An International Welfare Analysis of In⁄ation-Indexed ... and Holden (2008).pdf · The U.S....

An International Welfare Analysis ofIn�ation-Indexed Government Bonds

Michael T. GapenBoard of Governors of the Federal Reserve System20th Street and Constitution Avenue, N.W.

Washington, D.C. 20551

Craig W. HoldenDepartment of FinanceKelley School of BusinessIndiana University

Bloomington, IN 47405E-mail: [email protected]: (812) 855-3383Fax: (812) 855-5875

September, 2008

Acknowledgments: The authors wish to thank an anonymous referee and seminar partici-pants at the International Monetary Fund, University of Notre Dame, and Indiana University.Any remaining errors are our responsibility. The authors also thank Anderson Silva and LenaOliveira de Carvalho of the Public Debt Strategic Planning Department in the Brazil Ministryof Finance for data assistance. None of these government o¢ cials, however, is responsible inany way for remaining errors or views expressed. The analysis and conclusions set forth arethose of the authors and do not indicate concurrence by other members of the research sta¤ orthe Board of Governors.

An International Welfare Analysis of In�ation-IndexedGovernment Bonds

Abstract

We analyze the introduction of an in�ation-indexed government bond in a setting where in-vestors maximize expected lifetime utility with constant relative risk aversion and where riskyassets follow geometric Brownian motion. We develop a theoretical metric for assessing theinvestor�s welfare gain from the introduction of an in�ation-indexed government bond in boththe unconstrained case and under the following constraints: no shorts sales, no borrowing, andhome bias. The welfare gain is estimated using data on real monthly rates of return on domesticand international assets from 1994�2003. Both unconditional moments and VAR processes areestimated. Optimal portfolios are calculated for hypothetical investors in �ve developed coun-tries (Australia, Canada, France, Sweden, and the United States) and two developing countries(Brazil and Mexico) before and after introduction of an in�ation-indexed government bond. We�nd that investors in Brazil and Mexico obtain large welfare gains. This is primarily due tothe fact that the new in�ation-indexed government bonds are also domestically-denominatedand thus have neither in�ation, nor exchange rate risk. By contrast, prior nominal governmentbonds were denominated in foreign currency U.S. dollars (committing a so-called �original sin�),which imposed relatively volatile in�ation and exchange rate risk on domestic investors. Thislarge welfare gain persists when constraints are added on short sales, borrowing, and homebias. We �nd that investors in the �ve developed countries increase their welfare gain: (1)when they can invest internationally not just domestically and (2) when expected returns areforecast using a VAR rather than historical returns. Their welfare gain is severely reducedwhen constraints are added on short sales, borrowing, and home bias, because much of theirunconstrained welfare gain comes from levered investments in international assets.

Journal of Economic Literature Classi�cation Numbers: G11; E31; D60.

Key Words: In�ation-indexed bonds, Portfolio Optimization, Financial Innovation.

1. Introduction

Global �nancial markets have seen a recent surge in the number of issuers of in�ation-indexed

government debt. For example, France began issuing in�ation-indexed government debt in 2001

with principal and interest payments linked to the nonseasonally adjusted Eurozone Harmo-

nized Consumer Price Index (Ex-Tobacco).1 Since France�s entry into the Euro in�ation-indexed

market, Greece and Italy entered the market in March and August 2003, respectively, while

Germany followed shortly thereafter in March 2006. The U.S. Treasury�s In�ation-Indexed Se-

curities, popularly referred to as TIPS, were �rst issued in 1997 and the Treasury now conducts

regular auctions of in�ation-indexed debt with maturities ranging between 5 and 30 years.2 ;3 In

the case of TIPS, principal and interest payments are indexed to the non-seasonally adjusted

Consumer Price Index (CPI-U).

Issuance of in�ation-indexed government debt by these developed countries complements

programs already in place in many emerging market economies. Since 1994 Brazil has issued

in�ation-indexed National Treasury Notes (NTN) of two types. Principal and interest of the

series NTN-B are linked to changes in the consumer price index (IPCA) while those of series

NTN-C are linked to changes in the index of general prices (IGP-M). The Mexican govern-

ment (Banco de México 1995) has also issued in�ation-indexed securities known as Los Bonos

Ajustables del Gobierno Federal (Adjustabonos). Adjustabonos are peso-denominated securi-

ties which are indexed to the consumer price index (INPC).4 3-year Adjustabonos were �rst

issued in July 1989, 5-year Adjustabonos began in November 1990, and 10-year Adjustabonos

followed shortly thereafter. In addition to these examples, in�ation-indexed government debt

has been issued by Argentina, Australia, Canada, Chile, Israel, New Zealand, Sweden, the U.K.,

1France has also issued in�ation-indexed debt with principal and interest payments indexed to the nationalconsumer price index (France CPI Ex-Tobacco All Households Index) since 1998.

2 In October 2004 the U.S. Treasury approached investors about a �pure� in�ation security that would com-plement the existing line of TIPS. The proposal, centered around the idea of making the STRIPS principal ofTIPS further strippable into a nominal zero coupon bond and a pure in�ation component, was subsequentlydropped. Investors interested in such securities can also engage in in�ation swaps where a �xed rate is exchangedfor realized in�ation on a notional underlying principal.

3The U.S. and U.K. are the largest investment-grade sovereign issuers of in�ation-indexed debt. As of March2008, the U.S. and U.K. accounted for 36 and 25 percent, respectively, of the Lehman Global In�ation-LinkedIndex, followed by France (16 percent), Italy (8 percent), Japan (6 percent), Canada (3 percent), Sweden (2.9percent), Germany (2 percent), and Greece (1 percent).

4Starting in May 1996, Mexico began issuing Federal Government Development Bonds, or Udibonos, which arespeci�ed in real investment units (UDIs) and whose exchange rate with the new peso is announced by the centralbank daily. Creation of an indexed unit of account allows for various contracts to be written in in�ation-adjustedterms simply be denominating payo¤ values in real units.

1

and others.5

Given the increase in issuance of in�ation-indexed government bonds, this paper exam-

ines the conditions under which the introduction of such securities will be valued by investors.

In�ation-indexed bonds are designed to provide a constant real rate of return and a nominal

return that varies directly with in�ation and perfectly correlated with unexpected in�ation.

If existing assets traded in �nancial markets proved to be e¤ective hedges against unexpected

in�ation then demand for in�ation-indexed securities would be low. Of all nominal securities,

equities traditionally have been though of as the best in�ation hedge available. Fischer (1975)

demonstrates that the covariance of returns on equity with in�ation is important in determining

demand for in�ation-indexed bonds. Yet many studies including those by Fama and Schwert

(1977), Schwert (1981), and Boyd, Levine, and Smith (2001) show a negative correlation be-

tween equity returns and unexpected in�ation.6 Fischer (1975), Price (1997), and Deacon and

Derry (1998) all suggest that the primary rationale for demanding in�ation-indexed securities

is protection from the burden of unexpected in�ation. Since existing �nancial instruments have

proven to be ine¤ective hedges against unexpected in�ation, these authors suggest gains can be

realized via the introduction of an in�ation-indexed security.

However, in�ation risk is only one type of risk faced by investors in perfect capital markets

with investment opportunity sets that include both domestic and international assets. Invest-

ments in international assets with nominal returns payable in foreign currency mean real rates

of return are also subject to exchange rate risk. Deviations from purchasing power parity (PPP)

will cause investors based in di¤erent home countries to view returns from the same security

di¤erently (Solnik 1974, Adler and Dumas 1983, and Dumas 1992). Violations of PPP cause

the same underlying asset to have di¤erent expected risk-return characteristics for investors in

di¤erent home countries, thereby producing divergent investment opportunity sets. Investors

from di¤erent home countries would only view the same security equally in a portfolio setting

if PPP held continuously. The fate of investors with investment opportunity sets of domestic

and international assets cannot be separated from exchange rate risk and associated deviations

5See Price (1997).6Boyd, Levine, and Smith (2001) �nd that higher rates of in�ation are not matched by increased nominal

equity returns in low in�ation countries. Schwert (1981) �nds that equity returns react negatively to the unex-pected in�ation component in consumer price announcements. Fama and Schwert (1977) document a negativerelationship between stock returns and expected and unexpected in�ation in monthly, quarterly, and semiannualdata. Boudoukh and Richardson (1993) use �ve year sample periods to �nd that equity acts as an in�ation hedgeover long-term horizons.

2

from PPP. Therefore, a comprehensive evaluation of the demand for in�ation-indexed assets

and associated welfare gains can only be conducted in a broader setting, one that includes

investors based in di¤erent home countries with overlapping investment opportunity sets. This

paper represents a �rst step in this direction. The welfare gain from �nancial innovation with

in�ation-protection securities is examined based on the use of in�ation-indexed debt in seven

countries: Australia, Brazil, Canada, France, Mexico, Sweden, and United States. Results

across this sample of countries should be illustrative of potential welfare gains to investors from

in�ation-indexed government debt programs.

Real exchange rate risk and its contributions to the �rst and second moments of asset

returns is of particular importance to investors based in emerging markets. Investors based

in these countries are more likely to face a limited domestic currency investment opportunity

set since home country sovereign and corporate sector debt may be denominated in one of the

international reserve currencies in order to facilitate widespread acceptance of such issues in

�nancial markets. This so-called �original sin� of emerging markets (e.g., Eichengreen et al.

2002) subjects home country investors to more real exchange rate risk than their counterparts

in developed economies who likely have access to a wider selection of assets with payo¤s in

local currency. Furthermore, such instances also increase the correlation of real returns when

international assets are included and limit potential bene�ts from diversi�cation since payo¤s

from each must be converted across the same nominal exchange rate to derive returns in local

currency. The Brazil and Mexico case studies are examples of such instances.

We assess the welfare gain from the introduction of an in�ation-indexed government bond in

a setting where investors maximize expected lifetime utility with constant relative risk aversion

and where risky assets follow geometric Brownian motion. We develop our �rst theoretical

metric for the investor�s welfare gain from the introduction of an in�ation-indexed government

bond in the unconstrained case, where there is an analytic solution for derived utility. We

develop our second theoretical metric for the investor�s welfare gain in the constrained case,

where the solution is obtained numerically. The constraints we impose are: no shorts sales,

no borrowing, and home bias. The home bias constraint is motivated by Tesar and Werner

(1998), who document the extent of home bias by showing that by the end of 1996 the fraction

of stock market wealth invested in foreign assets was 10% for U.S. investors, 11% for Canadian

investors, 18% for German investors, and 22% for U.K. investors. International Monetary Fund

(2005) and Amadi (2005) �nd that fraction invested in foreign assets has continued to rise over

3

time, but still falls far short of global market-value weights.

We estimate the welfare gain using data on real monthly rates of return on domestic and

international assets from 1994�2003. Both unconditional moments and VAR processes are

estimated. Optimal portfolios are calculated before and after introduction of the in�ation-

indexed government bond. We �nd that investors in Brazil and Mexico obtain large welfare

gains. This is primarily due to the fact that the new in�ation-indexed government bonds are

also domestically-denominated and thus have neither in�ation, nor exchange rate risk. By

contrast, prior nominal government bonds were denominated in a foreign currency U.S. dollars

(committing a so-called �original sin�), which imposed relatively volatile in�ation and exchange

rate risk on domestic investors. This large welfare gain persists when constraints are added on

short sales, borrowing, and home bias. We �nd that investors in the �ve developed countries

increase their welfare gain: (1) when they can invest internationally not just domestically and

(2) when expected returns are forecast using a VAR rather than historical returns. Their

welfare gain is severely reduced when constraints are added on short sales, borrowing, and

home bias, because much of their unconstrained welfare gain comes from levered investments

in international assets.

The plan of the paper is as follows. Section 2 develops a theoretical metric of the welfare

gain. Section 3 describes the data. Section 4 presents the empirical results. Section 5 concludes.

2. Theoretical Metrics of the Welfare Gain

We use the Markowitz (1952, 1959) framework of individual agent portfolio optimization to

assess the gain in investor welfare from the introduction of an in�ation-indexed government

bond in the individual investor�s home country that provides a riskfree real rate of return. The

setting is similar to the intertemporal consumption and portfolio choice problem of Campbell

et. al (2004) with the speci�cation of power utility as a special case of the Du¢ e and Epstein

(1992a, b) parameterization of preferences in continuous time. We choose this speci�cation

since it yields a closed-form solution to the unconstrained portfolio optimization problem and

a tractable framework for the constrained case.

4

2.1. The benchmark problem

Consider an investor that has power utility of consumption, U(C; t) = exp��tC = , where �

is the subjective discount factor. All assets in the benchmark set of assets are risky to the

individual investor in real terms (i.e., risky relative to the individual investor�s consumption

bundle). In total, there are n risky assets available to the investor. Let P be a n � 1 vector

of prices of the risky assets which follow geometric Brownian motion according to dP=P =

�dt+�dz, where � and � are n�1 vectors of instantaneous means and instantaneous standard

deviations, respectively.7

At each instant, the investor chooses a rate of consumption and an n� 1 vector of portfolio

weights w to maximize indirect utility of wealth, J (W (t); t), according to

J (W (t); t) = MaxfC(s);w(s)g

Et

�Z T

tU (C; s) ds

�s:t: w(s)01 = 1 8s: (2.1)

Replacing the right-hand side with the utility of current instant consumption plus the indirect

utility of wealth at t+ dt and then using Ito�s Lemma, we get

0 = MaxC(t);w(t)

U (C; s) dt+ JW��C +Ww0�

�dt+

1

2JWWW

2w0�wdt� ��1�w01

�dt; (2.2)

where � is a Lagrange multiplier and � is an n�n variance-covariance matrix with ijth element

of �i(P; t)�j(P; t)cov(dzi; dzj). The �rst order conditions to this problem are

UC � JW = 0; (2.3)

JWW�+ JWWW2�w � �1 = 0; (2.4)

1�w01 = 0: (2.5)

where subscripts denote partial di¤erentiation. Manipulation of equations (2.4) and (2.5) results

in optimal portfolio weights of

w =

��JWWJWW

��1�+

�1

A��JWWJWW

��B

A

��11; (2.6)

7We follow the standard notation conventions with boldface type indicating vectors or matrices, a tildadenoting randomness, and an overbar denoting expected values or means.

5

where A � 10��11 and B � 10��1�. Substitution of the �rst-order conditions and optimal

weights into the maximization problem results in the following partial di¤erential equation

0 = exp��t�1

� 1��exp�t JW

� �1+Jtdt�

1

2

(JWW )2

JWWCdt+

1

2JWWW

2 1

A+JWW

B

A+1

2

(JWW )2

JWW

B2

A;

which yields the following exact analytical solution for derived utility under the benchmark set

of assets

J1(W (t); t) = exp��t

1� exp�a1(T�t)

a1

!1� W

; (2.7)

where

a1 = �1

2

�

( � 1)2

�C +

1

2 1

A+

1� B

A+1

2

�

( � 1)2

�B2

A� �

( � 1) ; (2.8)

and C � �0��1�. The subscript 1 is used to denote derived utility under the benchmark set

of assets.

2.2. The expanded problem

The expanded set of assets includes n assets that are risky to the individual investor in real

terms and an in�ation-indexed government bond from the individual investor�s home country,

which is a riskfree asset to the individual investor in real terms.8 Let r be the real riskfree

rate (i.e., measured relative to the individual investor�s consumption bundle). The individual

investor chooses the risky assets weights w, and places the remainder, w0, in the riskfree asset,

so as to maximize indirect utility of wealth

J (W (t); t) = MaxfC(s);w(s)g

Et

�Z T

tU (C; s) ds

�s:t: w(s)01+w0(s) = 1 8s: (2.9)

Replacing the right-hand side with the utility of current instant consumption plus the indirect

utility of wealth at t+ dt and then using Ito�s Lemma, we get

0 = MaxC(t);w(t)

U (C; s) dt+ JW��C +W

�w0 (�� r1) + r

��dt+

1

2JWWW

2w0�wdt; (2.10)

8The in�ation-index government bond is assumed to be perfectly indexed to individual investor�s home countryin�ation. In practice, there may be slight imperfections, such as indexing with a lag (von Furstenberg and Gapen1998, Gapen 2003).

6

The �rst order conditions to this problem are

UC � JW = 0; (2.11)

JWW (�� r1) + JWWW2�w = 0: (2.12)

Solving for the optimal weights yields

w =

��JWWJWW

��1 (�� r1) : (2.13)

Insertion of the optimal weights and �rst-order conditions into the maximization problem results

in the following partial di¤erential equation

0 = exp��t�1

� 1��exp�t JW

� �1 � 1

2

(JW )2

JWW

�C � 2rB + r2A

�+ JW rW + Jt;

which yields the following exact analytical solution for derived utility under the expanded set

of assets

J2(W (t); t) = exp��t


a2

!1� W

; (2.14)

where

a2 =r � � � 1 �

1

2

( � 1)2�C � 2rB + r2A

�: (2.15)

In this instance the subscript 2 is used to denote derived utility under the expanded set of

assets.

We wish to construct a metric for the welfare gain in the unconstrained case from adding an

in�ation-indexed government bond, which is riskfree in real terms. We de�ne the unconstrained

welfare gain metric � as the percent increase in wealth under the benchmark set of assets which

is required to make the investor indi¤erent between the unconstrained expected utility under

the benchmark set of assets and the unconstrained expected utility under the expanded set of

assets. Speci�cally, � is de�ned by

J1 ((1 + �)W; t) = J2 (W; t) ; (2.16)

7

which is equivalent to

exp��t


a1

!1� ((1 + �)W )

= exp��t


a2

!1� W

;

using the de�nitions of a1 and a2 from above. Solving for �, we get

� =

0@ 1�exp�a2(T�t)a2

1�exp�a1(T�t)a1

1A1�

� 1: (2.17)

A larger value for � implies a greater gain from adding an in�ation-indexed government bond.

2.3. Adding constraints to the benchmark and expanded problems

Next we add a variety of real-world constraints, which may imposed on the investor by law or

by custom or which the investor may self-impose. Speci�cally, we add the following constraints:

no short-selling (wi � 0 8i), no borrowing (when a riskfree asset exists) (w0 � 0), and three

home bias constraints that limit the weight in foreign equities (� 25%), foreign bonds (� 25%),

and total foreign assets (� 35%). The three home bias constraints are stylized representations

of recent evidence from the literature and allow some leeway between foreign equity versus

foreign bonds, while also placing a cap on the total investment in foreign securities. Tesar and

Werner (1998) found that in 1996 the fraction of stock market wealth invested in foreign assets

by investors from di¤erent countries ranged from 10% to 22%. These numbers are up from

1987 when U.S. investors invested 4% abroad, Canadians 6%, and U.K. investors 17%. Similar

evidence is found in International Monetary Fund (2005) which aggregates across U.S., Japan,

U.K., Germany, France, and Netherlands investors and �nds approximately 18% in foreign

bonds and 30% in foreign equity. Finally, Amadi (2005) examines trends in equity home bias

across twelve developed countries between 1986 and 2001 and �nds that international portfolio

diversi�cation has risen to an average foreign equity share of around 35% in 2001.9

First consider an investor facing the benchmark set of assets and these real-world constraints.

9Earlier evidence for home bias can also be found in French and Poterba (1991).

8

Adding these constraints to equation (2.2), we have

0 = MaxC(t);w(t)

U (C; s) dt+ JW��C +Ww0�

�dt+

1

2JWWW

2w0�wdt (2.18)

s:t: w01 = 1; wi � 0 8i; (2.19)

wforeign equity � 25%; (2.20)

wforeign bonds � 25%; and (2.21)

wforeign equity + wforeign bonds � 35%: (2.22)

Dividing through by JWWdt, we obtain

0 = MaxC(t);w(t)

U (C; s)

JWW� C

JWW+w0�� 1

2

��JWWW

JW

�w0�w; (2.23)

subject to the constaints above. There is no analytic solution for derived utility J . So, we

numerically solve for the optimal weights by maximizing the same expression less the terms

that don�t have weights in them

Maxw(t)

w0�� 12(RRA)w0�w; (2.24)

subject to the constaints above and where Relative Risk Aversion (RRA) � �JWWWJW

.

Now consider an investor facing the expanded set of assets. Adding the same constraints to

equation (2.10), we have

0 = MaxC(t);w(t)

U (C; s) dt+ JW��C +W

�w0 (�� r1) + r

��dt

+1

2JWWW

2w0�wdt (2.25)

s:t: wi � 0 8i; w0 � 0 (2.26)

wforeign equity � 25%; (2.27)

wforeign bonds � 25%; and (2.28)

wforeign equity + wforeign bonds � 35%: (2.29)

9

Dividing through by JWWdt, we obtain

0 = MaxC(t);w(t)

U (C; s)

JWW� C

JWW+w0 (�� r1) + r � 1

2

��JWWW

JW

�w0�w; (2.30)

subject to the constaints immediately above. Again, there is no analytic solution for derived

utility J . So we numerically solve for the optimal weights by maximizing the same expression

less the terms that don�t have weights in them

Maxw(t)

w0 (�� r1) + r � 12(RRA)w0�w; (2.31)

subject to the constaints above.

The constrained welfare gain metric � is the amount that the expected return under the

benchmark set of assets would have to be increased by in order to make the investor indi¤erent

between the constrained expected utility under the benchmark set of assets and the constrained

expected utility under the expanded set of assets. Speci�cally, � is de�ned by

Maxw(t)

w0�+ �� 12(RRA)w0�w =Max

w(t)w0 (�� r1) + r � 1

2(RRA)w0�w: (2.32)

Solving for �, we get

� =

�Maxw(t)

w0 (�� r1) + r � 12(RRA)w0�w

��Maxw(t)

w0�� 12(RRA)w0�w

�: (2.33)

A larger value for � implies a greater gain from adding an in�ation-indexed government bond.

3. The Data

We compute historical returns for seven developed and emerging market economies (Australia,

Brazil, Canada, France, Mexico, Sweden, and the United States) which have been long-time is-

suers of in�ation-indexed government debt or have undertaken issuance more recently. Returns

are computed using widely accepted indices from publicly available sources that serve as rep-

resentative benchmarks for asset class performance. Equity and �xed income indices from JP

Morgan (JPM), Merrill Lynch (ML), Morgan Stanley Capital International (MSCI), and Stan-

dard & Poor�s are used to construct the domestic and international portfolios for each country.

The MSCI equity indices are free �oat-adjusted market capitalization indices which are de-

10

signed to more accurately re�ect the actual investment opportunity set available to investors.10

The free-�oat adjustment process begins by removing all non-investable opportunities, such as

privately held shares, from the universe of equity securities. MSCI then creates a market cap-

italization weighted index equal to 85% of the total free-�oat adjusted market capitalization.

Such an adjustment is warranted in the case of Brazil, for example, since many listed compa-

nies on the São Paulo Stock Exchange (BOVESPA) stock exchange have voting and non-voting

shares. While voting shares may trade at signi�cant premiums to non-voting shares, they are

often closely held and less liquid.11 Each MSCI equity index used in this analysis is a gross

total return index which approximates the maximum possible dividend reinvestment. The �xed

income indices are also total return indices and include interest income accrued or received dur-

ing the period. Each of the Merrill Lynch indices is re-balanced on the last calendar day of the

month in order to account for new issues, changes in amounts outstanding resulting from buy-

backs or re-openings, and redemptions. For additional information on calculation methodology

and classi�cation see Merrill Lynch (2000).12

The choice of a common sample period presents challenges since both Brazil and Mexico

faced �nancial crises in the 1990s. The associated �nancial turbulence was in part responsible

for the introduction of in�ation-indexed debt in each country. The time frame of this analysis

was chosen based on data availability and to minimize any net disequilibrium in the real ex-

change rate across the countries in the sample in order to derive clean estimates of the portfolio

characteristics of the portfolios of available assets. Otherwise, choosing a time period which

begins or ends with a currency crisis could result in exchange rate changes that dominate the

input con�guration of assets, hugely boosting or undercutting average total rates of return in a

10The MSCI USA Index re�ects US equity behavior on a wider scale than the more narrow large cap indexeslike the DJIA since it captures 85 percent of the free-�oat market capitalization in U.S. equity markets. This isnearly equivalent to the Russell 1000 Index captures 90 percent of the free-�oat adjusted market capitalizationof the U.S. equity market.11Claessens, Klingebiel, and Lubrano (2000) �nd that the average premium of voting over non-voting shares

in Brazil was 23 percent. In response to this and other corporate governance issues, the Brazilian Securities andExchange Commission, Comissão de Valores Mobiliários (CVM), and the São Paulo Stock Exchange (BOVESPA)created the Novo Mercado whereby �rms can voluntarily submit to higher standards of corporate governance.12Merrill Lynch (2000) reports qualifying countries and minimum size requirements for the Merrill Lynch

Global Government Bond Index (Ex-U.S.). These are: Australia (AUD1 billion), Canada (CAD1 billion), Den-mark (DKK5 billion), Euro-sovereigns (EUR1 billion), Japan (JPY200 billion), New Zealand (NZD1 billion),Sweden (SEK5 billion), Switzerland (CHF500 million), the U.K. (GBP500 million), and the U.S. (USD1 billion).Qualifying bonds for the Merrill Lynch U.S. Corporate Index must have a remaining term greater than one yearand a minimum outstanding amount of more than US$150 million. Finally, the Merrill Lynch U.S. TreasuryIndex tracks the performance of U.S. Treasury Notes and Bonds having a remaining maturity greater than oneyear and minimum outstanding size of US$1 billion. Government bills and in�ation-linked notes are not includedin any of the �xed income indices, regardless of provider.

11

manner that cannot be subsumed in a forward looking investment program. The period from

January 1994 to December 2003 is chosen since it minimizes deviations in absolute terms for

most countries in the database relative to the years immediately before and after 2003 while

including additional observations on both sides of the �nancial crises in Mexico (1994�95) and

in Brazil (1998�99 and 2002). Figure 1 plots the real e¤ective exchange rates using data from

the International Financial Statistics database of the International Monetary Fund.13 Mean

monthly rates of change in the real exchange rate and other summary statistics for each coun-

try are displayed in Table 1. During this ten-year period the overall change in the real exchange

rate resulted in an 11% depreciation in Mexico and a 46% depreciation in Brazil. The large

depreciation in Brazil will therefore likely result in an overestimation of gains from in�ation-

indexed government bonds, but we proceed nonetheless since its inclusion in the sample remains

illustrative.

3.1. Characteristics of the risky assets

Each index is a monthly total return series and returns are �rst converted into local currency.

Each series is then converted into real terms by de�ating by the change in the relevant local

consumer price index. Summary statistics for consumer prices are contained in Table 2. In

computing real returns for France-based investors we convert returns into the French franc

and de�ate returns by the local consumer price index as opposed to using the euro and Euro

consumer price index.14 We do this mainly under the assumption that investors based in

France are concerned with minimizing risk to the local currency denominated consumption

bundle. We note, however, that the alternative approach is also viable since France has issued

in�ation-indexed securities with returns linked to the CPI-France and CPI-Eurozone, but would

likely not a¤ect the results due to the high degree of correlation between the Franc and the

Euro during the sample period by construction.15 Summary statistics and sample correlations

13The real e¤ective exchange rate in the IFS database is calculated by adjusting the trade weighted nominale¤ective exchange rate by relative changes in consumer price indices. Since the nominal e¤ective exchange ratesshown here are trade weighted indices, they should only be viewed as a general indicator of real exchange ratechanges relative to asset returns. A more appropriate real exchange rate measure would be portfolio speci�c,weighted relative to actual positions in foreign currency denominated assets.14A theoretical franc exchange rate is calculated using the �xing of the franc versus the euro at the time of

conversion. The same process can be used in reverse to compute a theoretical euro dating back to the startingpoint in the sample. The consumer price index used to de�ate returns is the non-seasonally adjusted France CPIproduced by the INSEE National Statistics O¢ ce.15Returns on French Government In�ation-Indexed Bonds are either linked to the France CPI Ex-Tobacco All

Households Index or the unrevised, non-seasonally adjusted Eurostat Eurozone HICP Ex Tobacco Index.

12

for each of the risky assets can be found in Table 3.

As expected, foreign currency denominated assets available to Brazil-based investors bene�t-

ted from the real exchange rate depreciation which boosted mean rates of return. Mexico-based

investors also received slightly higher mean monthly real rates of return on foreign currency

denominated assets due to the real depreciation of the peso on average over the sample period,

but the e¤ect is less noticeable since mean rates of return are generally consistent with that

found in the remaining country samples. These results can only be attributed to movements

in real exchange rates since the underlying securities in two indices�the MSCI World Index

and the ML Global Government Bond Index�are the same for both Mexican and Brazilian

investors. The average monthly depreciation of the peso real exchange rate was �0.09% while

the average monthly depreciation of the Brazilian real was �0.38% in real terms.16 The MSCI

World Index returned an average of 0.91% per month for Brazilian investors but only 0.52%

per month on average for Mexican investors, the di¤erence being only slightly larger than the

di¤erence between the mean rates of change of the real peso and real Brazilian real exchange

rates.

Real exchange rate variability also increased standard deviation of returns for Brazil and

Mexico based investors. The standard deviation of the monthly real exchange rates for Brazil

and Mexico in Table 1 are 5.28% and 4.47%, respectively, compared to the range of 0.69% to

2.16% in the remaining developed countries in the sample. Examination of the returns from the

ML Global Government Indices whose returns are derived from �xed income sovereign bonds

highlights the negative impact of excessive real exchange rate volatility.17 Standard deviation

of returns on the ML Global Government Indices in the developed markets ranged from a low

of 1.88% for France to a high of 2.99% for Australia. In contrast, standard deviation of monthly

real returns for this index was 5.48% for Mexico and 7.03% for Brazil.

Exchange rate behavior also a¤ects the covariance structure between foreign currency assets.

For example, the correlation between the ML Global Government (Ex-U.S.) Index and the ML

U.S. Treasury Index and ML U.S. Corporate Index is 32% and 29%, respectively, for U.S. based

investors. These correlations are relatively low since returns in the Ex-U.S. component of the

index includes returns denominated in a currency other than the U.S. dollar. A similar pattern

16We use real in italics to denote the currency as separate from discussion about real versus nominal variables.17The securities in the ML Global Government Index vary slightly across countries in the sample since the

Ex-Canada, Ex-France, Ex-Sweden, and Ex-US indices were used to avoid duplication of securities. The resultsdescribed in the text would still prevail if each portfolio included the full ML Global Government Index.

13

appears for Australia, Canada, and Sweden. In contrast, the correlation between the ML Global

Government Index and the ML Global Sovereign Brazil Index and JPM LEI Brazil Corporate

Index are 37% and 49%, respectively. The same �gures for Mexico based investors are 62% and

55%, respectively, and for France 47% and 89%. The higher correlations in Mexico and Brazil

are due to the fact that the ML Global Government Index contains a high weight in U.S. dollars

and both the sovereign and corporate indices for Brazil and Mexico are also predominantly U.S.

dollar based. These dollar based returns need to be converted across the peso and Brazilian real

exchange rates in order to convert them to local currency returns for Mexican and Brazilian

investors. For France, the high correlation is a re�ection of the introduction of the euro and

the high weight of the franc in its composition. Correlations drop dramatically when one of

the indices involves returns in the local currency of each developing economy. The only indices

for Mexico and Brazil that do not carry the common exchange rate factor is the MSCI Mexico

Index and the MSCI Brazil Index. The correlation between the MSCI Mexico Index and the

ML Global Government Index is �14%. For Brazil the correlation is �24%.

Consequently, the so-called �original sin� for emerging markets (Eichengreen et al. 2002)

limits the ability of investors in Mexico and Brazil to invest in asset classes that earn domestic

currency returns and may limit diversi�cation opportunities due to the prominent role that real

exchange rate changes played in the risk-return pro�le of available investments. Mean returns

and covariance structures on the foreign currency-based assets available to investors in Mexico

and Brazil will be similar on account of the behavior of the respective real exchange rates. The

correlation of returns is necessarily higher between these indices in real peso (and real Brazilian

real) than in U.S. dollars alone because the volatile real exchange rate changes of the peso and

real are added at the same time to each series, thereby increasing their correlations due to the

addition of a perfectly correlated and identical common element.

Another contributing factor to real rates of return in each country is the in�ation process,

whether as a driver of exchange rate dynamics or driven in part by the exchange rate pass

through. Changes in domestic prices, as measured through changes in the consumer price index

of each country, are used to de�ate foreign currency returns after translating them across the

exchange rate and directly on assets earning domestic currency returns. While the depreciating

real exchange rate bene�tted mean rates of return for Brazil investors and less so Mexico

investors, the volatility of the exchange rate and in�ation process meant that asset returns

were also volatile. Over the sample studied in�ation rates in Brazil and Mexico were much

14

higher than those in the developed markets as shown in Table 2. The mean monthly rate of

in�ation as measured by the consumer price index was 2.59% for Brazil and 1.16% for Mexico,

while the remaining developed economies exhibited very low monthly rates of in�ation between

0.13% and 0.22%. The standard deviation of in�ation in Brazil was 7.71%, much higher than

the 1.15% registered in Mexico, and signi�cantly more than the 0.17% to 0.44% range for the

remaining developed countries in the sample. The in�ation process contributed to more volatile

real rates of return on Brazilian assets which can be seen in Table 3 as standard deviations of

asset returns are much higher for Brazil and slightly higher for Mexico. Much of the volatility

in Brazilian consumer prices occurred during the early and late years of the sample, particularly

in 1994, prior to the introduction of the Real Plan which implemented a �xed nominal exchange

rate target. While both Mexico and Brazil operated under �xed exchange rate systems during

a portion of the sample period, the Mexican currency crisis in 1994 and the Brazilian currency

crisis in 1998 caused both countries to abandon this policy stance.18 The stable in�ation process

found in the remaining developed markets during the sample period contributed to the very

low standard deviation of real returns, particularly on the �xed income indices.

3.2. The riskfree assets: adjusting for country risk

The respective in�ation-indexed security is used to de�ne the characteristics of the real riskfree

asset for each country portfolio. While previous studies have showed that in�ation-indexed

securities are somewhat �awed in practice due to the use of price indices that are not seasonally

adjusted and/or published with a lag (von Furstenberg and Gapen 1998, Gapen 2003), well

designed in�ation-indexed securities can minimize these biases and may be viewed by market

participants as the best available proxy for a riskfree security. For the purposes of this paper,

we assume that the indexation process for each of the in�ation-indexed bonds in this sample is

well designed and minimizes potential indexation bias.

However, even well designed in�ation-indexed securities still contain elements of risk which

are not representative of riskfree assets in real terms. The risk characteristics of in�ation-

indexed government debt depend on term to maturity and may contain an illiquidity premium

if the respective issues are not deep and frequently traded. Furthermore, in�ation-indexed

18The in�ation process has stabilized in both Brazil and Mexico during recent years. Therefore, the welfaregains discussed in this paper should be viewed as representative of high in�ation, high volatility economies ingeneral and not necessarily evidence of gains in these speci�c markets going forward.

15

securities may also contain country risk, which is a function of the quality of their issuer. While

country risk can be ignored for the developed countries in the sample without loss of generality

as each carries the highest possible rating from the respective rating agencies, it cannot be

ignored in the cases of Mexico and Brazil. Existence of country risk imparts additional real

return into the in�ation-indexed asset and, if maintained in this analysis, would create a highly

attractive riskless real investment opportunity dominating every other asset available except

under extremely high levels of risk tolerance. Consequently, adjustments for country risk are

made to the real returns on Mexico and Brazil in�ation-indexed government debt that result

in a more accurate estimation of the introduction of a riskfree asset in real terms.

In order to adjust for country risk, the real riskfree rate is modeled as the intercept of an

equation that regresses the real rate of return on each in�ation-indexed security with the yield

di¤erential between yields on U.S. dollar-denominated sovereign debt of each respective country

and comparable U.S. Treasury securities. Since daily or monthly price and yield information

are not available on Mexican UDIBONOS or Brazilian NTNs, the adjustment for country risk

is made using historical price and yield information from auction results.19 Only auction results

on shorter-term in�ation-indexed debt are considered to minimize term structure maturity risk.

Using auction results for 5-year UDIBONOS and 5-year or less NTN-Cs and NTN-Bs yields

estimates for the riskfree rate of 3.2% in Mexico and 4.8% in Brazil. Each is converted to a

monthly measure and is used as the real riskfree rate for these countries.

For the remaining developed countries in the sample actual monthly yields from traded

in�ation-indexed debt are used to estimate the riskfree rate. Canada, for example, has issued

Real Return Bonds since 1991 and the average real yield for each traded bond was used to

construct a time varying riskfree rate which averaged 3.9% over the entire sample. Sweden �rst

issued in�ation-indexed debt in early 1994 and then began more regular issuance beginning

in 1995. Australia, France, and the U.S. began their in�ation-indexed bond programs later,

with Australia beginning regular auctions in 1995, the U.S. in January 1997, and France in

1998. For Australia, France, and the U.S., the earliest yield information was used to estimate

the riskfree rate prior to the launch of their respective in�ation-indexed programs. Overall the

19Auction results for Mexico UDIBONOS were obtained from Banco de Mexico. Auction results for BrazilNTNs can be found on the National Treasury website (http://www.tesouro.fazenda.gov.br/). Data from thissource was augmented with additional historical data provided by the Public Debt Strategic Planning Depart-ment. Fully adjusting for country risk in Brazil is di¢ cult given the persistently high real rates of return presentin the economy.

16

average annual real riskfree rates over the entire sample for Australia, France, Sweden, and the

United States averaged 4.1%, 3.2%, 4.6%, and 3.3%, respectively. Finally, the parameter values

for risk aversion were obtained from the literature. Following Campbell and Viceira (1999) we

consider relative risk aversion coe¢ cients of [1:5; 2; 4; 10; 20; 40] since the literature has shown

that high levels of relative risk aversion are needed to reconcile consumption data with market

data under power utility.

4. Empirical Results

While it may be the case that investors based in the developed market economies have wide-

spread access to international diversi�cation and investors based in emerging markets do not, it

may also be the case that investors behave in a manner consistent with home bias. In order to

avoid making any speci�c assumptions over access to international markets and home bias, gains

are calculated in three ways. First, a �ve-year window of historical returns are used to compute

unconditional moments, determine the unconstrained optimal portfolios, and compute uncon-

strained welfare gains using equation 2.17. Second, a vector autoregressive process (VAR) is

used to capture the conditional distribution of expected returns, where returns follow an AR(1)

process (Campbell et. al, 2004). Then we determine the unconstrained optimal portfolios, and

compute unconstrained welfare gains using equation 2.17. Both of these methods are applied to

an investment opportunity set consisting of domestic assets only, and later with domestic and

international assets.20 Third, the constrained optimal portfolio is determined under the combi-

nation of no shorts sales, no borrowing, and home bias, where the investment opportunity set

containing domestic and international assets with home bias constraints is de�ned in equations

2.20�2.21. Then the constrained welfare gain is computed using equation 2.33.

4.1. Gains based on unconstrained optimization

The use of a �ve year rolling window of observations implies that an investor making a forward

looking investment decision in January 1999 relies on the most recent sixty months of data from

January 1994 to December 1998 to de�ne expectations of risk-return characteristics of available

assets.21 The investor then uses this information to optimally choose portfolio weights in the

20 In this paper, domestic or international refers to the country of origin of the security issuer and not currencydenomination.21 Implementing a rolling 5-year window over a 10 year period results in a maximum of 60 utility calculations

for each level of risk aversion. The mean-variance analysis and expected utility speci�cations assumed in this

17

risky and riskfree assets until one month later when portfolio weights are rebalanced. A rolling

window also limits the ability of periods which contain abnormal returns or variance-covariance

patterns from dominating a �xed sample period.

Table 4 shows the unconstrained welfare gains on average over rolling �ve year windows

based on our �rst metric in equation 2.17. This metric is the percent increase in wealth necessary

to make the investor indi¤erent between the benchmark set of risky assets and the expanded

set of risky and riskfree assets under the unconstrained optimization. Panels A and B use

historical returns to forecast future average returns, variances, and covariances. Panel A limits

the investor in each country to domestic assets only, whereas B allows both domestic and

international assets. In all cases, the gain from adding an in�ation-indexed bond is strictly

positive. Looking country-by-country, the gains are U-shaped in relative risk aversion (RRA).

As RRA is increased, the gains decline, reach the bottom, and then increase. The U-shaped

pattern can be see in Figure 2, which graphs the gains (on a log scale) by RRA for each country.

The graphs 2A through 2D correspond to the same four cases as panels 4A through 4D.

The U-shaped pattern makes intuitive sense, because the gain will be exactly zero for one

particular value of RRA22 that leads an investor with the expanded set of assets to invest in

the tangent portfolio.23 Investors with higher RRA than that particular RRA will invest to

the left of tangent point and will experience larger gains at higher RRAs. Investors with lower

RRA than that particular RRA will invest to the right of the tangent point and will experience

larger gains at lower RRAs. This results in the U-shaped pattern of gain. In geometric terms,

the gain is related to the gap between the capital allocation ray and the opportunity set curve

of risky assets. The gap is zero at the tangent point. As an investor moves away from the

tangent point to either the left or right the gap increases and so the gain increases. Both the

gap and the gain are U-shaped in RRA.

Looking at graphs 2A and 2B, the gains for high risk aversion investors (RRA � 10) are

much larger in Brazil and Mexico than in any other country. This large gain is driven by the

large in�ation and exchange rate risk that �original sin�exposes Brazilian or Mexican investors

paper can sometimes result in inconsistencies. In particular, some of the rolling return calculations produce amean expected rate of return on the global minimum variance portfolio which lies below the riskless real returnfrom indexed bonds. In cases like this, the tangent portfolio lies on the bottom side of the portfolio frontier.Such perverse cases were eliminated from the sample.22This particular value is not necessarily one of the six RRA values that we evaluate. In principle, each of the

U-shaped curves touches the x-axis at this particular value of RRA.23The tangent portfolio is the unique portfolio in mean-standard deviation space, located where the capital

allocation ray starting from the (real) riskfree asset touches the opportunity set curve of (real) risky assets.

18

to. A domestic currency denominated, in�ation-indexed bond eliminates these risks, which is

especially valuable for high risk aversion investors.

Panels C and D of Table 4 use the estimated VAR to predicted future average returns. In

panel C, the investor in each country is limited to domestic assets only, whereas in panel D

allows both domestic and international assets. As before, the gain from adding an in�ation-

indexed bond is strictly positive. Looking country-by-country, the gains for Brazil and Mexico

are U-shaped, but gains for the developed countries (Australia, Canada, France, Sweden, and

the U.S.) monotonically decrease as RRA increases. This implies that whenever a developed

country investor using VAR returns faces an expanded set of assets, the optimal portfolio is

to the right of the tangent portfolio (i.e., involves borrowing at the real riskfree rate). Said

di¤erently, the developed country gains will hit zero at a RRA greater than 40.

The last column in each panel reports the average gain for each country. It is the simple

average of each row, which provides a convenient summary statistic to compare the magnitude

of the gain. Comparing the average gains for each country in panel C vs. panel A, we �nd that

the average gains for developed countries are much larger with VAR returns than with historical

returns. Apparently, the VAR predicted returns provide favorable risk-return opportunities in

developed countries compared to historical returns and investors facing an expanded set of

assets �nd it advantageous to borrow at the real riskfree rate in order to make an optimally

levered investment in those favorable opportunities. By contrast, the average gains in Brazil

and Mexico are about the same in panel C and panel A. This situation changes somewhat when

we look at combined domestic and international assets. Comparing the average gains for each

country in panel D vs. panel B, we �nd that all countries experience much larger average gains

with VAR returns than with historical returns. Thus, Brazilian and Mexican investors also

bene�t from the favorable risk-return opportunities under VAR returns when they have access

to investing in international assets. But the largest average gains are in Canada, France, and

the United States, as is clear from graphs 2C and 2D.

We can see this another way by �xing the method of predicting returns and compare do-

mestic plus international vs. domestic only. Holding constant the use of historical returns and

comparing panel B vs. panel A, the average gain for developed countries are about the same.

By contrast, holding constant the use of VAR returns and comparing panel D vs. panel C, the

average gain for developed countries is double or more for domestic plus international assets

vs. domestic only. Thus, we �nd that the greatest welfare gains in developed countries are at

19

the union of VAR returns and domestic plus international assets.

4.2. Gains based constrained portfolio optimization

Next we redo the same exercises as above, but with the real-world constraints of no short-selling,

no borrowing, and home bias present in the investor�s problem. The gain in welfare from the

introduction of an in�ation-indexed security under these constraints is displayed in Table 5.

Panel A displays the gain based on historical returns. All of the constrained welfare gains are

strictly positive. For all countries, the gains monotonically increase as RRA increases. This

implies that for all of the cases analyzed it is optimal to invest to the left of tangent point,

where there is lending of the real riskfree asset, but no borrowing. By contrast in unconstained

case in panel 4B, investors in all countries that had a RRA of 1.5 found it optimal to borrow.

Thus, the no borrowing constraint is binding and signi�cantly a¤ects the outcome.24

For every RRA, the gains are largest in Brazil and Mexico. Even with the constaints,

Brazilian and Mexican investors are able to signi�cant reduce their in�ation and exchange rate

risk by investing in domestically denominated in�ation-indexed bonds. The constaints do not

impact the main source of their welfare gains. However, the constraints greatly impact investors

in developed countries. Without constraints, they would signi�cantly short sell, signi�cantly

borrow, and invest heavily in international assets. With constraints, they can�t short sell, can�t

borrow, and must be much more modest in investing internationally. Thus, their gains from

the introduction of an in�ation-indexed bond are relatively limited. Intuitively speaking, for

investors who prefer to leverage their position and internationally diversify, the gains are rela-

tively limited because the constrained case is e¤ectively an intermediate point on the spectrum

between full segmentation (domestic assets only) and full integration (investing in domestic

plus international assets).

Panel B reports the results based on VAR returns. As above, the gains are all positive,

monotonically increasing in RRA, and are generally larger for Brazil and Mexico. Comparing

panel B vs. panel A, for the developed countries the average gains are larger under VAR returns

24For the expanded set of assets under the no borrowing constraint, the e¢ cient opportunity set includes thelower portion of the capital allocation ray between the (real) riskfree asset and the tangent portfolio, but doesnot include the upper portion of the capital allocation ray above the tangent portfolio, because the upper portionrequires borrowing. Instead to the right of the tangent portfolio, the e¢ cient set follows the opportunity setcurve of risky assets. An investor with very low RRA (lower than the 1.5 RRA we consider) might �nd it optimalto invest to the right of the tangent portfolio on the opportunity set curve of risky assets. For such an investor,the welfare gain from the introduction of in�ation-indexed bonds would be exactly zero, because he wants toborrow and this is not allowed.

20

than under historical returns. This is consistent with the unconstrained results in Table 4 that

the VAR predicted returns provide favorable risk-return opportunities in developed countries.

5. Conclusion

In this paper we analyze the introduction of an in�ation-indexed government bond in a setting

where investors maximize expected lifetime utility with constant relative risk aversion and where

risky assets follow geometric Brownian motion. We develop a theoretical metric for assessing

the investor�s welfare gain from the introduction of an in�ation-indexed government bond in

both the unconstrained case and in the constrained case of no shorts sales, no borrowing,

and home bias. We �nd that investors in Brazil and Mexico obtain large welfare gains. This is

primarily due to the fact that the new in�ation-indexed government bonds are also domestically-

denominated and thus have neither in�ation, nor exchange rate risk. By contrast, prior nominal

government bonds were denominated in a foreign currency U.S. dollars (committing a so-called

�original sin�), which imposed relatively volatile in�ation and exchange rate risk on domestic

investors. This large welfare gain persists when constraints are added on short sales, borrowing,

and home bias. We �nd that investors in the �ve developed countries increase their welfare

gain: (1) when they can invest internationally not just domestically and (2) when expected

returns are forecast using a VAR rather than historical returns. Their welfare gain is severely

reduced when constraints are added on short sales, borrowing, and home bias, because much

of their unconstrained welfare gain comes from levered investments in international assets.

21

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Table 1: Summary Statistics - Real exchange rates (Negative values = depreciation).Mean Std. Deviation Minimum Maximum

Real Exchange Rate (Monthly, in percent) (In percent)Australia 0.14 2.16 �4.98 4.95Brazil �0.38 5.28 �21.52 20.97Canada 0.00 1.29 �3.65 3.68France �0.01 0.69 �2.45 1.47Mexico �0.09 4.47 �31.57 11.82Sweden 0.01 1.44 �3.62 3.84United States 0.07 1.40 �4.08 3.67

Table 2: Summary Statistics - In�ation.Consumer Price Index Mean Std. Deviation Minimum Maximum

(Monthly, in percent) (In percent)Australia 0.22 0.21 �0.14 1.22Brazil 2.59 7.71 �0.51 38.82Canada 0.15 0.30 �0.86 0.86France 0.13 0.21 �0.39 0.72Mexico 1.16 1.15 �0.32 7.67Sweden 0.13 0.44 �0.85 2.57United States 0.19 0.17 �0.33 0.67

24

Table 3: Summary Statistics and Sample Correlation Matrix in Local Currency.

Mean Std DevMSCI World Index 0.30 3.91 1.00 MSCI Australia Index 0.39 3.64 0.54 1.00 ML Global Govt (Ex. Aus) Index 0.25 2.99 0.14 0.29 1.00 ML Global Sovereign Australia Index 0.36 1.52 0.06 0.19 0.31 1.00 UBS Australia Credit Index 0.39 0.96 0.08 0.23 0.27 0.93 1.00

Mean Std DevMSCI World Index 0.70 6.97 1.00 MSCI Brazil Index 0.91 10.38 0.26 1.00 ML Global Government Index 0.64 7.03 0.78 0.14 1.00 ML Global Sovereign Brazil Index 1.16 7.17 0.61 0.61 0.37 1.00 JPM LEI Brazil Corporate Index 1.33 6.66 0.67 0.50 0.49 0.85 1.00

Mean Std. Dev.MSCI World Index 0.44 3.88 1.00 S&P TSX Canada Index 0.67 13.01 0.52 1.00 ML Global Govt (Ex. Can) Index 0.38 2.21 0.07 0.39 1.00 ML Global Sovereign Canada Index 0.46 1.44 0.07 0.08 0.24 1.00 ML Canada Corporate Index 0.51 1.35 0.16 0.17 0.16 0.97 1.00

Mean Std. Dev.MSCI World Index 0.37 5.17 1.00 MSCI France Index 0.46 5.94 0.84 1.00 ML Global Govt (Ex. Fra) Index 0.31 1.88 0.49 0.26 1.00 ML Global Sovereign France Index 0.40 1.19 0.04 0.03 0.47 1.00 MSCI Eurodollar Corporate Index 0.35 2.77 0.51 0.29 0.89 0.33 1.00

Mean Std. Dev.MSCI World Index 0.52 5.71 1.00 MSCI Mexico Index 0.01 8.11 0.25 1.00 ML Global Government Index 0.47 5.48 0.66 0.24 1.00 ML Global Sovereign Mexico Index 0.72 3.95 0.59 0.30 0.62 1.00 JPM LEI Mexico Corporate Index 0.60 3.86 0.64 0.25 0.55 0.68 1.00

Mean Std. Dev.MSCI World Index 0.37 4.69 1.00 MSCI Sweden Index 0.80 7.63 0.72 1.00 ML Global Govt (Ex. Swe) Index 0.32 2.19 0.27 0.14 1.00 ML Global Sovereign Sweden Index 0.52 1.31 0.08 0.06 0.12 1.00 MSCI Eurodollar Corporate Index 0.48 1.22 0.08 0.16 0.29 0.58 1.00

Mean Std. Dev.MSCI World Index 0.22 4.45 1.00 MSCI USA Index 0.69 4.66 0.78 1.00 ML Global Govt (Ex. US) Index 0.30 2.46 0.23 0.00 1.00 ML US Treasury Index 0.34 1.35 0.15 0.08 0.32 1.00 ML US Corporate Index 0.41 1.42 0.06 0.16 0.29 0.89 1.00

Note: Mean monthly real rate of return, standard deviation of real montly returns, and correlation of realmonthly asset returns are experessed as a percent, in local currency terms.

SwedenCorrelation Matrix

United States

Correlation Matrix

Brazil

CanadaCorrelation Matrix

AustraliaCorrelation Matrix

Correlation Matrix

FranceCorrelation Matrix

MexicoCorrelation Matrix

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Table 4: Unconstrained welfare Gains by Risk Aversion: Average over Rolling 5 Year Windows.

Average1.5 2 4 10 20 40 Gain

Austrailia 1.22 0.87 0.36 0.08 0.01 0.04 0.43Brazil 0.10 0.06 0.37 1.99 5.07 11.92 3.25Canada 0.89 0.62 0.24 0.04 0.04 0.14 0.33France 1.42 1.01 0.41 0.08 0.02 0.08 0.50Mexico 0.08 0.06 0.09 0.37 0.90 2.02 0.59Sweden 1.02 0.73 0.30 0.07 0.02 0.07 0.37United States 0.46 0.32 0.11 0.01 0.03 0.13 0.18

Average1.5 2 4 10 20 40 Gain


Average1.5 2 4 10 20 40 Gain


Average1.5 2 4 10 20 40 Gain


Panel B. Historical Returns: Domestic and International Assets

Relative Risk Aversion


Panel A. Historical Returns; Domestic Assets Only



Panel D. VAR Returns; Domestic and International Assets

Panel C. VAR Returns; Domestic Assets Only

Notes: The unconstrained welfare gain is the amount, in percent, that the investor's wealth under thebenchmark set of assets would have to be increased by in order to make the investor indifferentbetween the benchmark set of assets and the expanded set of assets. All figures have been multipliedby 100.

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Table 5: Constrained Welfare Gains by Risk Aversion: Average Over Rolling 5 Year Windows.

Panel A: Historical Returns; Domestic and International AssetsAverage

1.5 2 4 10 20 40 GainAustrailia 0.0017 0.0023 0.0045 0.0073 0.0196 0.0680 0.0172Brazil 0.0285 0.0418 0.2634 1.5417 3.8446 8.5005 2.3701Canada 0.0007 0.0022 0.0078 0.0247 0.0557 0.1467 0.0396France 0.0002 0.0003 0.0007 0.0029 0.0201 0.0882 0.0187Mexico 0.0294 0.0400 0.0998 0.3550 0.8140 1.7077 0.5076Sweden 0.0014 0.0018 0.0039 0.0098 0.0220 0.0720 0.0185United States 0.0017 0.0023 0.0047 0.0171 0.0560 0.1688 0.0417

Panel B: VAR Returns; Domestic and International AssetsAverage

1.5 2 4 10 20 40 GainAustrailia 0.0483 0.0494 0.0537 0.0672 0.0956 0.1670 0.0802Brazil 0.1551 0.1816 0.3169 1.0346 3.0289 7.5816 2.0498Canada 0.1612 0.1896 0.2426 0.2946 0.3388 0.4015 0.2714France 0.0642 0.0762 0.1223 0.2152 0.3176 0.4800 0.2126Mexico 0.2015 0.2124 0.2627 0.4331 0.7896 1.6257 0.5875Sweden 0.0039 0.0044 0.0069 0.0193 0.0493 0.1041 0.0313United States 0.0485 0.0544 0.0784 0.1379 0.2006 0.2854 0.1342



Notes: The constrained welfare gain is the amount, in percent, that the expected return under the benchmarkset of assets would have to be increased by in order to make the investor indifferent between the benchmarkset of assets and the expanded set of assets. All figures have been multiplied by 100.

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Figure 1: Real Exchange Rates 1994-2003 (Jan. 1994=100).

40

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Jan94 Jul95 Jan97 Jul98 Jan00 Jul01 Jan0340

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United States

Brazil

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Figure 2: Utility Gains by Risk Aversion: Unconstrained Case.

e

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The unconstrained welfare gain is the amount, in percent, that the investor's wealth under the benchmark setof assets would have to be increased by in order to make the investor indifferent between the benchmark setof assets and the expanded set of assets.

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Figure 3: Utility Gains by Risk Aversion: Constrained Case.

E. Constrained Welfare Gain; Historical Returns; Domestic Assets Only

0.0001

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1.0000

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F. Constrained Welfare Gain; VAR Returns; Domestic and Int'l Assets

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The constrained welfare gain is the amount, in percent, that the expected return under the benchmark set ofassets would have to be increased by in order to make the investor indifferent between the benchmark set ofassets and the expanded set of assets.

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An International Welfare Analysis of In⁄ation-Indexed ... and Holden (2008).pdf · The U.S....

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