Comments on the Bomhoff-Schotman paper: “The term structure in the United States, Japan, and West Germany”

Carnegie-Rochester Conference Series on Public Policy 28 (1988) 3 19-324 North-Holland

COMMENTS ON THE BOMHOFF-SCHOTMANPAPER: "THE TERM STRUCTURE IN THE UNITED STATES, JAPAN, AND WEST GERMANY" LEONARDO LEIDERMAN Tel Aviv University*

1.

INTRODUCTION

The main goal of the Eomhoff-Schotman paper is to explore empirically the link between holding-period returns based on portfolios that exploit term-structure investment opportunities and a set of explanatory variables that intend to capture elements of "news" and uncertainty. goal, the paper uses a two-stage procedure. are constructed

using

term-structure

series is then regressed, variables.

Some

of

the

in the main

To achieve this

First, latent variable indices

data

for each country.

The

index

second stage, on a set of explanatory

findings

are

that

determinants

of

term-

structure yields differ across the three countries considered, the United States term-structure index affects those of Germany and Japan in a timevarying fashion, and there is time variation in risk premia, variation that cannot be solely attributed to movements in the measured variance of bond returns. The results econometric being

work

in the paper are useful and informative. takes

time-varying

seriously

parameters

into account

in the

estimated

the

possibility

relations

multivariate Kalman filter techniques and ARCH models. focus my comments on what

Moreover, the and

of thus

there uses

In what follows,

I

I consider to be some of the limitations of the

present analysis and point out how these limitations could be overcome in future work.

*Department University

0 167

-

of

of

Economics.

currently

on

leave

at

the

Graduate

Chicago.

2231/88/$03.50

01988

Elsevier

Science

Publishers

B.V.

(North-Holland)

School

of

Business,

2. ON THE TWO-STAGE APPROACH The way

in which the two-stage approach is implemented in the paper

gives rise to questions on the extent to which the analysis in each one of the stages is consistent with that in the other one.

In the first stage,

the authors construct portfolio weights on bonds of different maturities and thus generate

a series of excess returns on mean-variance

portfolios for each country.

efficient

Though it is indicated that a limited set of

returns on foreign bonds was also considered, the main series generated in this first stage treats each country separately. risk

premium

developed

in

the

international diversification

second

stage

However, the model of the

is based

of a portfolio.

on

the

notion

of

In fact, it is not clear

that investors who have access to foreign securities will want to hold the type of portfolio generated

in the first stage of the present analysis.

Given the nature of the model, it would have been interesting to construct portfolios

in

the

first

stage

upon

allowing

investors

access

to

both

domestic and foreign term structures. An alternative and

approach, where

research

short-

and

work.

and

For

Ingersoll,

excess example

and

Ross to

returns

of

how

functions

observable

are

intertemporal model

simultaneously

could

then

be

theoretical work

(1985),

assumptions,

be not to adopt a two-stage

equilibrium

determined

as

The implications of such a model for optimal

returns

an

of

a general

long-term

functions of fundamentals. portfolios

strategy would

instead develop

obtain

who

actually

closed-form

economic

the

subject

along these showed,

solutions

of

empirical

lines, see Cox, restrictive

under

for

bond

prices

For empirical work

variables.

as

in the

spirit of this approach based on term-structure Euromarket data, see Hakkio and Leiderman (1986) and Campbell and Clarida (1987).

3. The

authors

ON THE MODEL FOR THE RISK PREMIUM

develop

in Section

III

of

their

paper

a

simple mean-

variance model with the main purpose of deriving an expression for the risk premium on bilateral

bonds

in an

setting, given

empirical analysis,

international that data

setting.

While

for three countries

they

do

are used

so

in a

in the

it would have been useful to see a derivation of the

premium in a three-currency model. The authors make a restrictive assumption about investors' access to 320

foreign

exchange

uncovered for

positions

foreign

Therefore, access the

that

markets

once

implies

a

foreign

exchange.

one

specific

pattern

for

Thus,

namely,

the

foreign

exchange

Another risk

restrictive

premium

especially one

is

of

the

that

Given

purchasing-power eighties,

it

would

depends

nominal

yields For

be

relevant

been

taken to

deviations

of

the

investors

useful

from

international

the

have

rates

of

that

are in

foreign

see

in

not

the

yields

that

the in term

which

bonds

Ingersoll,

parity.

purchasing-power

the

(or

risk,

risk of

purchasing-

the

and

context

Ross

uncertainty

For

and

inflationary

in

however,

countries

from

structures

of

how inflation

task,

is

on as

seventies

where

different

different

later

deviations

a model

inflation an easy

the

term-structure

and of

nominal

Cox,

for This

appears

structures of

model

estimated

and

of

or is

possibility

under

domestic

investigated

and

during

term

pricing

purchasing-power

portfolios

to

analysis

the

located

and

arbitrage

uncertainty.

observed

embody

model

be

domestic

movements

uncertainty,

models,

portfolio

for

structures

inflation

price

were

inflation

affects

Hakkio

forward

can

price-level

in

of

purchasing-power

international must

that

intertemporal

Incorporating

no

unexpected

a theoretical

uncertainty

equilibrium

is that

implicitly

expectations.

of

of

made when developing

variables

have

on

term and

structures

magnitude

parity

premium

power)

the

three

by

interest

structure

markets

assumption constructed

yields

covered

may be

the

those

stressed

for

volatility

rates.

there given

explanatory

regressions.

are

assumption

surprising

as

of

covered

(1984)

of

under

from

only

markets

take

considerations

differ

term

by financial term

these

fact,

to

a period

term-structure

the

there

this

forward

In

take

see Stulz

in

be optimal

assumption

determined

context:

would

may well

determines

the

simultaneously

and of

sample,

assumption.

securities,

risk;

that

to

forward

agents

exchange-rate

portfolios

allowed

however,

enable

seems plausible paper’s

forward

(1986),

foreign

these

the

alternative

Leiderman and

to

in

are

In reality,

as

against It

as

investors

markets. used,

hedge

rates,

relevant.

under

these

analysis.

exchange

no

Specifically,

are

and hence

a theoretical

of

in

exchange

positions

in

markets.

of

(1985).

into in

price and that

that

an

account

deflators

are

there

may be

analysis

of

optimal

see Stulz

(1984).

4. ON THE ESTIMATED TERM-STRUCTURE MODELS Tables

8,

9,

and

10

in

the

paper

321

report

the

results

of

regressing

term-structure indices on a constant, unexpected change in the short-term interest rate, unexpected inflation, unexpected money growth, the expected level of short interest rate, expected long-term inflation, expected longterm real money growth, and the variance in short-term interest rates.

The

equations for Germany and Japan include also explanatory variables aimed at capturing effects of United States yields on the term structures in these countries. The before what

specifications used

give

interpreting the results,

the

"correct"

signs

for

rise to

a

number

of

issues.

First,

the authors provide their priors as to

the

explanatory

variables

should

be.

A

feature of models in which expectations about future variables may affect current variables the

(like the current slope of the term structure) is that

sign of a given explanatory

variable may depend

content of that variable for future variables. sign on interest-rate innovations.

on the

information

Consider for example the

That sign is likely to depend on how

the arrival of interest-rate news affects expectations of future interest rates,

and

this

in

turn,

under

rational

expectations,

stochastic process followed by interest rates.

depends

on

the

Thus, unless one considers

the stochastic processes of the "news" variables in conjunction with the term-structure model,

it may be difficult to determine a priori what the

"correct" signs should be. growth me.

in real money

Second, the rationale for including expected

balances

as an explanatory

variable

is unclear

In most models, real money balances are endogenously determined

typically depend on income (or wealth) and interest rates. already

included

as

explanatory

variables

in

the

to and

The latter are

equations,

so

one

possibility would be to include some measure of income as an explanatory variable.

With monthly data, industrial production could be a proxy for

such a variable, and in fact Chen, Roll, and Ross (1986) have shown that movements in industrial production contain explanatory power for movements in some financial involving

real

returns--

money

though

balances

whether

is an

open

this issue.

is due

to

Third,

a mechanism it would

be

interesting to investigate the role of forward interest and exchange rates as explanatory variables, since these variables typically reflect current expectations about future developments. changes

in fiscal

policies

term-structure movements. estimated equations, for

attempting

to

are

Similarly, variables proxying for

likely to contain

explanatory

power

Last, while these are detailed comments on the

I would like to emphasize that my own preference

provide

for

a

tighter

equations. 322

link between

the

theory

and

is

these

REFERENCES Campbell, J.Y. and Clarida, R.H. (1987)

The Term Structure of Euromarket Interest Rates: An Empirical Investigation.

Journal of Monetary Economics,

19: 25-44.

Chen, N.F., Roll, R., and Ross, S.A. (1986)

Economic Forces and the Stock Market.

Journal

of Business,

59:

283-404. Cox, J.C., Ingersoll, Jr., (1985)

A

Theory

and Ross, S.A.

J.E.,

the

of

Term

Structure

of

Interest

Rates.

53: 385-408.

Econometrica, Hakkio, C. and Leiderman, L. (1986)

Intertemporal

Asset

Pricing

and

the

Term

Structures

of

Exchange Rates and Interest Rates: The Eurocurrency Market. European

Economic

30: 325-44.

Review,

Stulz, R.M. (1984)

Currency

Preferences,

Determination

of

Purchasing

Exchange

Journal of Money, Credit,

Rates

and Banking,

323

Power in

an

Risks,

and

Optimizing

16: 302-16.

the

Model.