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The purposes of this empirical study are to compare the predictive ability of five different models (the naive market return, the market model, the CAPM, the APT, and the LAPT) The market model and the CAPM are evaluated under two different parameter adjustments of the discount weighted estimation method (DWE) — (i) filtering and (ii) combined filtering and smoothing discussed earlier The constant individual-asset factor loadings for the APT and the constant individual-unlevered- asset factor loadings for the LAPT are estimated by using the factor analysis

To test the predictive ability o f the different models, the realised security

return, R,u , was compared to five appropriate benchmark expected returns, /•„'[/<,,,].

The null hypothesis is that the actual return and the expected return are not

significantly different (i e that the residual, elU , is not significantly different from

zero)

12This includes preference capital and total loan capital Total loan capital relates to all loans repayable in more than I year Loans from group companies and associates arc included

/■ -R ,] = o

Actual security returns were taken from the LSPD monthly returns file from January 1976 to December 1990 The monthly series of dividend adjusted logarithmic returns are calculated as

where P, is the last traded price in the month if the transaction is not on the last day of

the month

d t is the dividend declared ex-div during month t adjusted for any capital

changes during the month

P, , is the last traded price in month t - 1

The five types of benchmark expected returns are: (1) a naive forecast equal to the market return

where Rmt is the Trade-to-Trade capitalisation weighted Financial Times Actuaries

Because the Trade-to-Trade (TT) method directly abandons the use of equal length periods and takes the actual timing o f trades into account instead, estimating parameters might induce heteroscedasticity in the residuals as each return datum might not cover an equal length period of time Of course, the return variation is expected to

/ R ] = *,

(FTA) all-share market index (II)

(II) forecast returns of the market model ] - a lU + KIM f i l l ^ m l

increase with the length o f the time period for the return To ensure that the Trade-to- Trade beta estimates are efficient as well as unbiased. Marsh (1979) proposed a

trades (When the expected return is compared with the actual return, the transformed expected return was converted to the originally expected return by multiplying by the square root of the elapsed time ) In addition to correcting for the problems of nontrading, the Discount Weighted Estimation Method was used to avoid the problems

of variations in parameters The parameters a lU and /?,,, were estimated by two

adjustment methods One is simply by filtering from the previous five years’ LSPD return data, the other is by both filtering from the previous five years and smoothing back from the time five years after time t

(III) forecast returns of the Capital Asset Pricing Model (CAPM)

where R„ is the risk-free rate, taken as the three-month Treasury Bill rate, and the

trade-to-trade capitalisation weighted Financial Time Actuaries (FTA) all-share market index was used as the proxy for the market The method and procedure of estimating

parameter CapmP« are the same as those described for the market model 11

11 Marsh (197V) assumed the variance of the residuals is approximately proportional to the length of the period

weighting scheme" to avoid heteroscedasticity in the residual if beta is estimated by using ordinary least squares The transformed regression becomes

(IV) forecast returns of the Arbitrage Pricing Theory (APT)

] ~ + aptPii^-u + ...+AnP(j i), ^-[j 1)1

The constant sensitivities. AI,TP ,, of asset i'.v monthly return to the factors

were obtained from factor analysis using all stocks that were continuously listed during

the ten-year period, Jan 1979 — Dec 1988 Then, these individual-asset factor loading

estimates were used to estimate the risk premiums, A, associated with the estimated

factors, and the procedure is similar to a cross-sectional generalised least squares regression

(V) forecast returns of the Leveraged Asset Pricing Theory (LAPT)

R fl

+ A.<

... + A .<

I)

where u ,.TP lfl)l - l-,, i *iavtP ,_KO f 1 + ^I) '

V IJlArTP’tfU)Pl(l,, The method and procedure

of estimating the individual-asset factor loadings, ,M.r P,ivy and risk premia, A, ,

associated with the estimated factors are the same as those mentioned in APT In the

practice, R,,, - R„ was used as the input data for extracting the factor loadings for the

APT, where as (/<,, - R„)\---- ^ -J

v " " V v , \J was used as the input data for extracting the

factor loadings for the LAPT

4.5. End Note

In this chapter, the predictive experimental procedures were designed to examine the ability of five operationalised models — the naive market index, the market model, the CAPM, the APT. and the LAPT — in order to evaluate the quality of the new-derived LAPT Over the estimation procedures, the Trade-to-Trade method is proposed to avoid the problem of the nontrading effect, the Discount Weighted Estimation is chosen to estimate changing parameters for the market model and the CAPM, and the factor analysis is used to estimate the constant individual-asset factor loadings for the APT and the constant individual-unlevered-asset factor loadings for the LAPT Moreover, the sample data, and methodology used in this study of forecasting performance of the five models were described in detail as well

CHAPTER 5