ñòð. 8 
Threemont h
 
6.78 8.06
Interbank
26.4
6.90
6.82 3.97
1 Year
62.1
7.27 2.92 7.44
2 Year
108.
7.76
7.5 1 2.44
3 Year
162.
7.66 7.97
2.17
4 Year
218.5
7.76 8.12
1.97
5 Year
293.0
8.24
1.83
7.84
6 Year
326.
1.71
7.89 8.31
7 Year
7.93 373.8
1.61 8.36
8 Year
423.0
8.39
1.53
7.95
9 Year
7.96 569.
8.40
1.49
10 Year
(a) Holding period yield less threemonth interbank rate.
Reproduced by permission of Joseph Bisignano.
(column 7). For the USA, results are even more nonuniform (Table 10.3).
HPY (column 5) for the USA shows no clear pattern and although the yiel
higher at the long end than the short end of the market, it does not rise mon
However, for very short maturities between two months and 12 months McCul
has shown that for US Treasury bills the excess holding period yield HI;:
monotonically from 0.032 percent per month (0.38 percent per annum) fo
0.074 percent per month (0.89 percent per annum) for n = 12 months. (Alth
is a â€˜blipâ€™ in this monotonic relationship for the 9/10month horizon, see
(1987)). Thus, for the UK there is no additional reward, in terms of the excess
the onemonth return) to holding long bonds rather than short bonds althou
a greater yield spread on long bonds. The latter conclusions also broadly a
USA for long horizons but for short horizons there is monotonicity in the ter
(McCulloch, 1987) which is consistent with the LPH. There are therefore
differences between the behaviour of â€˜returnsâ€™ in these countries.
A much longer series for yields to maturity on long bonds for the USA
corporate bonds which carry some default risk) and on a perpetuity (i.e. the Co
for the UK are given in Figures 10.2(a) and 10.2(b), together with a represen
rate. The data for yields on the two long bonds appear stationary up until about
yields rise steeply. Currentperiod short rates (for both the USA and the UK
be more volatile than long rates so that changes in the spread Sr = (RI  r t ) a
dominated by changes in rr rather than in Rr.
According to the expectations hypothesis the perfect foresight spread R T
weighted (moving) average of future short rates r, and hence should be
series than r,. It appears from Figures 10.3(a) and 10.3(b) for the USA an
respectively, that R â€˜tracksâ€™ R, fairly well, as we would expect if the expe
T
liquidity preference hypotheses (with a time invariant term premium) hold. H
require more formal test procedures than the quick â€˜data analysisâ€™ given abov
Quality of Data
The â€˜qualityâ€™ of the data used in empirical studies varies considerably. This
comparisons of similar tests on data from a particular country done by different
or crosscountry comparisons somewhat hazardous.
For example, consider data on the yield to maturity on â€˜fiveyear bondsâ€™.
be an average of yields on a number of bonds with four to six yearsâ€™ matu
maturities between five years and five years plus 11 months. The data used by
might represent either opening or closing rates (on a particular day of the m
may be â€˜bidâ€™ or â€˜offerâ€™ rates, or an average of the two rates. The next issu
â€˜timingâ€™. If we are trying to compare the return on a threeyear bond with the
investment on three oneyear bonds, then the yield data on the long bond for
be measured at exactly the same time as that for the short rate and the investme
should coincide exactly. In other words the rates should represent actual deali
which one could undertake each investment strategy.
238
Table 10.2 Summary Market Yield and Oneperiod Holding
Holding Period
Market Yield Return
Maturity Mean Variance Mean Varia
 
8.45 10.44
91 Day
9.09
9.45 906.
5 Year 8.60
9.89 1579.
8.80
9.99
10 Year
2608.
8.62
10.14 9.96
20 Year
˜˜ ˜ ˜
Reproduced by permission of Joseph Bisignano.
Empirical Evidence on the Term Structure
Table 10.3 Summary Market Yield and Onep
H
Market Yield
Sample
Period Maturity Mean Variance Mea
Jan. 1960Aug. 1986 9.16
6.32
3 Month
Jan. 1960Aug. 1986 6.50
6 Month 6.49
8.72
Jan. 1960Aug. 1986 1 Year 6.97
6.99 10.14
Jan. 1978Aug. 1986 10.79
2 Year(a) 11.01
5.79
Jan. 1960Aug. 1986 7.28
3 Year 7.12
9.35
Jan. 1960Aug. 1986 9.14
7.40 7.09
5 Year
July 1969Aug. 1986 9.08
7 Year(a) 8.94
6.38
7.48
Jan. 1960Aug. 1986 8.94
10 Year 6.77
Jan. 1960Aug. 1986 9.04
7.50 6.28
20 Year
Mar. 1977Aug. 1986 4.16
10.67
30 Year 10.84
Reproduced by permission of Joseph Bisignano.
11
10
9
8
7
6
5
4
3
2
1
I
0 I
I I
1 I I
I I 1
I I
1860 1920 19
(a)
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
1830 1910
(b)
Figure 10.2 Long Term (Rr) and Short Term (rr). (a) US Longterm Corporate Bon
and US Four to Sixmonth Commercial Paper Rate rr (Biannual Data 18571 to 198
Consolidated Yield R, and UK Threemonth Bank Bill Rate r, (Annual Data 1842 to 19
Shiller, (1989) Market Volatility. 0 1989 by the MIT Press. Reproduced by permission o
Bond prices are required to measure HPYs. However, if data on bond pri
available (e.g. on a monthly basis) researchers often approximate them from pub
on yields to maturity (Rr).The simplest case here is a perpetuity where the bond
C / R , (where C = coupon payment), but for redeemable bonds the calculati
complex and the approximation may not necessarily be accurate enough to
test the particular hypothesis in question. As we noted in the previous chapt
the expectations hypothesis in principle require data on spot yields. The latter
not available for maturities greater than about two years and have to be estim
data on yields to maturity: this can introduce further approximations. These dat
I
I I I
I I I
I I I 1
I
1860 1880 1900 1920 1940 1960 198
(a)
10
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
o y I I
1
1 I 1 1
1 1 I
I I
[
1830 1850 1870 1920 1940 1960 19
1900
(b)
Figure 103(a) and (b) Long Rates R, and the Perfect Foresight Long Rate Rf: US
Source: Shiller, (1989) Market Volatility. 0 1989 by the MIT Press. Reproduced by p
MIT Press
must be borne in mind when assessing empirical results but in what follows w
dwell on these issues.
10.2 PURE DISCOUNT BONDS
A great deal of empirical work has been undertaken using three and sixm
These are pure discount bonds (zero coupon bonds), their rates of return are
which are continuously quoted and are readily available for most industrialised
The term structure relationship under the EH and risk neutrality is extreme
For quarterly data, the sixmonth rate R, is a weighted average of threem
r t + j ( j = 0, 1):
+ (1 A)&rf+l + 4
R, = Art
where a0 = @/(l  A) and = A / ( l  A), or
a1
 A, or
where bo = 4/(l  A) and bl = 1/(1 )
where CO = 24, c1 = 1 and Rf+l = 2R,  rf+l.Since the variables on the RHS
equations are dated at time t they are uncorrelated with the RE forecast erro
hence OLS on these regression equations yields consistent parameter estim
G M M correction to the covariance matrix may be required for â€˜correctâ€™ stand
Under risk neutrality we expect
H o : a1 = 1 in (10.2)
H o : bl = 2 in (10.3)
H o : c1 = 1 in (10.4)
Regressions using either of the above three equations give similar inferen
estimated parameters are linear transformations of each other. It may not b
ately obvious but the reader should also note that the above three regressions
discussed in the previous chapter. For example, (10.3) is equivalent to a regres
perfect foresight spread S,(6â€™3â€™*= (1/2)Arf+1 on the actual spread S!6â€™3â€™ = R,
for the scaling factor of 2. (See equation (9.4) Chapter 9.) Equation (10.2) i
sion of the change in the long rate on the spread (since the sixmonth bond
threemonth bond after threemonths then rr+l  R, is equivalent to ?:Il 
l
notation of equation (9.46) of Chapter 9). Because n = 2m the perfect foresi
sion (equation (10.3)) yields identical inferences to the â€˜change in the long rat
(10.2), and hence here we need not explicitly consider the latter. It can als
demonstrated(â€™) that under the null of the EH, equation (10.4) is a regression o
on r, (as in equation (9.17), Chapter 9).
Various researchers have used one of the above equivalent formulations to
+ RE on three and sixmonth Treasury bills. On US quarterly data, 1963(1
Mankiw (1986) finds a1 = 0.407 (se = 0.4) which has the wrong sign. Sim
using US weekly data on Treasury bills, 19611988, finds bl = 0.04 (
Although for one of the subperiods chosen, namely the 19721979 period, S
bl = 1.6 (se = 0.34) and hence bl is not statistically different from 2. Both
that the expectations hypothesis is rather strongly rejected. The longshort sprea
is of little or no use in predicting changes in short rates for most subsamples
study and the value of 61 is rather unstable (it ranges between 0.33 and
various subperiods examined).
Jones and Roley (1983) using weekly data on newly issued US Treasury
particular attention to matching exactly the investment horizon of the two, t
(0.58) (0.088)
2 January 197013 September 1979, E' = 0.75, SEE = 0.98,
W(l) = 0.09 ( . ) = standard error
where is (a linear transformation of the) holding period yield (see footn
Wald test (a type of t test) for the restriction c1 = 1 is not rejected, thus sup
+
EH RE (W(1) = 0.09, critical value = 3.8). However, some fairly strong ca
order. First, a statistical point. It is likely that r, is nonstationary but bein
is not. This would lead to a nonstationary error term and hence the statistics
standard errors and the Wald statistic have nonstandard distributions and give
inferences. (This type of statistical problem was not prominent in the literature
this article was published.) Second, Jones and Roley find that if additional v
known at time t are added to equation (10.5) they are sometimes statistically sig
particular, net inflows of foreign holdings of US Treasury bills are found to be
significant, although others such as the unemployment rate, the stock of thre
month bills (i.e. market segmentation hypothesis) are not. Thus one can be cri
results on statistical grounds and it appears that there is a failure of the RE or
condition.
Mankiw (1986) seeks to explain the failings of the EH by considering the
that the expectations of r,+l by market participants as a whole consists of
average of the rationally expected rate (Efr,+l)of the smart money traders an
naive myopic forecasting scheme (i.e. noise traders) based simply on the cu
rate. If Ff+l denotes the market's average expectation then Mankiw assumes:
where 0 = w < 1. The EH then becomes
Substituting (10.6) in (10.7) and rearranging gives an equation similar to (10.3)
+
bl = (1 w)/(l  w) > 1. However, incorporating this mixed expectations sc
not rescue the expectations hypothesis since Mankiw finds that bl is negative.
The study of Mankiw (1986) fails to rescue the EH by assuming that
expectation is a weighted average of the expectations of the smart money
traders. In a later paper by Mankiw and Miron (1986) they examine the EH and
why the EH using three and sixmonth bills fails so abysmally post1915 b
to perform much better in the period 18901914. As with previous studies,
(10.3) on four subperiods (regimes) between 1915 and 1979, Mankiw and M
is approximately zero and the R2 is very low (< 0.06). For 18901914 (quar
and using the interest rate data for time loans by banks they find a distinct imp
+ 1.51 (R, 
Art+, = 0.57
(0.14) (0.18)
which can be represented as
ErAtf+l = O
that is, r,+l follows a random walk (strictly speaking, a martingale). If we
premium T , to the EH we have from (10.3):
where #? = 2. Using (10.9) and (10.10) we see that
(R,  rr) = T ,
Hence post1915 the spread would have no predictive power for future change
rates and would merely mimic movements in the term premium. More form
metricians will recognise that in (10.10) if we exclude T , then the (OLS) esti
coefficient on (R,  r , ) will be biased.
The relationship between the estimate of and the variance of E,(Ar,+l
Figure (10.4). When Ar,+l is unpredictable we have:
EfAr,+l = 0 and 02(E,Ar,+l)= 0
b b
hence plim = 0. The estimated value of approaches its true value of 2 as t
of E,Ar,+1 increases. Mankiw and Miron show that in a simple predictiv
for Arr+l
+
Ar,+1 = @1(L)r, @2(L)R,
I
2
Figure 10.4 p = Correlation Coefficient between T, and E,Ar,+,.Source: Mankiw
(1986). 1986 by the President and Fellows of Harvard College.
The Spread as an Optimal Predictor
Tests of the EH (with a constant term premium) between nperiod and rnperiod
are based on the fact that the spread Sin'"') is an optimal predictor of both futu
in short rates (the perfect foresight spread) and changes in long rates, as rep
the following two equations:
+p s y , + +
=a
sjn,m)* El
 RI") = a + /Y[rn/<n r n ) ˜ , ( ˜+ ˜ ) ] + qf
, y'R,
'
where
s 1
Sf(n.m)* = rn ( m )
(l/˜) A Rt+im
i=O
is the perfect foresight spread. Under the EH we expect /?= / '= 1 and if
I
information known at time t is included we expect y = y' = 0.
Campbell and Shiller (1991) use monthly US data from January 1952 t
1987. They used the McCulloch (1990) pure discount (zero coupon) bond yi
government securities which included maturities of 0, 1, 2, 3, 4, 5, 6 and 9
1, 2, 3, 4, 5 and 10 years. They find little or no support for the EH at the shor
maturity spectrum. Regressing the perfect foresight spread on the actual spread
and Shiller obtained slope coefficients @ ranging between 0 and 0.5 for matu
two years. For maturities greater than two years, the beta coefficients increase s
and are around 1 for maturities of four, five and 10 years. Campbell and Shill
therefore on the basis of this test, that the EH holds at the long end of th
spectrum but not at the short end. Regressing the change in longterm intere
the predicted spread yields negative p' coefficients which are statistically s
different from unity. The latter results hold for the whole maturity spectrum
various subperiods and hence reject the EH.
Cuthbertson (1996) uses London Interbank (offer) rates with maturities
1 month, 3 months, 6 months and 1 year to test the EH at the short end o
structure in the UK. The data was sampled weekly (Thursdays, 4 pm) and ran
January 1981 to 13 February 1992. Using equation (10.14) Cuthbertson could
the null, H o : j = 1, y = 0 which is consistent with the EH for the UK at th
3
of the maturity spectrum. (See also Hurn et a1 1996 and Cuthbertson et a1 (19
On balance the above results suggest that the EH has some validity. The s
some use in forecasting over long horizons (i.e. a weighted average of short ra
life n of the bond) but it gives the wrong signals over short horizons (i.e. the
+
the long rate between t and t rn, where m may not be large). The latter may
of the substantial 'noise' element in changes in long rates.
These results can be summarised on the term structure using pure discoun
follows:
For the US the expectations hypothesis does not perform well at the sh
0
the maturity spectrum (i.e. less than four years). In the 19501990 period
(i.e. an unbiased) predictor of future changes in short rates over long hor
than short horizons.
Failure of the EH at the short end of the maturity spectrum may be
0
deficiencies or to the presence of a time varying term premium.
More complex tests of the EH are provided in Chapter 14 but now we turn to
EH based on coupon paying bonds with a long term to maturity.
10.3 COUPON PAYING BONDS: BOND PRICES AN
THE YIELD TO MATURITY
+
If the EH RE holds and the term premium depends only on n (i.e. is tim
then the variance of the actual long rate should be less than the variability in
foresight long rate. Hence the variance ratio:
should be less than unity. However, in initial variance bounds tests by Sh
using US and UK (19561977) data on yields to maturity 19661977 and
(1983) on Canadian bonds, these researchers find that the VR exceeds unity.
was confirmed by Singleton (1980) who provided a formal statistical test of
he computed appropriate standard errors for VR) (also, see Scott 1991, page
If we assume that a time varying term premium T,'"' can be added to E
violation of the variance bounds test could be due to variability in T i n ) .If
case, the variability in the term premium would have to be large in order to
empirical results based on the variance bounds tests reported above.
However, there are some severe econometric problems with the early varia
studies on long rates discussed above. First, if the interest rate series have stoch
(i.e. are nonstationary) then their variances are not defined and the usual te
are inappropriate. Second, even assuming stationarity Flavin (1983) demon
there may be substantial small sample bias in the usual test statistics used. T
the latter problem Shiller (1989, Chapter 13) used two very long data sets f
(18571988) and the UK (18241987) to compare R, and the long moving
short rates, namely the perfect foresight spread RT. Graphs of R, and R ar T
Figures 10.3(a) and 10.3(b) and 'by eye' it would appear that the variability i
are roughly comparable and indeed the variance ratio (VR) for both the US
is only mildly violated.
However, the apparent nonstationarity of Rf towards the end of the sa
imply that sample variances are a poor measure of population variances. To
the latter, we can look at the following regression which uses a transforma
variables which are more likely to be stationary:
+ p(R,  Rr1) +
R  R,1 =
: Vf
b
For the USA we can accept the EH hypothesis, since is not statistically dif
unity but for the UK, the EH is rejected at conventional significance levels.
this long date set for the USA using the yields to maturity, the EH (with co
premium) holds up quite well but the results for the UK are not as supportive
10.3.2 Bond Prices
Scott (1991) has conducted variance bounds tests using bond prices. The
analogous to that of variance bounds tests on stock prices. The perfect fore
price (for term to maturity n) is given by:
C+M
C
P* z=

â€˜t
0
where kt+i = time varying discount rate, C = coupon payment and the redem
is M (see equation (9.6)). In Scottâ€™s â€˜simple modelâ€™ k,+i equals the shortterm i
rt+i, while in his â€˜second modelâ€™ the discount rate is equal to rt+i plus a term
that declines as term to maturity decreases. Scott calculates the perfect fore
price given in (10.18) for short, medium and longterm US Treasury bond
data, 19321985) and compares these series with the series for actual bond pri
+
maturities. Since Pt = P , q, where qr is the RE forecast error of future disc
we expect var(P,) 6 var(PT). Scott finds that the variance bounds test on bon
not violated for US data. It is also the case that in a regression of P: on P, w
coefficient of unity and hence in:
+ bP, + et
[P:  P t ] = a
we expect b = 0. Using US Treasury bond data, Scott finds that b = 0 for all the
he examined and his results are very supportive of the EH (with a time inv
premium).
10.3.3 Holding Period Yields
For HPYs the variance bound inequalities using Shillerâ€™s approximation form
< a2var(r,)
var(G,+l)
var(fit+l) 6 b2var(Art)
where a is a known constant and b = l/E (see Chapter 9). For the US and UK
in Figures 10.2(a) and 10.2(b) Shiller (1989, page 223) finds:
a(l?)/ua(r) = 1.14 18571987
USA:
a(H)/ua(r)= 1.57 18241986
UK:
a(l?)/aa(r)= 1.13 1924 1930
UK:
for other countries (USA, UK,Canada) the variance ratio often greatly exceede
is of the order 34 for maturities greater than five years. The above variance
may also be calculated using a ( A r f )rather than a ( r f )as the benchmark. For U
data Shiller (1989, page 269) finds that (10.20b) is not violated and hence sta
r, is a key issue in interpreting these results.
Next we discuss evidence on the zerobeta CAPM where the betas are assum
over time, but may vary for bonds of different maturities. There is a separate
for E,H![t), for each maturity band (i.e. for n = 1 , 2 , 3 , .. .) and the assump
allows the use of actual returns Hi:: in place of the unobservable expect
Bisignano (1987) checks that the chosen zerobeta portfolio (which consists
bills) has returns that are uncorrelated (orthogonal) with the return on the m
portfolio, The results for the model were most favourable for Germany. F
for fiveyear and 10year bonds Bisignano (Table 22) finds:
+ 0.249 R
(5)
H,+l = 0.739 :
,
(3.1) (3.58)
1978(2)1985(12) R2 = 0.137, DW = 1.93
+ 0.332 Rl:
H ! y / = 0.646 Rf+l
(1.69) (2.90)
1978(2)1985(2) R2 = 0.089, DW = 2.26
where the coefficient on R" is the beta for the bond of maturity n. In general th
Germany show that (i) systematic (nondiversifiable) risk as measured by bet
maturity (i.e. as n increases, b(") increases), (ii) all p(")sare less than unity a
sum of the two estimated coefficients on the E&+, and E,R?, in equation (1
unity as suggested by the theory. The above results hold when White's (1980
for heteroscedasticity is implemented (although no test or correction for high
correlation appears to have been undertaken). For the U K and USA the esti
p(")s is also statistically significant and rises with term to maturity n. Thu
consider a portfolio model which explicitly includes a risk premium, whi
on term to maturity, we find that expected holding period yields do have a
pattern. This is in contrast to the expost average HPY, which for the U K and U
exhibit systematic behaviour. But this is perfectly consistent, since the theory
expected returns at a point in time, conditional on other variables and not fo
sample averages of actual returns. For five and 10year bonds for the USA th
#1(5) = 0.71, p(lo) 0.92 and hence the risk premium for the USA is about
=
that for Germany.
The above evidence suggests that holding period returns are broadly in
with the zerobeta CAPM. Hence expected HPYs on long bonds depend on th
of such bonds where the latter varies with the term to maturity. Chapter 17
CAPM model to allow for a time varying term premium (as well as one that
term to maturity), that is we consider the case where T = T ( n ,z,).
For spot yields on three and sixmonth bills (i.e. pure discount bonds) the U
tends not to support the EH. For US spot yields on longerterm bonds (i.e. n
the spread tends to be an unbiased predictor for future changes in shor
thus supporting the EH at the long end of the maturity spectrum. For the U
test is broadly supported by the data, even at the short end.
For longer maturity coupon paying bonds, regression and variance bounds
on the yield to maturity, the holding period yield and bond prices tend to
EH on US data. On UK data variance bounds tests on HPYs and long ra
supportive of the EH yet the latter does not appear to be grossly at odds w
There is some evidence that the (zerobeta) CAPM may provide a usefu
holding period yields.
Coupon paying bonds with long maturities are rather like stocks (except th
payment is known and largely free of default risk). We therefore have som
paradox in that longterm bonds broadly conform to the EMH whereas stocks
both types of asset are traded in competitive markets. Similarly, on the evid
us, short maturity bonds (bills) do not conform to the EMH based on the US
tentative hypothesis to explain the different results for longterm bonds and st
noise traders are more active in the latter than in the former market. It may
case that the greater volatility in short rates relative to long rates noted in S
may imply that agents perceive that taking positions at the short end is fairl
hence a time varying risk premium could explain the failure of the EH and t
the short end. The modelling of time varying risk premia is examined in Cha
APPENDIX 10.1 IS THE LONG RATE A MARTINGA
In this appendix we briefly examine (i) the conditions under which the long rate is
and (ii) the use of forward rates in testing hypotheses about the term structure.
Is the Long Rate a Martingale?
In some of the early empirical work on the term structure researchers focused on whe
rate behaved as a martingale. This evidence will not be examined in detail but the basic
important early strand in the term structure literature will be set out. To investigate th
152,) =
under which longterm interest rates exhibit a martingale property, that is E,(R,+I
the EH applied to spot yields:
where a term premium TI"' on the nperiod bond has been included. Leading (1) onepe
+
the nperiod rate at t 1 is given by:
1
+ [Er+lrr+n  rrl
+ [T!;:  T 9
= n'[A + B + C +D]
where A = RE forecast error: qf+l = rf+l  E f r f + l ,B = revisions to forecasts: w!yl =
Err,+,, C = Ef+lrf+n r, and D = change in the term premium: Ti:),  TI"'.

There is no guurantee that 'C'is either a constant or zero. However, for large
C/n may be small relative to the sum of the other terms, although this is not guarant
speaking we need to assume a transversality condition, such that C / n + 0. If the te
is constant and the term 'C' is small (i.e. approaches zero) then we can write (3) as
where pf+l is the weighted sum of error terms {qf+l, w:yl) in ( 3 ) and hence Ef(pf
follows immediately from (4) that under these conditions Rj"' is a martingale, that
RI"' = 0.
+
According to (3) the only reason we get a change in R(") between t and t 1 is:
+
a nonzero forecast error for the short rate at c 1 (term 'A'),
+
revisions to expectations between t and t 1, about short rates in one or more fu
that is term B (e.g. 'news' of a credible counterinflationary policy might imply a
rf+j in future periods and hence a decrease in some or all of the (Er+lrf+j  Ef
a change in the agent's views about Ef+lrf+n(i.e. term 'C'),
a change in the agent's perceptions of the term premium required on longterm
term 'D).
The first three items in the above list involve the arrival of new information or 'news' an
the monetary authorities cannot systematically influence long rate. At best, the authorit
cause 'surprise' changes in the long rate by altering expectations of future short ra
instituting a tough antiinflation package). If the authorities could systematically influe
premium then it would have some leverage on long rates. However, it is difficult to
authorities might accomplish this objective by, for example, open market operations. He
+
cited implication of the above analysis is that under the EH RE the authorities canno
yield curve.
Empirical tests of the martingale hypothesis are based on (4) and usually involve a r
AR,':: on informatiod dated at time c or earlier Q. In general AR!:: is found to depend
in $2, although the explanatory power is low (e.g. Pesando (1983) using US data). How
is close to a martingale process this is consistent with the evidence that long rates ten
conform to the EH (with a time invariant term premium).
structure. (The concepts used will also be useful in analysing the forward foreign exch
in Part 4.) The methodology employed is shown by using simple illustrative example
follows the notation in Fama (1984).
Consider the purchase of a twoperiod (zero coupon) bond. Such a purchase autom
you in to a fixed interest rate in the second period. At time â€˜tâ€™ the investor know
oneyear spot interest rate, and R(2, t ) the twoyear spot rate (expressed at an annual
he can calculate the implicit interest rate he is receiving between years 1 and 2. Deno
+ +
as the forward rate applicable for years t y to t n. Then the forward rate between
+
and t 2 is given by:
+ R(2, ?)I2 = [l + R(1, t>][l + F(2, 1 : t ) ]
[l
F(2, 1 : t ) is the implicit forward rate you â€˜lock inâ€™ when purchasing a twoyear
ranging (1):
+ +
F ( 2 , l : t ) = [(l R(2, t)I2/(1 R(1, t))]  1
#
For example, if you purchase a twoyear bond at R(2, t) = 10 percent per annum a
9 percent per annum then you must have â€˜locked inâ€™ to a forward rate of 11.009 percen
in the second year. Note that (4)is an â€˜identityâ€™, there is no economic or market behavio
If we let lower case letters denote continuously compounded rates (i.e. r(n, t) = ln[
then (1) and (2) can be expressed as linear relationships and
f(2, 1 : t ) = 2r(2, t )  r(1, t )
For a threeperiod horizon we have
+ 2f(3,1 : t )
3r(3, t ) = r(1, t )
+ 1 to t + 3 and hence a
where f(3, 1 : t) is the implicit forward rate for the years t
investment horizon of 3  1 = 2 years. Note also that
+f(3,2 :t )
343, t ) = 2r(2, t )
Equations (4) and ( 5 ) can be used to calculate the implicit forward rates f(3, 1 : t
from the observed spot rates. Implicit forward rates can be calculated for any horiz
appropriate recursive formulae if data on spot rates are available. From the above e
following recursive equation is seen to hold:
We now return to the twoperiod case, and examine variants of the expectations hypo
in terms of forward rates. If the EH plus a risk premium T(2, t) holds then
Comparing (3) and (7) we see that
Hence the implicit forward rate is equal to the marketâ€™s expectation of the return on
bond, starting one period from now, plus the term premium. If T(2, t) = 0 then (8)
with the pure expectations hypothesis. The PEH therefore implies that the implicit fo
an unbiased predictor of the expected future spot rate. Subtracting r(1, t) from both sid
Tests of the PEH (i.e. T = 0), or the EH (T = constant) or the LPH (i.e. T = T"),
assume a time invariant term premium, are usually based on regressions of the form:
+ 1)  r(1, t ) = a + P[f(2,1 : t )  4,r ) ] +
r(1, t qr+1
where we expect a = T and fi = 1. Thus under the pure expectations hypothesis w
forward premium to be an unbiased predictor of change in the future spot rate (i.e
a = 0). Under a constant term premium we also expect that no other variables dated
are statistically significant in (10). Note, however, that if T is nonconstant and correla
forward premium, then OLS on (10) yields inconsistent (biased) estimates. Similar
(10) apply to implicit forward rates over different horizons.
Mishkin (1988) examines equations like (10) for short horizons, namely for two
horizons, using data on US Treasury bills over the period 19591982. He finds t
s
month ahead forecasts = 0.40 (se = 0.11) and R2 = 0.11 but as the horizon is exten
r(1, t + m )  r(1, t ) , m = 3 , 4 , 5 , 6 ) the forward premium generally has little or no pred
(i.e. $ * 0 statistically). In all cases Mishkin finds he can reject Ho:# 1 and this
=I
with the regression tests reported in the main text, which tend to reject the expectation
on US data at the very short end of the maturity spectrum. Fama (1987) presents resul
horizons using (approximate) spot rates on US Treasury bills from one to five years'
finds that one can reject H o : p = 0 for horizons greater than one year, although in m
also finds H o : p # 1 is rejected. Hence the EH (with a constant term premium) is
invalid. However, the forecast power of regressions like (10) improve as the horizon is
+
For example, for fouryear changes in oneyear spot rates r(1, t 4)  r(1, t ) the forw
explains 0.48 percent of the variability in the dependent variable (see Figure 10.A1
not reject H o : /3 = 1. The above results using forward rates are consistent with those
this chapter, namely that at the very short end (less than four years) the EH perform
improves somewhat at longer maturities. For further evidence on these types of tests
of the term premium to forecast inflation, see inter alios Mishkin (1988, 1990) and F
646566676869707172737475767778798081
Figure 10A1 Fouryear Change in Spot Rate (Solid Line) and Forecast Change (D
using the ForwardSpot Spread. Source: Fama and Bliss (1987). Reproduced by perm
American Economic Association
equation (10) will not yield an estimate of = 1 in the sample.
The presence of the Peso problem implies that the forward rate is a biased
+
E r r ( l ,t 1) within the sample period examined. The Peso problem may be viewed
finite sample problem or a â€˜missing variableâ€™. If we had a long enough data set it is (ju
able that over the whole sample, positive and negative â€˜Peso effectsâ€™ would cancel. A
one could also argue that we obtain the result / # 1 because the â€˜missing variableâ€™ in th
l
equation (10) is a term premium which might vary over time as the perceivedfuture b
the monetary authorities alters. If the variability in the term premium is correlated with
premium, then the OLS estimate of is biased.
ENDNOTE
1. This is most easily demonstrated using continuously compounded spot ra
We have:
The logarithmic HPY is
The null hypothesis is that the HPY is equal to the riskfree (threemonth
= (1/4)rt
Using (3) and (4):
2R,  rr+l = rf
Equation (5) is equivalent to (10.4) in the text under the null of t
similar equation to (5) can be derived using simple interest rates (i.e.
+
Pj6â€™)/(Pi6), = 4(M  P,â€˜3â€™)/P!3â€™ we use the approximation (1 r,+1/4
if
rf
This is left as a simple exercise for the reader.
FURTHER READING
Most basic texts on financial markets and portfolio theory provide an intro
alternative measures of bond returns together with theories and evidence o
structure. More practitioner based are Fabozzi (1993) and Cooke and Rowe
the USA and for the UK, Bank of England (1993). At a more technical level, a
of tests of the term structure can be found in Section I1 of Shiller (1989), p
Chapters 12, 13 and 15, and Melino (1988).
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PART 4
I
The Foreign Exchange Market
The behaviour of the exchange rate particularly for small open economies tha
a substantial amount of international trade has been at the centre of macr
policy debates for many years. There is no doubt that economistsâ€™ views abo
exchange rate system to adopt have changed over the years, partly because ne
has accumulated as the system has moved through various exchange rate reg
worthwhile briefly outlining the main issues.
After the Second World War the Bretton Woods arrangement of â€˜fixed but
exchange ratesâ€™ applied to most major currencies. As capital flows were smal
subject to government restrictions, the emphasis was on price competitiveness
that had faster rates of inflation than their trading partners were initially allowed
from the International Monetary Fund (IMF) to finance their trade deficit. If a â€˜fu
disequilibriumâ€™ in the trade account developed then after consultation the defi
was allowed to fix its exchange rate at a new lower parity. After a devaluatio
would also usually insist on a set of austerity measures, such as cuts in public e
to ensure that real resources (i.e. labour and capital) were available to switch
growth and import substitution. The system worked relatively well for a numb
and succeeded in avoiding the reemergence of the use of tariffs and quotas tha
a feature of 1930s protectionism.
The US dollar was the anchor currency of the Bretton Woods system and the
initially linked to gold at a fixed price of $35 per ounce. The system began to c
strain in the middle of the 1960s. Deficit countries could not persuade surplus c
mitigate the competitiveness problem by a revaluation of the surplus countries
There was an asymmetric adjustment process which invariably meant the defi
had to devalue. The possibility of a large step devaluation allowed speculat
way betâ€™ and encouraged speculative attacks on those countries that were pe
have poor current account imbalances even if it could be reasonably argued
imbalances were temporary. The USA ran large current account deficits which
the amount of dollars held by third countries. (The US extracted seniorage by th
Eventually, the amount of externally held dollars exceeded the value of gold in
when valued at the â€˜official priceâ€™ of $35 an ounce. At the official price, free co
of dollars into gold became impossible. A twotier gold market developed (w
market price of gold very much higher than the official price) and eventually co
the Bretton Woods system, and floated their currencies.
In part, the switch to a floating exchange rate regime had been influenced b
economists. They argued that control of the domestic money supply woul
desired inflation and exchange rate path. In addition, stabilising speculation
agents would ensure that large persistent swings in the real exchange rate an
price competitiveness could be avoided by an announced credible monetary poli
in the form of money supply targets). Some of these monetary models of exc
determination will be evaluated in Chapter 13.
Towards the end of the 1970s a seminal paper by Dornbusch (1976) sho
FOREX dealers are rational, yet goods prices are â€˜stickyâ€™, then exchange rate ov
could occur. Hence a contractionary monetary policy could result in a lo
competitiveness over a substantial period with obvious deflationary consequen
trade, output and employment. Although in longrun equilibrium the econo
move to full employment and lower inflation, the loss of output in the transi
could be more substantial in the Dornbusch model than in earlier (nonrational
models, which assume that prices are â€˜flexibleâ€™.
The volatile movement in nominal and real exchange rates in the 1970s led
to consider a move back towards more managed exchange rates which was
reflected in the workings of the Exchange Rate Mechanism (ERM) from the e
European countries that joined the ERM agreed to try and keep their bilatera
rates within announced bands around a central parity. The bands could be either
percent) or narrow ( 2.5 percent). The Deutschmark (DM) became the ancho
k
In part the ERM was a device to replace national monetary targets with Germa
policy, as a means to combat inflation. Faced with a fixed exchange rate again
a high inflation country has a clear signal that it must quickly reduce its rate of
that pertaining in Germany. Otherwise, unemployment would ensue in the hig
country which would then provide a â€˜painful mechanismâ€™ for reducing inf
ERM has a facility for countries to realign their (central) exchange rates in th
fundamental misalignment. However, when a currency hits the bottom of its ba
of a random speculative attack, all the Central Banks in the system may try a
the weak currency by coordinated intervention on the FOREX market.
The perceived success of the ERM in reducing inflation and exchange rate v
the 1980s led the G10 countries to consider a policy of coordinated interventi
Plaza and Louvre accords) to mitigate â€˜adverseâ€™ persistent movements in their o
cies. The latter was epitomised by the â€˜inexorableâ€™ rise of the US dollar in
which seemed to be totally unrelated to changes in economic fundamentals. Rec
economists have suggested a more formal arrangement for currency zones an
bands for the major currencies, along the lines of the rules in the ERM.
Very recently the ERM itself has come under considerable strain. Increas
mobility and the removal of all exchange controls in the ERM countries facilita
ulative attack on the Italian lira, sterling and the franc around 16 September 19
as Black Wednesday). Sterling and the lira left the ERM and allowed their cu
monetary union in Europe are complex but one is undoubtedly the desire t
the problem of floating or quasimanaged exchange rates. One of the main t
part of the book is to examine why there is such confusion and widespread d
the desirability of floating exchange rates. It is something of a paradox that
are usually in favour of â€˜the unfettered marketâ€™ in setting â€˜pricesâ€™ but in the
exchange rate, perhaps the key â€˜priceâ€™ in the economy, there are such diverge
This section of the book provides the analytic tools and ideas which will
reader to understand why there is a wide diversity of views on what drives th
rate. We discuss the following topics:
the interrelationships between covered and uncovered interest parity, purcha
0
parity and real interest rates
testing for efficiency in the spot and forward markets and whether market
0
are rational when setting FOREX â€˜pricesâ€™
whether economic fundamentals drive the exchange rate and under what
0
exchange rate overshooting might occur
the impact of â€˜newsâ€™ on the volatility of exchange rates, the socalled Pe
0
and the influence of noise traders in the FOREX market
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11
I
Basic Arbitrage Relationships in
FOREX Market
This chapter outlines the basic concepts needed to analyse behaviour in t
market. These concepts are first dealt with sequentially, in isolation, before dis
interrelationship between them.
11.1 COVERED AND UNCOVERED INTEREST PARITY
There are two main types of â€˜dealâ€™ on the foreign exchange (FOREX) market.
the â€˜spotâ€™ rate, which is the exchange rate quoted for immediate delivery of th
to the buyer (actually, delivery is two working days later). The second is t
rate, which is the guaranteed price agreed today at which the buyer will take
currency at some future period. For most major currencies, the highly traded
are for one to six months hence and, in exceptional circumstances, three to
ahead. The marketmakers in the FOREX market are mainly the large banks.
The relationship between spot and forward rates can be derived as follows. A
a UK corporate treasurer has a sum of money, LA, which he can invest in the
USA for one year, at which time the returns must be paid to his firmâ€™s UK sh
Assume the forward transaction is riskless. Therefore, for the treasurer to be
as to where the money is invested it has to be the case that returns from inve
UK equal the returns in sterling from investing in the USA. The return from
+
in the UK will be A ( l r) where r is the UK rate of interest. The return
from investing in the USA can be evaluated using the spot exchange rate S (E
forward exchange rate F for one year ahead. Converting the A pounds into d
+
give us A / S dollars which will increase to (A/S) (1 r*) dollars in one yearâ€™s
is the US rate of interest. If the forward rate for delivery in one yearâ€™s time
then the UK corporate treasurer can â€˜lock inâ€™ an exchange rate today and re
+ r)F in one yearâ€™s time. (We ignore default risk.) Equalis
certainty, f(A/S)(l
we have:
+
+
A ( l r ) = (A/S)(l r*)F
which becomes
F
 + r
l
1+r*
S
where r is measured as a decimal. The above equations represent the â€˜cove
parityâ€™ (CIP) condition which is an equilibrium condition based on riskless a
CIP doesnâ€™t hold then there are forces which will restore equilibrium. For e
r > r* and f = s then US residents would purchase UK securities pushing
up and interest rates down. US residents would also have to buy sterling sp
dollars forward, hence spot sterling would appreciate (i.e. s falls) and f woul
tending to restore equality in (11.3). In fact, because the transaction is riskles
+
dealers will tend to quote a forward rate that is equal to s r*  r . Use of t
rate eliminates risk from future exchange rate changes as the forward rate is ag
even though the transaction takes place in (say) one yearâ€™s time.
Uncovered Interest Parity (UIP)
We can repeat the above scenario but this time assuming the UK corporat
is willing to take a guess on the exchange rate that will prevail in one yearâ€™s
when he converts his dollar investment back into sterling. If the corporate treas
neutral, he is concerned only with the expected return from the two alternative i
and he will continue to invest in the US rather than the UK until expected
equalised
+
S ; + i / S t = (1 rr)/(l+ r:>
or approximately:
 st = rr  r;
where sf+1= In S,+l. above relationship is the condition for equilibrium on
The
account under the assumption of risk neutrality. The UK corporate treasurer
he is taking a risk because the value of the exchange rate in one yearâ€™s time is
however, he ignores this risk when undertaking his portfolio allocation decisi
We could of course relax the risk neutrality assumption by invoking the C
the UK treasurer the riskfree rate is r and the expected return on the â€˜round
investment in the US capital market is
The CAPM then predicts
where pi is the beta of the foreign investment (which depends on the covarian
the market portfolio and the US portfolio) and E&â€œ+, is the expected return on
portfolio of assets held in all the different currencies and assets. The RHS o
a measure of the risk premium as given by the CAPM. Loosely speaking, re
like (11.7) are known as the International CAPM (or ICAPM) and this â€˜glob
is looked at briefly in Chapter 18. For the moment notice that in the context
the CAPM, if we assume pj = 0 then (11.7) reduces to UIP.
by risk neutral speculators and that neither risk averse â€˜rational speculators
traders have a perceptible influence on market prices.
11.2 PURCHASING POWER PARITY (PPP)
PPP is an equilibrium condition in the market for tradeable goods and for
building block for several models of the exchange rate based on economic fun
It is a â€˜goods arbitrageâ€™ relationship. For example, if applied solely to th
economy it implies that a â€˜Lincoln Continentalâ€™ should sell for the same pr
York City as in Washington DC (ignoring transport costs between the two citie
are lower in New York then demand would be relatively high in New York
Washington DC. This would cause prices to rise in New York and fall in Wash
hence equalising prices. In fact the threat of switch in demand would be su
wellinformed traders to make sure that prices in the two cities were equal. P
the same arbitrage argument across countries, the only difference being tha
convert one of the prices to a â€˜common currencyâ€™ for comparative purposes.
If domestic tradeable goods are perfect substitutes for foreign goods and
market is â€˜perfectâ€™ (i.e. there are low transactions costs, perfect information
flexible prices, no artificial or government restrictions on trading, etc.), then â€˜m
or arbitrageurs will act to ensure that the price is equalised in a common cu
PPP view of price determination assumes that domestic (tradeable) goods pri
subject to arbitrage and will therefore equal the price in domestic currency
foreign goods. If the foreign currency price is P* dollars and the exchange rat
as the domestic currency per unit of foreign currency (say sterling per dollar) is
price of a foreign import in domestic currency (sterling) is (SP*). Domestic p
a close (perfect) substitutes for the foreign good and arbitrageurs in the market
that domestic (sterling) prices P equal the import price in the domestic curren
P = SP* (strong form)
or
p=s+p*
+ P*
P =S (weak form)
or
Ap=As+Ap*
where lower case letters indicate logarithms (i.e. p = lnP, etc). If domestic
higher than P*S, then domestic producers would be priced out of the market. Al
if they sold at a price lower than SP* they would be losing profits since they b
can sell all they can produce. This is the usual perfect competition assum
applied to domestic and foreign firms.
imports) to domestically produced substitutes (or vice versa).
The real exchange rate is a measure of the price competitiveness or th
domestic relative to foreign goods. The price of imports into the domestic ec
the UK, is P*S in the domestic currency (sterling). This can be compared wit
of goods produced domestically in the UK, P, to give the real exchange rate
S = P*S/P
'
A similar argument applies had we considered the price of exportsfrom the U
of the foreign currency PIS and compared this with the price of competing g
US, P*. It follows from the definition of the real exchange rate that if PPP hol
real exchange rate or price competitiveness remains constant.
If goods arbitrage were the only factor influencing the exchange rate then th
rate would have to obey PPP:
s=pp*
or
AS = A p  A p *
Hence movements in the exchange rate would immediately reflect different
inflation and the latter is often found to be the case in countries suffering f
inflation (e.g. some Latin American countries, economies in transition in East
and Russia around 1990). In contrast, one might expect goods arbitrage to w
imperfectly in moderate inflationary periods in complex industrial economies w
variety of heterogeneous tradeable goods. Hence PPP may hold only in the ve
in such economies.
There have been a vast number of empirical tests of PPP with only the
using the statistical technique of cointegration (see Chapter 20). Time does n
examination of these studies in detail and the reader is referred to a recent com
study by Ardeni and Lubian (1991) who examine PPP for a wide range of
of industrialised nations (e.g. USA, Canada, UK, France, Italy). They find n
that relative prices and the exchange rate are 'linked' when using monthly da
post1945 period. However, for annual data over the longer time span of 1878
do find that PPP holds although deviations from PPP (i.e. changes in the rea
rate) can persist for a considerable time. Hence if we were to plot the PPP ex
denoted Sp where:
sp = P / P *
against the actual exchange rate S,then although there is some evidence from co
analysis that S, and Sp move together in the long run, we find that they can a
substantially from each other over a run of years. It follows that the real exc
is far from constant (see Figures 11.1 and 11.2).
The evidence found by Ardeni and Lubian reflects the difficulties in testin
run equilibrium relationships in aggregate economic time series even with a
span of data. Given measurement problems in forming a representative index o
! lMO
0
$ 100.0
?
t
s
= 80.0
B
60.O
73 74 75 76 77 78 79 80 8 82 83 04 85 86 87 88 89 90 91
1
Year
and Real (+ + +
Figure 11.1 The Evolution of the DollarPound Nominal ( 
)
Rate, 1973 1991. Source: Pilbeam (1992). Reproduced by permission of Macmillan P
120.0
110.0
100.0
fa 90.0

g 80.0
5 70.0
60.0
50.0
40.0
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
Year
and Real (+ + +) Ex
Figure 11.2 The Evolution of the YenDollar Nominal (
)
1973 1991. Source: Pilbeam (1992). Reproduced by permission of Macmillan Press L
goods, it is unlikely that we will be able to get more definitive results in the
One's view might therefore be that the forces tending to produce PPP are r
although in the very long term there is some tendency for PPP to hold (see
Kaminsky (1991) and Fisher and Park (1991)). The very long run here could
years. Hence in the models of exchange rate determination discussed in Chap
is often taken as a Zongrun equilibrium condition.
resulting equation which explains domestic prices is
where y  7= deviation of output from its natural rate, f = â€˜wage pushâ€™ fa
exogenous growth in real wages, X p = growth in labour productivity. It follow
will hold if
++
f a2(y  7) 0
bl(XW  X p ) =
Hence PPP holds either when output is at its natural rate or â€˜wage pushâ€™ facto
or real wages grow at the rate of labour productivity. One can see that the
(11.15) involve rather complex, slowly varying longterm economic and so
forces and this may account for the difficulty in empirically establishing PPP
very long span of data.
11.3 INTERRELATIONSHIPS BETWEEN CIP, UIP AN
Forward Rate Unbiasedness and Real Interest Parity
If CIP and UIP hold simultaneously then this implies that the forward rate is a
predictor of the future spot rate (see Table 11.1). The latter condition is referr
forward rate unbiasedness (FRU) property:
Note that unbiasedness holds regardless of the expectations formation process
(i.e. one need not assume rational expectations) but it does require risk neutra
Table 11.1 Relationship between CIP, UIP, FRU, RIP and PPP
Forward Rate Unb
Covered Interest Parity (CIP)
fi  sI = ( r  r*)f fi = $;+I
Uncovered Interest Parity (UIP)
sF+,  st = ( r  r*),
Purchasing Power
Real Interest Rate Parity (RIP)
(Fisher Hypothesis)
r,  Ap: = r:  Apt *e
Real Exchange Rate
Cf = PI  p:  Sf
(i) As:+, = Efs,+1  s,.
We could have started with FRU. Under risk neutrality, if (11.16) did not
would be (risky) profitable opportunities available by speculating in the forward
an efficient market (with risk neutrality) such profits should be instantaneously
so that (1 1.16) holds at all times. Whether (1 1.16) holds because there is active
in the forward market or because CIP holds and all speculation occurs in the s
so that UIP holds doesnâ€™t matter for the EMH. The key feature is that th
unexploited profitable opportunities.
If UIP holds and there is perfect goods arbitrage in tradeable goods
periods then:
It follows that
r,  Ap;+l = r;  Ap;Tl
and hence
+ UIP jReal Interest Rate Parity (RIP)
PPP
Again, it is easily seen from Table 11.1 that if any two conditions from the
PPP and RIP are true then the third is also true.
11.4 SUMMARY
In the real world one would accept that CIP holds as here arbitrage is riskless.
tentatively accept that UIP could hold in all time periods since financial capit
mobile and speculators (i.e. FOREX dealers in large banks) may act as if th
neutral (after all itâ€™s not their money they are gambling with, but the bank
one would then expect FRU to hold in all periods. In contrast, given rela
information and adjustment costs in goods markets one might expect PPP to
over a relatively long time period (say, 510 years). Indeed in the short run
in the real exchange rate are substantial. Hence even under risk neutrality (i.e.
one might take the view that expected real interest rate parity would only h
rather long horizon. Note that it is expected real interest rates that are equalised
if over a run of years agents are assumed not to make systematic errors when
price and exchange rate changes then, on average, real interest rates would b
in actual expost data.
The RIP condition also goes under the name of the international Fisher
It may be considered as an arbitrage relationship based on the view that â€˜c
investment funds) will flow between countries to equalise the expected real ret
country. One assumes that a representative basket of goods (with prices p and
country gives equal utility to the international investor (e.g. a â€˜Harrodsâ€™ ham
UK is perceived as equivalent to a â€˜Sakâ€™s hamperâ€™ in New York). Internationa
then switch funds via purchases of financial assets or by direct investment to
he will have to exchange sterling for dollars at the end of the investment period
if PPP holds over his investment horizon then he can obtain the same purcha
(or set of goods) in the US as he can in the UK.
From what has been said above and oneâ€™s own casual empiricism about the
it would seem highly likely that CIP holds at most, if not at all, times. Ag
FOREX market are unlikely to â€˜missâ€™ any riskfess arbitrage opportunities. O
might accept that it is the best approximation one can get of behaviour in
marketâ€™: FOREX dealers do take quite large open speculative positions, at
main currencies, almost minute by minute. FOREX dealers who are â€˜on t
and actively making the market may mimic risk neutral behaviour. Provided
available (i.e. no credit limits) one might then expect UIP to hold in acti
FOREX markets. However, since information processing is costly one might
and even CIP to hold only in actively traded markets. In â€˜thinâ€™ markets (e.g. fo
rupee) CIP and UIP may not hold at all times. Because â€˜goodsâ€™ are heterog
because here information and search costs are relatively high, then PPP is lik
at best, in the very long run. Hence so will RIP.
It is worth emphasising that all the relationships given in Table 11.1 are arb
librium conditions. There is no direction of causality implicit in any of these re
They are merely â€˜no profitâ€™ conditions under the assumption of risk neutrali
the case of UIP it cannot be said that interest differentials â€˜causeâ€™ expectations
in the exchange rate (or vice versa). Of course our model can be expanded
other equations where we explicitly assume some causal chain. For example,
assert (on the basis of economic theory and evidence about government beha
exogenous changes in the money supply by the central bank â€˜causeâ€™ changes
interest rates. Then, given the UIP condition, the money supply also â€˜cause
in the expected rate of appreciation or depreciation in the exchange rate. The
change in the money supply influences both domestic interest rates and th
change in the exchange rate. Here â€˜moneyâ€™ is causal (by assumption) and th
in the UIP relationship are jointly and simultaneously determined.
In principle when testing the validity of the three relationships UIP, CIP
or the three conditions UIP, PPP and RIP we need only test any two (ou
since if any two hold, the third will also hold. However, because of data avai
the different quality of data for the alternative variables (e.g. Fr is observabl
frequently, but P and P are available only infrequently and may be subje
t :
number measurement problems) evidence on all three relationships in each se
investigated by researchers.
APPENDIX 11.1 PPP AND THE WAGEPRICE SPIR
In the wages version of the expectations augmented Phillips curve, wage inflation, W,i
by price inflation, p , and excess demand (y  7).To this we can add the possibility
may push for a particular growth in real wages xw based on their perceptions of their
There may also be other forces f (e.g. minimum wage laws, socioeconomic forces
influence wages. It is often assumed that prices are determined by a markup on uni
A dot over a variable indicates a percentage change and x,, is the trend growth ra
productivity. Imports are assumed to be predominantly homogeneous tradeable goo
cultural produce, oil, iron ore, coal) or imported capital goods. Their foreign price is
markets and translated into domestic prices by the following (identity):
+s
P, = P*
Substituting (1) into (2) we obtain
Equation (3) is the price expectations augmented Phillips curve (PEAPC) which
inflation to excess demand ( y  7 )and other variables. If we make the reasonable assu
in the long run there is no money illusion (al = 1, that is a vertical long run PEAPC)
homogeneity with respect to total costs ( b l + b2 = 1) then (3) becomes
P= bt [ f + bdxw  X,) + a2(y  ,)I + (P* + $)
161
If we assume that in the long run the terms in square brackets are zero then the long
influences on domestic prices are P* and S, and PPP will hold, that is:
P=i)*+$
A rise in foreign prices P* or a depreciation of the domestic currency (S rises) leads
domestic prices (via equation (2)) which in turn leads to higher wage inflation (via e
The strength of the wageprice feedback as wage rises lead to further price rises, etc.
the size of a and b l . Under the homogeneity assumptions a1= 1 and bl + 6 2 = 1, th
1
the feedback is such that PPP holds in the long run. That is to say, a 1 percent deprec
domestic currency (or rise in foreign prices) eventually leads to a 1 percent rise in th
domestic price index, ceterisparibus. Of course, PPP will usually not hold in the shor
model either because of money illusion a < 1 or less than full mark up of costs bl
1
because of the influence of the terms in square brackets in equation (4).
12
I
1
Testing CIP, UIP and FRU
In this chapter we discuss the methods used to test covered and uncovered int
and the forward rate unbiasedness proposition, and find that there is stron
in favour of covered interest parity for most maturities and time periods st
evidence in favour of uncovered interest parity is somewhat mixed although the
of making supernormal profits from speculation in the spot market seems remo
the unbiasedness of the forward rate generally find against the hypothesis and
some tests using survey data to ascertain whether this is due to a failure of ris
or RE. Since only two out of the three conditions CIP, UIP and FRU are indep
the simultaneous finding of a failure of both FRU and UIP is logically cons
tests discussed in this chapter may be viewed as 'single equation tests'. Mo
tests of UIP and FRU are possible in a multivariate (VAR) framework whic
account of the nonstationarity in the data. The latter test procedures are d
Part 5.
12.1 COVERED INTEREST ARBITRAGE
Let us consider whether it is possible, in practice, to earn riskless profits v
interest arbitrage. In the real world the distinction between bid and offer rat
interest rates and for forward and spot rates is important when assessing pot
opportunities. In the strictest definition an arbitrage transaction requires no
agent borrows the funds. Consider a UK investor who borrows U in the E
market at an offer rate rfo. At the end of the period the amount owing will be
where A = amount of borrowed (Es), C = amount owed at end of period (Es)
rate (proportionate) on Eurosterling loan and D = number of days funds are
Now consider the following set of transactions. The investor takes his U and
sterling for dollars at the bid rate Sb in the spot market. He invests these d
Eurodollar deposit which pays the bid rate r:. He simultaneously switches th
into sterling at the forward rate Fo (on the offer side). All these transactions
instantaneously, The amount of sterling he will receive with certainty at the en
Note that the convention in the USA and followed in (12.2) is to define â€˜one y
days when reducing annual interest rates to their daily equivalent. The percen
return ER to investing &A in US assets and switching back into sterling on
market is therefore given by
[;:[  [I+&]]
E R ( f + $) = 100  = 100  1 + r ; O
;]
which is independent of A. Looking at the covered arbitrage transaction from
view of a US resident we can consider the covered arbitrage return from mo
$s into sterling assets at the spot rate, investing in the UK and switching back
at the current forward rate. This must be compared with the rate of return he
by investing in dollar denominated assets in the US. A similar formula to th
(12.3) ensues and is given by
[S[ 3 [l+rGi]l
3 
f ) = 100  1 + r ; 
ER($ +.
Given riskless arbitrage one would expect that ER(f + $) and ER($ + E) ar
.
Covered arbitrage involves no â€˜price riskâ€™, the only risk is credit risk due to
the counterparty to provide either the interest income or deliver the forward
we are to adequately test the CIP hypothesis we need to obtain absolutely si
â€˜dealingâ€™ quotes on the spot and forward rates and the two interest rates. There
many studies looking at possible profitable opportunities due to covered intere
but not all use simultaneous dealing rates. However, Taylor (1987, 1989a) ha
the CIP relationship in periods of â€˜tranquillityâ€™ and â€˜turbulenceâ€™ in the foreig
market and he uses simultaneous quotes provided by foreign exchange and mo
brokers. We will therefore focus on this study. The rates used by Taylor rep
offers to buy and sell and as such they ought to represent the best rates (h
lowest offer) available in the market, at any point in time. In contrast, rates
the Reuters screen are normally â€˜for information onlyâ€™ and may not be act
rates. Taylor uses Eurocurrency rates and these have very little credit counte
and therefore differ only in respect of their currency of denomination.
Taylor also considers brokerage fees and recalculates the above returns
assumption that brokerage fees on Eurocurrency transactions represent abou
1 percent. For example, the interest cost in borrowing Eurodollars taking
brokerage charges is
ri + 1/50
While the rate earned on any Eurodollar deposits is reduced by a similar amo
ri  1/50
Taylor estimates that brokerage fees on spot and forward transactions are so
they can be ignored. In his 1987 study Taylor looked at data collected every
reexamined the same covered interest arbitrage relationships but this time in
â€˜market turbulenceâ€™ in the FOREX market. The historic periods chosen wer
devaluation of sterling in November of that year, the 1972 flotation of sterling
that year as well as some periods around the General Elections in both the U
US in the 1980s. The covered interest arbitrage returns were calculated for m
1, 2, 3, 6 and 12 months. The general thrust of the results are as follows:
In periods of â€˜turbulenceâ€™ there were some profitable opportunities to be m
0
The size of the profits tend to be smaller in the floating rate period than
0
rate period of the 1960s and became smaller as participants gained exp
floating rates, post 1972.
The frequency, size and persistence over successive time periods of profitab
0
opportunities increases as the time to maturity of the contract is lengthened
say there tended to be larger and more frequent profit opportunities when co
12month arbitrage transaction than when considering a onemonth covere
transaction.
Let us take a specific example. In November 1967, Elm arbitraged into do
have produced only E473 profit, however just after the devaluation of sterling (i
of turbulence) there were sizeable riskless returns of about E4000 and E8000
arbitrage at the threemonth and sixmonth maturities, respectively. Capital c
UK sterling outflows) which were in force in the 1960s cannot account for th
since Eurosterling deposits/loans were not subject to such controls. Clearly th
not always perfectly efficient in that riskless profitable opportunities are not im
arbitraged away. In periods of turbulence, returns are relatively large and
persist over a number of days at the long end of the maturity spectrum, while
end of the maturity spectrum profits are much smaller.
The reason for small yet persistent returns over a onemonth horizon may w
to the fact that the opportunity cost of tradersâ€™ time is positive. There may not
traders in the market who think it is worth their time and effort to take advant
small profitable opportunities. Given the constraint of how much time they ca
one particular segment of the market they may prefer to investigate and exe
with larger expected returns, even if the latter are risky (e.g. speculation on
spot rate by taking positions in specific currencies). It may even be more wor
them to fill in their dealersâ€™ pads and communicate with other traders rathe
advantage of very small profitable opportunities.
The riskless returns available at the longer end of the market are quite
represent a clear violation of market efficiency. Taylor puts forward several hy
to why this may occur, all of which are basically due to limitations on the cred
dealers can take in the foreign exchange market.
Marketmakers are generally not free to deal in any amount with any c
that they choose. Usually the management of a bank will stipulate which o
it is willing to trade with (i.e. engage in credit risk), together with the max
preference for covered arbitrage at the short end of the market since funds are
relatively frequently.
Banks are also often unwilling to allow their foreign exchange dealers
substantial amounts from other banks at long maturities (e.g. one year). Fo
consider a UK foreign exchange dealer who borrows a large amount of doll
New York bank for covered arbitrage transactions over an annual period. If th
wants dollar loans from this same New York bank for its business customers
thwarted from doing so because it has reached its credit limits with the New Yo
so, foreign exchange dealers will retain a certain degree of slackness in their c
with other banks and this may limit covered arbitrage at the longer end of th
spectrum.
Another reason for selfimposed credit limits on dealers is that Central B
require periodic financial statements from banks and the Central Bank may c
shortterm gearing position of the commercial bank when assessing its â€˜sou
foreign exchange dealers have borrowed a large amount of funds for covere
transactions, this will show up in higher shortterm gearing. Taylor also notes
of the larger banks are willing to pay up to 1/16th of 1 percent above the mar
Eurodollar deposits as long as these are in blocks of over $loom. They do so
order to save on the â€˜transactions costsâ€™ of the time and effort of bank staff. He
recognises that there may be some mismeasurement in the Eurodollar rates h
hence profitable opportunities may be more or less than found in his study.
Taylor finds relatively large covered arbitrage returns in the fixed exchange
of the 1960s, however in the floating exchange rate period these were far le
and much smaller. For example, in Table 12.1 we see that in 1987 there were
no profitable opportunities in the onemonth maturities from sterling to dollars
at the oneyear maturity there are riskless arbitrage opportunities from dollars in
on both the Monday and Tuesday. Here $ l m would yield a profit of around $1
oneyear maturity.
Taylorâ€™s study does not take account of any differential taxation on intere
from domestic and foreign investments and this may also account for the ex
persistent profitable covered arbitrage at maturities of one year. It is unlikely t
participants are influenced by the perceived relative risks of default between sa
ling and Eurodollar investments and hence this is unlikely to account for arbitr
even at the oneyear maturities. Note that one cannot adequately test CIP betw
Table 12.1 Covered Arbitrage: Percentage Excess Returns (1987)
1 month 6 month 1
(E + $) $1
+ f) + $)
Monday 8/6/87 ($ (& ($ + f) (f +
ñòð. 8 