Bonds Canada 80 0 5.3 0.50 0.81 1.33 0.92 0.00 5.66Corporate Bonds EMU 80 0 4.6 0.46 0.74 1.16 0.83 0.00 5.57Corporate Bonds Japan 80 0 4.2 0.26 0.41 1.05 0.54 0.00 5.27Corporate Bonds Switz. 80 0 3.0 0.24 0.39 0.74 0.46 0.00 5.19Corporate Bonds UK 80 0 7.3 0.70 1.14 1.84 1.28 0.00 6.04Corporate Bonds USA 80 0 5.6 0.60 0.97 1.40 1.06 0.00 5.81Convertible Bonds Euro 80 0 9.6 1.09 1.76 2.40 1.88 0.00 6.67High Yield Bonds US 70 0.25 9.0 0.80 1.29 2.25 1.58 0.40 6.63RRB Canada 80 0 6.7 0.25 0.40 1.67 0.65 0.00 5.38ILG UK 80 0 5.2 0.19 0.30 1.30 0.50 0.00 5.22Tips US 80 0 4.8 0.19 0.31 1.20 0.49 0.00 5.21Bonds Emerging Markets 65 0.08 12.0 0.85 1.36 3.00 1.94 0.40 7.09Cash Australia 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Canada 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Denmark 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Euro 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Hong Kong 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Japan 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash New Zealand 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Norway 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Singapore 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Sweden 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Switzerland 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash UK 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash US 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Brazil 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Chile 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash China 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Czechia 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Hungary 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash India 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Indonesia 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Korea 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Malaysia 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Mexico 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Philippines 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Poland 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Russia 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70






Cash South Africa 100% 0 0.5% 0.00 0.00% 0.13% 0.00% 0.00% 4.70%Cash Taiwan 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Cash Thailand 100 0 0.5 0.00 0.00 0.13 0.00 0.00 4.70Venture Early Benelux 60 4 52.0 4.39 7.08 13.01 9.45 12.84 29.31Venture Early France 60 4 50.0 4.17 6.73 12.51 9.04 10.96 26.68Venture Early Germany 60 4 50.0 4.18 6.74 12.51 9.05 10.97 26.70Venture Early Italy 60 4 52.0 4.39 7.09 13.01 9.46 12.85 29.33Venture Early Scandinavia 60 4 48.0 4.43 7.14 12.01 9.09 9.96 25.60Venture Early Spain 60 4 52.0 4.39 7.08 13.01 9.45 12.85 29.32Venture Early Switzerland 60 4 48.0 3.76 6.06 12.01 8.44 9.23 24.02Venture Early UK 60 4 45.0 4.19 6.75 11.26 8.55 8.14 22.90Venture Early US 60 4 43.0 3.90 6.29 10.76 8.08 7.01 21.09Venture Late Benelux 60 2.5 42.0 3.99 6.43 10.51 8.06 4.82 18.59Venture Late France 60 2.5 40.0 3.72 6.00 10.01 7.60 4.26 17.46Venture Late Germany 60 2.5 40.0 3.70 5.96 10.01 7.58 4.25 17.42Venture Late Italy 60 2.5 42.0 3.95 6.37 10.51 8.03 4.79 18.52Venture Late Scandinavia 60 2.5 38.0 3.43 5.54 9.51 7.13 3.74 16.36Venture Late Spain 60 2.5 42.0 3.96 6.38 10.51 8.03 4.79 18.53Venture Late Switzerland 60 2.5 38.0 3.24 5.22 9.51 6.93 3.62 16.01Venture Late UK 60 2.5 36.0 3.60 5.80 9.01 7.08 3.56 16.10Venture Late US 60 2.5 34.0 3.33 5.37 8.51 6.62 3.11 15.11LBO Benelux 60 3 34.0 3.02 4.87 8.51 6.33 3.18 14.86LBO France 60 3 36.0 2.74 4.41 9.01 6.25 3.33 14.95LBO Germany 60 3 36.0 2.96 4.77 9.01 6.46 3.45 15.32LBO Italy 60 3 40.0 2.46 3.97 10.01 6.39 3.94 15.78LBO Scandinavia 60 3 34.0 2.57 4.14 8.51 5.89 2.93 14.11LBO Spain 60 3 38.0 2.57 4.14 9.51 6.29 3.59 15.28LBO Switzerland 60 3 34.0 2.64 4.25 8.51 5.95 2.96 14.22LBO UK 60 3 30.0 2.56 4.12 7.51 5.48 2.38 13.07LBO US 60 3 29.0 3.22 5.18 7.26 6.01 2.65 13.94Mezzanine Benelux 60 3 17.0 1.09 1.76 4.25 2.76 0.72 8.36Mezzanine France 60 3 17.0 0.94 1.52 4.25 2.61 0.69 8.17Mezzanine Germany 60 3 17.0 1.02 1.65 4.25 2.69 0.70 8.27Mezzanine Italy 60 3 17.0 0.81 1.30 4.25 2.48 0.66 8.00Mezzanine Scandinavia 60 3 17.0 0.97 1.57 4.25 2.64 0.69 8.21Mezzanine Spain 60 3 17.0 0.84 1.35 4.25 2.51 0.66 8.04Mezzanine Switzerland 60 3 17.0 0.89 1.44 4.25 2.57 0.68 8.11Mezzanine UK 60 3 17.0 1.09 1.76 4.25 2.76 0.72 8.36Mezzanine US 60 3 18.0 1.48 2.38 4.50 3.23 0.89 9.04Distressed Debt US 60 2 20.5 1.88 3.03 5.13 3.87 1.08 9.93Real Estate Australia 70 1 16.0 0.93 1.50 4.00 2.25 0.47 7.56Real Estate France 60 2 16.0 0.88 1.42 4.00 2.45 0.58 7.88Real Estate Germany 60 2 16.0 0.92 1.48 4.00 2.49 0.58 7.93Real Estate Netherlands 60 2 13.5 0.74 1.19 3.38 2.06 0.44 7.33Real Estate Switzerland 60 2 15.5 0.78 1.26 3.88 2.31 0.53 7.69Real Estate UK 70 1 12.5 0.70 1.13 3.13 1.73 0.32 6.85Real Estate US 70 1 10.0 0.72 1.15 2.50 1.56 0.27 6.62Real Estate US Apartment 70 2 9.3 0.47 0.76 2.32 1.23 0.21 6.21Real Estate US Industrial 70 2 10.8 0.67 1.09 2.70 1.57 0.29 6.65Real Estate US Office 70 2 11.6 0.75 1.21 2.90 1.71 0.32 6.84Real Estate US Retail 70 2 11.5 0.68 1.10 2.89 1.64 0.31 6.75






Reits US Unleveraged 80% 0 8.9% 0.46 0.74% 2.22% 1.04% 0.16% 5.96%Reits US Apartment 80 0.25 13.2 0.78 1.25 3.31 1.66 0.29 6.75Reits US Industrial 80 0.25 13.7 0.86 1.39 3.42 1.79 0.32 6.92Reits US Office 80 0.25 15.2 0.94 1.51 3.80 1.97 0.36 7.15Reits US Retail 80 0.25 15.0 0.88 1.42 3.75 1.88 0.34 7.04Timber Argentina 40 6 29.0 0.76 1.23 7.26 4.85 3.80 13.95Timber Australia 50 7 16.0 0.47 0.77 4.00 2.38 0.86 8.12Timber Brazil 40 6 24.0 0.71 1.14 6.01 4.06 2.32 11.48Timber Chile 40 6 20.0 0.55 0.88 5.00 3.36 1.51 9.85Timber New Zealand 50 7 22.0 0.80 1.29 5.51 3.40 1.81 10.22Timber US South 50 7 14.5 0.72 1.16 3.63 2.39 0.74 8.00Timber US West 50 7 17.0 0.78 1.25 4.25 2.75 1.02 8.68Timber Uruguay 40 6 25.0 0.66 1.07 6.25 4.18 2.56 11.87Farmland US Row Crop 50 4 13.5 0.51 0.82 3.38 2.10 0.53 7.46Farmland US Perm. Crop 50 4 18.0 0.67 1.09 4.50 2.80 0.89 8.59HF US Market-Neutral 70 0.5 11.0 0.16 0.26 2.75 1.01 0.19 5.96HF US Convertible Arbitrage 60 0.5 11.0 0.16 0.26 2.75 1.26 0.24 6.27HF US Fixed-Inc. Arbitrage 75 0.5 11.0 -0.08 -0.13 2.75 0.59 0.35 5.68HF US Merger-Arbitrage 60 0.5 11.0 0.14 0.23 2.75 1.24 0.24 6.25HF US Distressed Securities 60 0.5 14.0 0.66 1.06 3.50 2.04 0.40 7.26HF US Fund Of Funds 70 0.5 11.0 0.46 0.75 2.75 1.35 0.24 6.36HF US Long/Short 70 0.5 23.0 1.38 2.22 5.76 3.28 0.78 8.98HF US Macro 70 0.5 20.0 0.00 0.00 5.00 1.50 0.41 6.70HF US Emerging Markets 50 0.5 23.0 0.12 0.19 5.75 2.97 0.86 8.74HF US Short Sellers 70 0.5 20.0 -0.62 -1.00 5.01 0.80 1.89 7.54Currency Australia 100 0 10.0 0.00 0.00 0.00 0.00 0.00 0.00Currency Canada 100 0 5.2 0.00 0.00 0.00 0.00 0.00 0.00Currency Denmark 100 0 10.7 0.00 0.00 0.00 0.00 0.00 0.00Currency Euro 100 0 10.5 0.00 0.00 0.00 0.00 0.00 0.00Currency Hong Kong 100 0 10.0 0.00 0.00 0.00 0.00 0.00 0.00Currency Japan 100 0 10.5 0.00 0.00 0.00 0.00 0.00 0.00Currency New Zealand 100 0 11.6 0.00 0.00 0.00 0.00 0.00 0.00Currency Norway 100 0 10.5 0.00 0.00 0.00 0.00 0.00 0.00Currency Singapore 100 0 6.1 0.00 0.00 0.00 0.00 0.00 0.00Currency Sweden 100 0 11.0 0.00 0.00 0.00 0.00 0.00 0.00Currency Switzerland 100 0 11.2 0.00 0.00 0.00 0.00 0.00 0.00Currency UK 100 0 9.1 0.00 0.00 0.00 0.00 0.00 0.00Currency US 100 0 0.0 0.00 0.00 0.00 0.00 0.00 0.00Currency Brazil 100 0 20.0 0.00 0.00 0.00 0.00 0.00 0.00Currency Chile 100 0 15.3 0.00 0.00 0.00 0.00 0.00 0.00Currency China 100 0 10.0 0.00 0.00 0.00 0.00 0.00 0.00Currency Czechia 100 0 11.2 0.00 0.00 0.00 0.00 0.00 0.00Currency Hungary 100 0 11.2 0.00 0.00 0.00 0.00 0.00 0.00Currency India 100 0 10.0 0.00 0.00 0.00 0.00 0.00 0.00Currency Indonesia 100 0 15.4 0.00 0.00 0.00 0.00 0.00 0.00Currency Korea 100 0 10.5 0.00 0.00 0.00 0.00 0.00 0.00Currency Malaysia 100 0 10.5 0.00 0.00 0.00 0.00 0.00 0.00Currency Mexico 100 0 10.0 0.00 0.00 0.00 0.00 0.00 0.00Currency Philippines 100 0 10.5 0.00 0.00 0.00 0.00 0.00 0.00Currency Poland 100 0 11.2 0.00 0.00 0.00 0.00 0.00 0.00Currency Russia 100 0 15.2 0.00 0.00 0.00 0.00 0.00 0.00Currency South Africa 100 0 15.5 0.00 0.00 0.00 0.00 0.00 0.00Currency Taiwan 100 0 10.5 0.00 0.00 0.00 0.00 0.00 0.00Currency Thailand 100 0 10.5 0.00 0.00 0.00 0.00 0.00 0.00

HF = Hedge Funds





References

[1] Brinson, G.P., L.R. Hood and G.L. Beebower. "Determinants of Portfolio Performance." Financial Analysts Journal, July/August 1986, pp. 39-44.

[2] Brinson, Gary P., Jeffrey J. Diermeier and Gary G. Schlarbaum: "A Composite Portfolio Benchmark for Pension Plans." Financial Analysts Journal, March-April 1986, pp. 15-23.

[3] Brinson, Gary P., Brian D. Singer and Gilbert L. Beebower. "Determinants of Portfolio Performance II: An Update." Financial Analysts Journal, May-June 1991, pp. 40-48.

[4] Goodall, Thilo, Antonio Manzini, and Thomas Rose. "Risk Premium Project." Working Paper, UBS Global Asset Management, 1999.

[5] Grinold, Richard C. and Ronald Kahn. "Active Portfolio Management." Probus Publications, Chicago, 1995.

[6] Hamilton, James D. "Time Series Analysis." Princeton University Press, 1994.

[7] Singer, Brian D. and Denis S. Karnosky. "Equilibrium Risk Premia Estimates." Working Paper, Brinson Partners, 1993.

[8] Singer, Brian D. and Kevin Terhaar. "Economic Foundations of Capital Market Returns." Research Foundation of the Institute of Chartered Financial Analysts, 1997.

[9] Staub, Renato and Jeffrey J. Diermeier. "Segmentation, Illiquidity, and Returns." Journal of Investment Management, Vol.1, No. 1, 2003.

[10] Staub, Renato. "Integration of Alternative Investments into the Market Covariance Matrix." Working Paper, UBS GlobalAsset Management, 2001.

[11] Terhaar, Kevin, Renato Staub and Brian Singer. "The Appropriate Policy Allocation for Alternative Investments." Journal of Portfolio Management, 2003, pp. 101-110.

Previously published papers in the White Paper Series include:

Renato Staub. “Asset Allocation vs. Security Selection—Baseball with Pitchers Only?” UBS Global Asset Management,November 2004.

Edwin Denson. “Dynamic Alpha Strategy.” UBS Global Asset Management, September 2004.

Tom Clarke. “Market Behaviour Analysis.” UBS Global Asset Management, August 2004.

Tom Clarke and Jonathan Davies. “Active Currency Management, Mean Reversion and Trading Rules.” UBS Global AssetManagement, June 2004.

Brian Singer. “Asset Allocation Revival.” UBS Global Asset Management, March 2004.

Brian Singer, Renato Staub and Kevin Terhaar. "An Appropriate Policy Allocation for Alternative Investments." Journal of Portfolio Management, Spring 2003.

Renato Staub and Jeffrey Diermeier. "Segmentation, Illiquidity and Returns."Journal of Investment Management, First Quarter 2003.

Author:

Renato Staub, Ph.DExecutive Director, Global Investment SolutionsTel. +312-525 [email protected]

To request any of our white papers, please contact:

April PowellTel. +1-312-525 [email protected]

This publication is intended for limited distribution to clients and associates of UBSGlobal Asset Management. Use or distribution by any other person is prohibited.Copying any part of this publication without the written permission of UBS GlobalAsset Management is prohibited.

The information and opinions contained in this document have been compiled orarrived at based upon internal research. All such information and opinions are sub-ject to change without notice and are for information purposes only. This docu-ment is not intended to be construed as a recommendation regarding the appro-priateness of any investment or an offer to buy or sell any securities. Investorsshould also be aware that past performance of investments is not necessarily aguide to future performance.

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