BID BEHAVIOUR AND THE DETERMINATION OF UKTREASURY BILL RATES 1970_1976*

By ANTHONY SAUNDERS and CHARLES WARD

I. INTRODUCTION

In the United Kingdom treasury bills are allotted by means of a weeklyauction.' At this auction the Bank of England adopts the role of a pricediscriminating monopolist, allocating bills in descending order of bid price until thetotal supply is exhausted. Those bidders who tender at low prices (high) yields areoften disappointed, as the total demand is always greater than the supply.

The major competitors at this auction are: overseas holders of sterling, industrialcompanies, non-bank financial intermediaries and a specialized group of moneymarket institutions, the discount houses. Most of these bidders have a great deal offreedom in formulating and entering their bids. Even the discount houses, whowere traditionally constrained by a number of collusive agreements on theirtenders, now have a good deal of individual freedom in determining their bids.2

The aim of this paper is to analyse bidding behaviour and rate determinationin the UK treasury bill market over the period 1970-76. Initially tworepresentative models of bidding behaviour are discussed. The first is based onrather naive assumptions about investors' behaviour, assuming a symmetricrectangular (or uniform) distribution of bids. The second is based on a morerational bidding strategy, which assumes that bids are asymmetrical andexponentially distributed. Two important statistical characteristics of thesedistributions are defined and empirically measured. In particular, it is argued thatsince the 'treasury bill rate' currently published by the Bank of England [2] is basedonly on the average of accepted bids, it is unrepresentative of the whole distributionof bids. Hence its use in empirical studies may result in a loss of importantinformation, especially on the nature and determination of bids at the lower end ofthe distribution.

Using derived characteristics of the two bid distributions as dependentvariables a small number of independent variables are then identified. Tests arcconducted to examine the extent to which bids in the bill market can be explainedwithin the framework of a relatively simple interest-rate determination model. Itis argued that while such models appear to offer some explanation of biddingbehaviour, investors do appear to be heterogeneous in their sensitivity todetermining variables. Moreover the more rational model (the exponential)

* We should like to acknowledge the helpful comments of P. Blandon, City of London Polytechnicand A. Kalay and J. Kallberg, New York University, Graduate School of Business Administration.

I All new Treasury bills have 91 day terms to maturity and are sold in six denominations rangingfrom £5,000 to £250,000. The minimum size of any lot is £50,000.

2 The introduction of the Competition and Credit Control reforms of May-June 1971 resulted in theabandonment of the houses collusive agreement whereby all bid at one price, collectively determinedprior to the auction, and their traditional obligation to cover the whole weekly supply of new bills wasreplaced with a new, more flexible, agreement.

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appears to offer a poorer explanation of bidding behaviour than the more naivemodel (the rectangular).

II. THE EXPECTED TREASURY BILL RATE

An important issue involved in any empirical investigation into treasury billinvestors' behaviour concerns the extent to which the observed prices or rates canbe taken to represent all bidders' expectations (the 'market view'). In otherfinancial markets it is often assumed that expectations are homogeneous within themarket and are fully reflected in the current market price.3 Alternatively ifexpectations are not homogeneous then by making assumptions about the utilityfunctions of participants, it is still possible to derive models in which prices observedin the market reflect an 'average' expectation.4 Neither of these approaches seemparticularly appropriate to the UK treasury bill market, since it is observed thatbids are tendered at different effective rates of interest, thereby making theassumption of homogeneous expectations implausible. Furthermore, it is difficultto argue that a single utility function can adequately represent the preferences ofindividual bidders. As a result, even if a single rate was taken to representexpectations, the selection of an appropriate rate would still have to be made.

Over the period January 1970 to December 1976 the Bank of Englandpublished two main series of rates; (a) the rate of interest associated with theaverage accepted bid and (b) the rate of interest associated with the lowest accepted(stop-out) bid. In most previous empirical studies of the UK treasury bill market(see Bain [1] for example), the rate of interest associated with the average acceptedbid has been employed as 'the treasury bill rate'. Indeed the Bank of England itselfappears to regard this rate as being representative of all market bids for eachauction.5 While the stop-out bid, the lowest accepted price (highest rate), is viewedas the rate which just clears the market. However, both of these rates ignoreimportant information on the auction. Especially on those bids which are notaccepted. If low (price) bidders are rational then an important question arises as tothe nature of their expectations and the determinants of their bidding behaviour.Moreover, the size of the unsuccessful group will tend to vary from auction toauction, fluctuating with, among other things, the size of the bill allotment and theheterogeneity of bidders expectations.

To generate information on the nature of the whole distribution of bids,statistical characteristics of the (whole) distribution need to be identified. Two ofthese characteristics are of particular interest, the average and lowest of all bids.The former because it more closely fits the idea of a 'market rate' being an averageof the heterogeneous expectations of all bidders, while the latter provides importantinformation on the nature of low bids, not reflected in published information,particularly on the possibilities of interest rate arbitrage. By assuming specificdistributions of bids and by using, in addition to the series of published rates

See Fama [5], for example.See Mossin [1 1], for example.The Bank of England publishes this rate as the treasury bill rate in its statistical bulletins, see [2]

p. 158, table 27, column 2, Volume II.

BID BEHAVIOUR AND THE DETERMINATION OF UK TREASURY BILL RATES 217

mentioned above, information on the total amount of bills tendered for and supplied(allotted), it is technically possible to estimate the average rate offered by all biddersas well as the lowest of all bids.

For the purpose of this investigation two simple alternative bid distributionswere assumed: the rectangular and the exponential. The justification for using therectangular or uniform distribution is that it is both bounded and symmetrical andsuggests a rather simple or naive form of investment behaviour (see Fig. 1).

Although the normal might have seemed a more reasonable choice as therepresentative symmetric distribution, there were a number of factors workingagainst its selection. In particular, the lowest bid could not be derived unless thedistribution was truncated in some ad hoc fashion. Once the normal had beeneliminated the rectangular seemed to be the logical choice, especially since theaverage and lowest bids could be derived fairly easily. The exponential waschosen to represent a particular asymmetrical type of bidding behaviour. Inparticular if bids are regularly made in the expectation of not being accepted (as islikely, given that the total bids made over the period always outweighed billsoffered) then bids made at the lower prices might well be made on an arbitragebasis. That is, some optimistic bids will be made to obtain new bills to resell at apremium in the secondary or 'resale market'. This behaviour might also result ininvestors bidding for treasury bills at a rate higher than those currently obtainableon alternative, slightly more risky, short-term assets such as Commercial bills andSterling Certificates of Deposit (SCD's).6 In these circumstances it might bereasonable to assume that the number of bids made will be an exponentiallyincreasing function of the bill rate (see Fig. 1).

Although there are a large number of alternative non-symmetric distributionswhich might have been chosen (including the beta, the gamma (or Erlangian), andthe Weibull amongst others), the derivation of the relevant bids for these higher-order, more complex distributions, was found to be intractable since this requiredestimation of more parameters than permitted by our data constraint (i.e. therewere not sufficient degrees of freedom). Nevertheless, the exponential distributionused in the paper is a special case of both the Weibull and gamma distributions7,and these latter distributions are believed to be sufficiently general to describe thewhole family of possible (non-symmetric) distributions of the type being consideredin this paper.8

6 More risky in the safety sense rather than interest or capital loss risk sense. This is because SCD'sand commercial bills are private sector instruments and cannot be implicitly underwritten by the taxor fiat currency base as can treasury bills.

See Zehna [15], for example.The relationship between the gamma and the exponential can be demonstrated fairly easily. The

gamma distribution takes the form(x)

nl!where n is the number of exponentials and x is the number of bids made at a given rate.

For n 1, density is,

f(x)=Ke=Kaewhich is the exponential.

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The Rectangular Distribution

Number ofbids made

MR H Bid price - Bid rate

The exponential distribution

Number ofbids made

looBid price

Bid rate

Fig. i.

On the basis of bids that are rectangularly distributed between a lower andupper bound, the lowest bid made (LR) will be given by,9

2Q1 1ff 1ff \ Otff 1ffR k i 2)m2 i

s

and the average bid PR by,

where QD=Quantity of treasury bills tendered forQs = Quantity of treasury bills supplied

M1 = Lowest bid acceptedM2 = Average bid accepted

= Average bid madeLR = Lowest bid made

Formal derivation of these equations is shown in Appendix I.

o LE ME

BID BEHAVIOUR AND THE DETERMINATION OF UK TREASURY BILL RATES 219

with the exponential distribution, the lowest bid made (LE) is given by,

L=Log(Mj M2)+M1 (3)

and the average bid (SUE) by,

[L=Log(M1M2)+M2 (4)

Using the published information on QD' Qs' M1 and M2 it is possible to generatetime series on LR, ILR, LE, and ILe for the period January 1970 to December 1976.10Clearly we now have two possible definitions for both the average treasury bill rate(/Lp.j and 4UE) and the lowest bid (L and LEE) in any time period, each representingdifferent assumptions about the nature of market bids.

III. A MODEL OF INTEREST RATE DETERMINATION

The simplest model of treasury bill interest rate determination is based on theFisher [8] hypothesis. In this model equilibrium changes in (one-period) nominalbill rates should reflect changes in either the expected rate of inflation or the realrate of interest, where the latter is usually assumed to be constant. Within thisframework the average nominal rate of interest demanded by investors isdetermined by equations of the form.

(1 +R) = (1 +E(i))(1 +r) (5)

R=E(i) +r+rE(i1) (6)

Where R = the average nominal rate of interestthe real rate of interest

Since the product of r, and E(z) in equation (6) is likely to be small it is generallydisregarded as being arithmetically insignificant in empirical tests. Hence, anestimating equation may be specified in the form of (7) below."

R=ri+ßE(i)+u (7)

Where is the ex-post (constant) real rate of interest, E(i) is the variablerepresenting the expected rate of inflation in period t and u is the disturbance orerror term. There were two reasons for assuming the real rate () to be constant.The first was the 'classical' argument (often associated with Fisher) that financialmarkets adjust to real forces such as productivity and thrift over long periods oftime, and that these real forces tend to change only gradually. For example, wemight expect the real rate to rise during major business expansions and fall during

Both weekly and monthly average time series can be derived. However since the inflation seriesis published monthly, only the monthly series is employed in the empirical tests of section III.

See Jaffe and Mandelker [10], for example.

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contractions. Since the data period covered by our study was relatively short(1970-76), the assumption of a constant real rate (and hence cc) seemed to be areasonable approximation. The second was that while it might have been possibleto include a variable real rate it would have been at the cost of building a largermodel to explain its determination. For example, business expectations regardingthe future rate of return on capital and other (real) forces that affect savingsdecisions would have had to be considered. It was felt that such a model wouldtend to detract somewhat from the objectives of the paper.

Turning next to the choice of the variable to measure expected inflation, therewere a number of considerations that led to the selection of the current inflationrate as the appropriate variable. The first was the developing literature andevidence in support of 'efficient' financial markets in the UK (a good review of theUK literature is provided by Henfrey, Albrecht and Richards [9]) and the strongsupport for this view in the US (see Fama [6] [7]). This view suggests that allcurrently available information (on inflation, for example) is considered byinvestors in setting market prices, and that all past information has already beendiscounted by the market (i.e. is reflected in past prices). As a result, past dataprovides no information for the investor on the future course of financial prices.Alternatively, this view can be restated as implying that for investors, the currentinflation rate is the best estimate of the expected inflation rate. Moreover, theresults of Fama appear to imply that US Treasury bill investors are fully pricerational since the estimated value of ß in equation (7) was not significantly differentfrom unity over the period January 1953 to July 1971.

The second consideration was that in the course of the study we did try anumber of simple lag specifications of the inflation variable, none gave us betterresults. Even entering lagged inflation rates explicitly into the model resulted ininsignificant coefficients for these variables. The third was the growing criticismof the theoretical and econometric justification for using expectation models thatcan be neatly transformed (by the Koyck, for example) into an expected inflationseries. For example, Roll [12] raises the spectre of data-mining if the investigatorseeks to find 'a best fit' by utilizing different data transformations. Finally, as thereis no regular, publicly available, UK series on business/investor price expectationscomparable to the Livingston series published regularly in the United States, thisprecluded the use of a 'directly' measured expected inflation surrogate. Althougha series has been derived from Gallup Poll data by Carlson and Parkin in theirstudy of the UK labour market (see [4]), this unfortunately terminated at the endof 1973 and could not be used for this study.

However, although we make the same basic choice as Fama on the selection ofthe variable to present E(i), we recognize that bidding in the market for newtreasury bills will not be adequately explained by expectations of the rate ofinflation alone. Generally we might expect to find that some investors informulating bids, especially those at the margin, will consider the returns obtainableon substitute assets of the same maturity, albeit of a slightly higher risk. Ourextended 'Fisherian' model is specified below, where bid rates (Rr) are assumed tobe determined by expectations of inflation (E(i)), and the rate on alternative assets

BID BEHAVIOUR AND THE DETERMINATION OF UK TREASURY BILL RATES 221

(Ra), represented in this paper by the rate on three month SCD's, as in equation (8)below,'2

RT=+ßjE(il)+ß2RA+u, (8)

While it is recognized that this is not a full model specification, it should providesome evidence on the sensitivity of the Fisher model to the inclusion of additionalexplanatory variables. Indeed Cargill [3], for the US has already shown that whenpercentage changes in real GNP and the money supply are included in the Fisherequation the coefficient on the inflation variable may no longer be statisticallysignificant. Furthermore, equation (8) also provides us with an additionalhypothesis. For when different segments of the distribution of bids are considered,R the rate on the alternative substitute asset may be expected to influence lowerbids (higher rates of interest) to a greater extent than the average bid.

Empirically however, since SCD's are substitute assets for treasury bills andtheir rate is competitively determined, R will tend to be interdependent withRTt. Important buyers of both SCD's and treasury bills are overseas holders ofsterling, who appear to vacillate between the SCD, the treasury bill and theexchange and foreign asset markets as the relevant opportunity costs change (seeSaunders and Woodward [14]). It is specified below (in equation (9)) that the rateon SCD's will be determined by the average rate on treasury bills and foreigninvestment opportunity costs (RFH). The implicit assumption being that foreignholders of sterling would, on selling their sterling assets, buy dollars and invest inthree month Euro-dollar deposits. Equation (10) below derives the relevantmonthly returns from this transaction.

RAdO+dlRT+d2RFH+el (9)

RFH=(l ::)(1 +RED,) 1 (10)

XF .where -- =3 month forward (spot) annualised £/$ premium (discount)I inAS, month t.RED,= annualised rate on 3 month Euro-dollar deposits in month t.RA, = annualised rate on 3 month SCO's in month t.

12 Sterling Certificates of Deposit were chosen as the alternative asset for a number of reasons.First their interest rates seemed to be highly competitive with other money market instruments.Especially, after the competition and Credit Control (CCC) reforms of 1971 when the London Clearingbanks started to issue considerable quantities in competition with US and other overseas banks.Second, they appeared to be extremely popular with overseas holders of sterling (assets) because of theirhigh nominal rates and negotiability. Third, and related to the previous point, overseas holders of T.bills seemed to be highly sensitive to interest rate changes and the exchange value of sterling. Forexample in 1970/1 overseas net purchases were - L6 12M compared to + / 123M by the domesticbanking sector, whereas in 1974/5 the respective figures were +1,l 11M for overseas holders and+ 437M for the domestic banking sector. Finally in the post-CCC period certain regulatory restrictionswere imposed which made prime Commercial bills (a possible candidate for the alternative asset) far lessattractive to the UK banking system. This was mainly due to the new (124%) reserve requirementwhich allowed commercial bills to comprise no more than 2% of the banking system's reserve assets.

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IV. ESTIMATION OF THE MODEL

Because of the likely interdependence between RT and RAE, equation (8) wasestimated by means of Two Stage Least Squares using a modified Cochrane-Orcuttmethod to adjust for first order auto-correlation in the residuals.

The results for the means and lower bounds of the two different distributions ofRT are presented in equations (11 )--( 14) below where j, is the actual (annualised)rate of inflation in month t and R is the value of R predicted from its reducedform equation.'3

LR = 2.716 + 0.026i + 0.620RA,(3.86) (2.22) (9.66)

R2 =0.55 DW=1.97 n=84

LE = 3.59 + 0.015j, + 0.529.ÑA,(5.05) (1.58) (8.73)

R2=0.49 DW=1.96 n=84

/IRt = 4.42 + 0.012i + 0.433.ÑA(5.83) (1.31) (7.62)

R2=rO.42 DW=1.96 n=84

PE1 = 4.62 +0.009i +0.4351A(5.9) (1.08) (7.45)

R2=0.41 DW=1.96 n=84

(tratios in brackets).

As can be seen, the rate of inflation offers very little independent explanation of thedetermination of UK treasury bill bids. One implication of this result is that theinflation rate or other expected inflation surrogates may well have acted as proxiesfor (other) market interest rates in previous tests of the simple Fisher hypothesis.For when an alternative interest rate (such as R) is independently included in theestimating equations, the 'Fisher effect' is seen to be almost insignificant inexplaining bid determination. This suggests that UK investors do not incorporateexpectations of inflation into their bids. While it is possible that the actual inflationrate does not correctly measure inflationary expectations, it is interesting to notethat other studies in the UK seeking to test the simple Fisher hypothesis have alsofound comparatively poor results for the inflation variable. For example, Demeryand Duck [4] found only a weak effect of inflationary expectations on short-terminterest rates.'4 Similarly Saunders [13], using a number of surrogate measures ofthe expected inflation variable, including that employed by Demery and Duck,found that none offered a convincing explanation of the determination of thereturns on UK shares.

' Since RED is likely to be largely deteinined by US monetary policy, it was assumed that RFH wasexogenously determined. Consequently RA, was derived by an ordinary least squares regression onRf if, and i, the two exogenous variables of the (two-equation) model.

14 Demery and Duck's [4] study covered the relatively low inflation period of 1961-1973 and theyemployed an expected inflation variable derived from Gallup Poll opinion data.

BID BEHAVIOUR AND THE DETERMINATION OF UK TREASURY BILL RATES 223

A further interesting result is that a comparison of the estimated coefficients onR indicate that the influence of the alternative asset is more important indetermining bids at the lower bound of each distribution. Indeed for eachdistribution the coefficients on R in the lower bound equations are significantlydifferent, at the 5% level, from those in the respective distributional meanequations. Indicating, as might (a priori) be expected, that lower bids are moresensitive to the rate on alternative assets. This result suggests that these bids tendto be marginal, in the sense of investors seeking to arbitrate between the primaryand secondary markets for bills and other short-term assets.

Finally a comparison of the overall results within the framework of the modelindicates that the exponential distribution, which is based on a more rationalinvestment strategy, does not offer a superior explanation of bidding behaviourthan the rectangular distribution. This is a surprising result which may be partlydue to the limitations of model specification and omitted variables. Nevertheless,it does appear to raise an additional question, as to the rational economic behaviourof treasury bill investors as a group.

Overall then, investors do appear to be heterogeneous in their bidding behaviourespecially with regard to the rates on alternative assets. However, the generalfailure of inflationary expectations in explaining rate determination, along with thesuperior explanatory power of the rectangular bidding model, suggests that UK billinvestors are either money illusioned and relatively naive in their bidding strategyor that their investment decisions are highly complex. If the latter is the case, thiswould require the specification of a far more extensive model of interest-ratedetermination than that employed in this study.

V. CONCLUSIONS

This paper considered simple methods of deriving expectations of potentialbuyers in the UK treasury bill market. Two distribution models were proposedbased on differing explanations of bidding strategy. Time series on differentsegments of these distributions were generated and employed in an analysis of thefactors influencing investors' bidding behaviour. It was demonstrated that (a) therate of interest on the alternative asset seemed to play an important part in thedetermination of low bids and (b) inflation expectations offered little additionalexplanation.

However it must be recognized that these results are dependent on the biddistributions assumed and that further tests employing different distributions mightappropriately be carried out. Nevertheless it is felt that the methodology of thisstudy represents a useful contribution to the analysis of an important market andmay provide a stimulus for further research in this area.

Graduate School of Business Administration, New York UniversityBusiness School, City of London Polytechnic

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REFERENCES

Bain, A. D., 'The Treasury Bill Tender in the UK', Journal of EconomicStudies, 1, 1965, pp. 62-67.

Bank of England, Statistical Abstracts, Volumes I and II, Bank of EnglandPrinting Works, 1970 and 1975.

Cargill, T. E., 'Anticipated Price Changes and Nominal Interest Rates in the1950's', Review of Economics and Statistics, 58, 1976, pp. 364-36 7.

Demery, D. and Duck, N. W., 'The Behaviour of Nominal Interest Rates inthe United Kingdom, 1961-1973', Economica, February 1978, pp. 23-37.

Fama, E. F., 'Efficient Capital Markets: A Review of Theory and EmpiricalWork', Journal of Finance, 25, 1970, pp. 383-417.

Fama, E. F., 'Short-term interest rates as predictors of inflation', AmericanEconomic Review, 65, 1975, pp. 269-282.

Fama, E. F., 'Inflation, Uncertainty and Expected Returns on TreasuryBills',Journal of Political Economy, 84, 1976, pp. 427-448.

Fisher, I., The Theory of Interest, New York, MacMillan, 1930.Henfrey, A., Albrecht, B., and Richards, P., 'The U.K. Stock Market and the

Efficient Market Model: A Review", The Investment Analyst, No. 48, pp. 5-24.Jaffe, J. F. and Mandelker, G., 'Inflation and the Holding Period Returns on

Bonds', The Wharton School, Working Paper No. 8-75 (1975).Mossin,J., The Theory of Financial Markets, Englewood Cliffs NJ., Prentice-

Hall, 1973.Roll, R., 'Interest Rates on Monetary Assets and Commodity Price Index

Changes',Journal of Finance, 27, 1972, pp. 25 1-277.Saunders, A., 'Expected Inflation, Unexpected Inflation and the Return on

U.K. Shares 1961-1973', Journal of Business Finance and Accounting, 5, 1978, pp.309-20.

Saunders, A. and Woodward, R. S., 'Monetary Policy, Exchange Rate Policyand the Determination of U.K. Interest Rates 1972-76', The Investment Analyst, 49,December 1977, pp. 15-20.

Zehna, P. W., Probability Distributions and Statistics, Boston, Alyn andBacon Inc., 1970.

APPENDIXThis appendix shows how the equations (1), (2), (3) and (4) in the text are

derived.

I. THE EXPONENTIAL DISTRIBUTION

Let the number of bids made at a rate x be given by f(x) where equation (Al)defines the distribution.

f(x)=Kc,ex (Al)

Thus the total demand at rate m will be

D(M)= Kccedx (A2)M

= K e - OEM

BID BEHAVIOUR AND THE DETERMINATION OF UK TREASURY BILL RATES 225

IfLe is the lowest bid made, then quantity demanded (QD) is given by

QDI< (A3)

and the quantity supplied (Qs) by

(A4)

where M1 is the lowest bid accepted. The average bid made may now be defined.Re-expressing function (A 1) as a relative frequency function the average bid made5 /L as defined in equation (A5).

xKc e_dx/1 Ke'

by integrating by parts this gives us,

= L 4Similarly the average bid accepted is given by equations (A6) and (A6').

Ç xKíe_dxM2

JM1KeM1

M2=M1+-

From equations (A3), (A4) and (A6')

QD_ (MiLeQSM2M1

and hence,

Log M2M1

Equation (3) in the text follows directly from equation (A7') by algebraicmanipulation.

Le=Log(M1 M2)+M1 (A8)

Substituting the formula for Le from equation (A8) into (A5') and also substitutingfor from equation (A6') gives us equation (4) in the text defining ¿cte, the averagebid made.

Q=K eM1

e0g(M1 -M2)+M2 (A9)

(A5)

(A5')

(A6)

(A6')

(A7)

(A7')

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II. THE RECTANGULAR DISTRIBUTION

The number of bids made at any rate within the upper and lower bounds H andLR is given byf(x) in the discontinuous function (Alo).

f(x) =x for LR<x<H (AlO)f(x) =0 for x<LR and x>H

Thus, the total demand at a rate M will be given by

D(M)=(MLR)x (All)

If L is the lowest bid made the quantity demanded (QD) will be given by

QD=(HLR)x (Al2)

and the quantity supplied by

Q=(HM1)x (A13)

from which may be derived the result

QDH-LRA14QsHM1

But the average bid accepted, M2, is known and, if the bid distribution isrectangular will be given by equation (A 15).

M2=M1 (A15)

whence

H=2M2M1 (A15')

Substituting equation (AIS') into (A 14) provides the means of deriving the equationfor LR; equation (1) in the text.

QD 2M2MtLRQ 2M2M1 M1

hence

LR=2(Ml M2)+2M2M1

The average bid accepted is given by equation (A 17),

LR + HI1R 2

and by substituting equations (AiG') and (A15') into (A17) we can derive (A18)

1R7(Ml M2)+2M2M1 (AlS)

which is equation (2) in the text.

(Al6')