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bond markets. If returns depend on a time varying risk premium which is pers
sharp movements in stock prices may ensue as a result of shocks to such pre
observed price movements may not be ˜excessively™ volatile. An analysis is m
usefulness of the CAPM with time varying variances and covariances which a
by ARCH and GARCH processes. This framework is applied to both the (in
stock and bond markets. There appears to be more support for a time varyin
type) risk premium influencing expected returns in the stock market than i
market. Some unresolved issues are whether such effects are stable over ti
robust to the inclusion of other variables that represent trading conditions (e
in the market).
As the book progresses, the reader should become aware that to establish
particular speculative market is efficient, in the sense that either no excess
profits can be earned or that market price reflects economic fundamentals,
straightforward. It often requires the use of sophisticated statistical tests man
have only recently appeared in the literature. Data on asset prices often exhi
and such ˜non-stationary ™ data require analysis using concepts from the li
unit roots and cointegration - otherwise grossly misleading inferences may e
readers will also be aware that, although the existence of time varying risk
always been acknowledged in the theoretical finance literature, it is only re
empirical work has been able to make advances in this area using ARCH an
book. However, I did not want these issues to dominate the book and ˜crow
economic and behavioural insights. I therefore decided that the best way forw
the heterogeneous background of the potential readership of the book, was to
overview of the purely statistical aspects in a self-contained section (Part 7)
of the book. This has allowed me to limit my comments on the statistical nu
minimum, in the main body of the text. A pre-requisite for understanding Pa
be a final year undergraduate course or a specialist option on an MBA in a
series econometrics.
Naturally, space constraints imply that there are some interesting areas tha
omitted. To have included general equilibrium and other ˜factor models™ of
returns based on continuous time mathematics (and associated econometric p
would have added considerably to the mathematical complexity and length o
While continuous time equilibrium models of the term structure would have
useful comparison to the discrete time approach adopted, I nevertheless felt i
to exclude this material. This also applies to some material I initially wrote on
futures - I could not do justice to these topics without making the book inordi
and there are already some very good specialist, academically oriented texts i
I also do not cover the recent burgeoning theoretical and applied literature
micro-structure™ and applications of neural networks to financial markets.

In order to make the book as self-contained as possible and noting the often sh
of even some central concepts in the minds of some students, I have included
basic theoretical material at the beginning of the book (e.g. the CAPM and i
the APT and valuation models). As noted above, I have also relegated detaile
issues to a separate chapter. Throughout, I have kept the algebra as simple as p
usually I provide a simple exposition and then build up to the more general
I hope will allow the reader to interpret the algebra in terms of the econom
which lies behind it. Any technically difficult issues or tedious (yet important)
I relegate to footnotes and appendices. The empirical results presented in th
merely illustrative of particular techniques and are not therefore meant to be
In some cases they may not even be representative of ˜seminal contributions™,
are thought to be too technically advanced for the intended readership. As
will already have gathered, the empirics is almost exclusively biased towards
analysis using discrete time data.
This book has been organised so that the ˜average student™ can move fr
to more complex topics as he/she progresses through the book. Theoretical
constructs are developed to a particular level and then tests of these ideas are
By switching between theory and evidence using progressively more difficu
the reader becomes aware of the limitations of particular approaches and ca
this leads to the further development of the theories and test procedures. Hen
less adventuresome student one could end the course after Part 4. On the o
the advanced student would probably omit the more basic material in Part 1
approach. In a survey article, one often presents a general framework from w
other models may be viewed as special cases. This has the merit of great el
it can often be difficult for the average student to follow, since it requires an
understanding of the general model. My alternative approach, I believe, is to b
on pedagogic grounds but it does have some drawbacks. Most notably, no
possible theoretical approaches and empirical evidence for a particular marke
stocks, bonds or foreign exchange, appear in one single chapter. However, this i
and I can only hope my ordering of the material does not obscure the underlyin
approaches that may be applied to all speculative markets.
The book should appeal to the rising undergraduate final year, core financ
area and to postgraduate courses in financial economics, including electives o
MBA finance courses. It should also provide useful material for those wor
research departments of large financial institutions (e.g. investment banks, pen
and central and commercial banks). The book covers a number of impor
advances in the financial markets area, both theoretical and econometric/empiri
innovative areas that are covered include chaos, rational and intrinsic bubbles
action of noise traders and smart money, short-termism, anomalies, predict
VAR methodology and time varying risk premia. On the econometrics sid
of non-stationarity, cointegration, rational expectations, ARCH and GARCH
examined. These issues are discussed with empirical examples taken from the
and FOREX markets.
Professional traders, portfolio managers and policy-makers will, I hope, fin
of interest because it provides an overview of some of the theoretical mod
explaining the determination of asset prices and returns, together with the
used to assess their empirical validity. The performance of such models provid
input to key policy issues such as capital adequacy proposals (e.g. for securiti
the analysis of mergers and takeovers and other aspects of trading arrangeme
margin requirements and the use of trading halts in stock markets. Also, to
that monetary policy works via changes in interest rates across the maturity sp
changes in the exchange rate, the analysis of the bond and FOREX markets
relevance. At a minimum the book highlights some alternative ways of exa
behaviour of asset prices and demonstrates possible pitfalls in the empirical
these markets.
I remember, from reading books dealing with the development of quantum
that for several years, even decades, there would coexist a number of competing
the behaviour of elementary particles. Great debates would ensue, where often
than light™ would be generated - although both could be construed as manife
(intellectual) energy. What becomes clear, to the layman at least, is that as one
closer to the ˜micro-behaviour™ of the atom, the more difficult it becomes to
the underlying physical processes at work. These controversies in natural sc
me a little more sanguine about disputes that persist in economics. We know (
think we know) that in a risky and uncertain world our ˜simple™ economic mode
not work terribly well. Even more problematic is our lack of data and inability
analysis of speculative asset prices and I hope this is reflected in the material i
It has been said that some write so that other colleagues can better unders
others write so that colleagues know that only they understand. I hope this
achieve the former aim and will convey some of the recent advances in t
of speculative asset prices. In short, I hope it ameliorates the learning proce
stimulates others to go further and earns me a modicum of ˜holiday money™.
if the textbook market were (instantaneously) efficient, there would be no ne
book - it would already be available from a variety of publishers. My expe
success are therefore based on a view that the market for this type of book is no
and is currently subject to favourable fads.
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I have had useful discussions and received helpful comments on various cha
many people including: David Ban, George Bulkley , Charles Goodhart, Davi
Eric Girardin, Louis Gallindo, Stephen Hall, Simon Hayes, David Miles, Mich
Dirk Nitzsche, Barham Pesaran, Bob Shiller, Mark Taylor, Dylan Thomas, Ian
Mike Wickens. My thanks to them and naturally any errors and omissions a
me. I also owe a great debt to Brenda Munoz who expertly typed the various
to my colleagues at the University of Newcastle and City University Busine
who provided a conducive working environment.
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L--- I
Returns and Valuation
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Basic Concepts in Finance

The aim in this chapter is to quickly run through some of the basic tools of an
in the finance literature. The topics covered are not exhaustive and they are d
a fairly intuitive level. The topics covered include

Compounding, discounted present value DPV, the rate of return on pu
bonds, coupon paying bonds and stocks.
Utility functions, indifference curves, measures of risk aversion, and in
utility .
The use of DPV in determining the optimal level of physical investme
optimal consumption stream for a two-period horizon problem.

Much of the theoretical work in finance is conducted in terms of compound rat
or interest rates even though rates of interest quoted in the market use ˜simp
For example, an interest rate of 5 percent payable every six months will be
simple interest rate of 10 percent per annum in the market. However, if an inv
over two six-month bills and the interest rate remained constant, he could ac
a ˜compound™ or ˜true™ or ˜effective™ annual rate of (1.05)* = 1.1025 or 10.
The effective annual rate of return exceeds the simple rate because in the form
investor earns ˜interest-on-interest™.
We now examine how to calculate the terminal value of an investmen
frequency with which interest rates are compounded alters. Clearly, a quoted
of 10 percent per annum when interest is calculated monthly will amount to
end of the year than if interest accrues only at the end of the year.
Consider an amount $x invested for n years at a rate of R per annum (
expressed as a decimal). If compounding takes place only at the end of th
future value after n years is FV, where
R / m is often referred to as the periodic interest rate. As rn, the frequency of com
increases the rate becomes continuously compounded and it may be shown that

where exp = 2.71828. For example, using (1.2) and (1.3) if the quoted (simp
rate is 10 percent per annum then the value of $100 at the end of one ye
for different values of m is given in Table 1.1. For practical purposes daily co
gives a result very close to continuous compounding (see the last two entries in
We now consider how we can switch between simple interest rates, per
effective annual rates and continuously compounded rates. Suppose an investm
periodic interest rate of 2 percent each quarter. This will usually be quoted in
as 8 percent per annum, that is, as a simple annual rate. The effective ann
exceeds the simple rate because of the payment of interest-on-interest. At the
year $x = $100 accrues to

The effective annual rate R f is clearly 8.24 percent since
$100(1+ R f ) = 108.24
The relationship between the quoted simple rate R with payments m times p
the effective annual rate Rf is

]: m
[l + R f ] = [ 1 +

We can use equation (1.6) to move from periodic interest rates to effectiv
vice versa. For example, an interest rate with quarterly payments that would
effective annual rate of 12 percent is given by

1.12 = [l

R = [(l.l2)lI4 l] 4 = 0.0287 x 4 = (11.48 percent)

'hble 1.1 Compounding Frequency
Compounding Value of $100
Frequency at End of Year ( R = 10%p.a.)
Annually (rn = 1) 110.00
Quarterly (rn = 4) 110.38
Weekly (rn = 52) 110.51
Daily (rn = 365) 110.52
Continuous (n = 1) 110.517
compounded rate, Re. One reason for doing this calculation is that much of th
theory of bond pricing (and the pricing of futures and options) uses co
compounded rates.
Suppose we wish to calculate a value for R, when we know the m-period ra
the terminal value after n years of an investment of $A must be equal when u
interest rate we have


Also, if we are given the continuously compounded rate R, we can use the abo
to calculate the simple rate R which applies when interest is calculated m time
R = rn[exp(R,/m) - 11
We can perhaps best summarise the above array of alternative interest rate
one final illustrative example. Suppose an investment pays a periodic inter
5 percent every six months (m = 2, R/2 = 0.05). In the market, this would
as 10 percent per annum and clearly the 10 percent represents a simple annu
investment of $100 would yield lOO(1 (0.1/2))2= $110.25 after one year (u
Clearly the effective annual rate is 10.25 percent per annum. Suppose we wish
the simple annual rate of R = 0.10 to an equivalent continuously compounded
(1.9) with rn = 2 we see that this is given by Re = 2 - ln(1 0.10/2) = 0.09
percent per annum). Of course, if interest is continuously compounded at an
of 9.758 percent then $100 invested today would accrue to exp(R,n) = $110.2
years' time.

Discounted Present Value (DPV)
Let the annual rate of interest on a completely safe investment over n years
r d n ) .The future value of $x in n years' time with interest calculated annually

It follows that if you were given the opportunity to receive with certainty $
years time then you would be willing to give up $x today. The value today o
payment of FV, in n years time is $x. In more technical language the discoun
value (DPV) of FV, is
(1 r d n ) ) n
We now make the assumption that the safe interest rate applicable to 1 , 2 , 3
horizons is constant and equal to r . We are assuming that the term structure
Physical Investment Project
Consider a physical investment project such as building a new factory whic
of prospective net receipts (profits) of FVi. Suppose the capital cost of the pro
we assume all accrues today (i.e. at time t = 0) is $ K C . Then the entrepren
invest in the project if
or equivalently if the net present value (NPV) satisfies
NPV = DPV- KC 2 0
If NPV = 0 it can be shown that the net receipts (profits) from the investment
just sufficient to pay back both the principal ( $ K C ) and the interest on the l
was taken out to finance the project. If NPV > 0 then there are surplus fund
even after these loan repayments.
As the cost of funds r increases then the NPV falls for any given stream
FVi from the project (Figure 1.1).There is a value of r (= 10 percent in Fig
which the NPV = 0. This value of r is known as the internal rate of return (
investment. Given a stream of net receipts F Vi and the capital cost KC for a p
can always calculate a project™s IRR.It is that constant value of y for which
i=l (1 Y)™
An equivalent investment rule to the NPV condition (1.15) is then to in
project ifcl)
IRR(= y) 2 cost of borrowing (= r)

Figure 1.1 NPV and the Discount Rate.
Suppose, however, that 'one-year money' carries an interest rate of rd'), two-y
costs rd2),etc. Then the DPV is given by


where Sj = (1 di))-'. rd') are known as spot rates of interest since t
rates that apply to money lent over the periods rdl) = 0 to 1 year, rd2) = 0
etc. (expressed at annual compound rates). The relationship between the spot
on default free assets is the subject of the term structure of interest rates. Fo
if rdl) < rd2) -c r d 3 ) .. . then the yield curve is said to be upward sloping
formula can also be expressed in real terms. In this case, future receipts FVi a
by the aggregate goods price index and the discount factors are then real rates
In general, physical investment projects are not riskless since the future r
uncertain. There are a number of alternative methods of dealing with uncerta
DPV calculation. Perhaps the simplest method and the one we shall adopt has t
rate Sj consisting of the risk-free spot rate rd') plus a risk premium rpi:

Equation (1.19) is an identity and is not operational until we have a model
premium (e.g. rpj is constant for all i). We examine some alternative model
Chapter 3.

Pure Discount Bonds and Spot Yields
Instead of a physical investment project consider investing in a pure discount
coupon bond). At short maturities, these are usually referred to as bills (e.g
bills). A pure discount bond has a fixed redemption price M1, a known matu
and pays no coupons. The yield on the bill if held to maturity is determined
that it is purchased at a market price Pt below its redemption price M1. For
bill it seems sensible to calculate the yield or interest rate as:

where rsj') is measured as a proportion. However, viewing the problem in term
we see that the one-year bill promises a future payment of M1 at the end of
exchange for a capital cost paid out today of PI,.Hence the IRR, ylt of the
calculated from
and hence the one-year spot yield rsf') is simply the IRR of the bill. Applying
principal to a two-year bill with redemption price M 2 , the annual (compou
rate rsi2) on the bill is the solution to

which implies
rst(2)= [M2/P2,I1'2 - 1
We now see how we can, in principle, calculate a set of (compound) spo
different maturities from the market prices of pure discount bonds (bills). O
practical issue the reader should note is that, in fact, dealers do not quote the
rates r#)(i = 1,2, 3 , 4 . . .) but the equivalent simple interest rates. For exam
periodic interest rate on a six-month bill using (1.20) is 5 percent, then the quot
be 10 percent. However, we can always convert the periodic interest rate to an
compound annual rate of 10.25 percent or, indeed, into a continuously compo
of 9.758, as outlined above.

Coupon Paying Bonds
A level coupon (non-callable) bond pays a fixed coupon $C at known fixe
(which we take to be every year) and has a fixed redemption price Mn payabl
bond matures in year n. For a bond with n years left to maturity let the cur
price be P f " ) .The question is how do we measure the return on the bond
to maturity? The bond is analogous to our physical investment project with
outlay today being Pf"' and the future receipts being $C each year (plus the
price). The internal rate of return on the bond, which is called the yield to m
can be calculated from
+... C + M n
p("' =

(1 + R : ) -k (1 + R r ) 2 (1 R:)"
The yield to maturity is that constant rate of discount which at a point in ti
the DPV of future payments with the current market price. Since P("',Mn an
known values in the market, equation (1.24) has to be solved to give the qu
rate for the yield to maturity RY. There is a subscript 't' on R because as
price falls, the yield to maturity rises (and vice versa) as a matter of actuaria
in equation (1.24). Although widely used in the market and in the financial pre
some theoretical/conceptual problems in using the yield to maturity as an un
measure of the return on a bond even when it is held to maturity. We deal w
these issues in Part 3.
In the market, coupon payments C are usually paid every six months and
rate from (1.24) is then the periodic six-month rate. If this periodic yield
is calculated as say 6 percent, then in the market the quoted yield to matu
pricing and return on bonds.
Aperpetuity is a level coupon bond that is never redeemed by the primary
n + 00). If the coupon is $C per annum and the current market price of the b
then a simple measure of the return Rfm) is the flat yield:
R(@ = c/pj"'
This simple measure is in fact also the yield to maturity for a perpetuity, since
in (1.24) then it reduces to (1.25). It is immediately obvious from (1.25) tha
changes, the percentage change in the price of a perpetuity equals the percent
in the yield to maturity.

Holding Period Return
Much empirical work on stocks deals with the one-period holding period re
which is defined as
Pr+l - Dr+l
pr p r ] + pt
Hr+l =

The first term is the proportionate capital gain or loss (over one period) and
term is the (proportionate) dividend yield. H t + l can be calculated expost but
viewed from time t, Pr+l and (perhaps) D1+l are uncertain and investors can o
forecast these elements. It also follows that

+ ++
where Ht+j is the one period return between t i and t i 1. Hence, expo
invested in the stock (and all dividend payments are reinvested in the stock) t
payout after n periods is

Beginning with Chapter 4 and throughout the book we will demonstrate how
one-period returns H r + l can be directly related to the DPV formula. Much o

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