The equity duration of South African growth companies : a theoretical and empirical evaluation

Barnard, Ian (2002-12)

Thesis (MComm)--Stellenbosch University, 2002.

Thesis

ENGLISH ABSTRACT: This assignment sets out to address the concept of equity duration, where equity duration is viewed as a measure of the interest rate sensitivity of common stock's market value. The traditional use of standard dividend discount models, results in extremely long duration estimates for equities - in the order of 10 years for income stocks to 25 years and more for growth companies whose cash flows are not expected to materialize until some future period. Leibowitz (1986) identified an alternative approach for assessing equity duration empirically. These empirical estimates of actual stock price sensitivity to underlying changes in interest rates imply that equities behave as if they are much shorter duration instruments. Various attempts have been made to reconcile the difference between theoretical predictions of equity duration and empirical findings. The differences in duration of assets in place and growth opportunities are given as a possible reason for the above mentioned differences. It is argued that investment opportunities are similar to options a company has. These option-like characteristics of growth opportunities may alter the basic relationship between equity valuation and interest rate changes. The option framework suggests that the duration of growth companies may be shorter (not longer) than those of assets in place. The results from option theory can however not be applied directly to growth options, since some of the assumptions may not be valid in the case of growth options. The presence of these growth options makes it virtually impossible to calculate equity duration theoretically. This study empirically tests the relationship between growth opportunities and equity duration by focussing the attention on the interest rate sensitivity of South African growth companies. The following hypotheses regarding equity duration and growth companies are postulated: • There is a significant difference in interest rate sensitivity between growth companies and low-growth companies. • There is a significant difference between duration of growth companies measured using nominal interest rates and duration of growth companies using real interest rates. All non-mining companies on the Johannesburg Securities Exchange SA, for the period 1980 to 2000, were analysed. These companies were sorted into different portfolios that reflected their growth opportunities. Market capitalisation, book-to-market and price-earnings ratios were used as proxies to rank companies according to growth opportunities. The results from univariate regressions suggest positive duration for common equities. The negative relationship between equity returns and changes in nominal interest rates are independent of size, book-to-market or price-earnings ratios of the sampled companies. Including the market factor as an independent variable results in markedly different equity duration. The duration is correlated with size, as both coefficients and t-statistics increase when moving from small companies to larger companies. In addition, the small companies have negative not positive duration, as was the case for simple univariate regressions. There is also some evidence that high growth portfolios, as measured by low book-to-market and high price-earnings ratios, are less sensitive to interest rate changes than low growth portfolios. Employing all three Fama and French's factors, there is no longer a cross-sectional dependence on company size, with the mean duration being close to zero and statistically insignificant in virtually all cases. Also, when dividing changes in the nominal interest rate into changes in real rates and changes in inflation, it does not significantly affect the estimates of equity duration. The author found no evidence to support the stated hypotheses, when employing the Fama and French's three factor model. This may mean that the relationships are subsumed in the Fama and French risk factors.

AFRIKAANSE OPSOMMING: Hierdie werkstuk bestudeer die konsep van die duur van gewone aandele (equity duration), waar die duur van 'n gewone aandeel gedefinieer word as 'n maatstaf van die rentekoerssensitiwiteit van die markwaarde van die aandeel. Die tradisionele gebruik van standaard dividend verdiskonterings modelle, lei tot uiters lang duur beramings vir gewone aandele - in die orde van 10 jaar vir inkomste aandele tot 25 jaar en meer vir groei ondernemings wie se kontantvloei nie verwag word om te materialiseer voor 'n sekere toekomstige datum nie. Leibowitz (1986) identifiseer 'n alternatiewe empiriese benadering vir die beraming van gewone aandeel duur. Hierdie empiriese bepaling van die sensitiwiteit van die werklike aandeelprys tot onderliggende veranderings in rentekoerse, impliseer dat gewone aandele reageer asof hulle baie korter duur instrumente is. Verskeie pogings is aangewend om die verskille tussen teoretiese voorspellings van gewone aandeel-duur en empiriese bevindings te rekonsilieer. Die verskille tussen duur van bates in plek en groei-geleenthede word aangevoer as 'n moontlike rede vir bogenoemde verskille. Dit word geargumenteer dat investeringsgeleenthede soortgelyk is aan die opsies wat 'n onderneming het. Hierdie opsie-soortgelyke eienskappe van groei-geleenthede kan die basiese verhouding tussen gewone aandeel waardasie en rentekoers verandering wysig. Die opsie raamwerk dui daarop dat die duur van groei-ondernemings korter kan wees (en nie langer nie) as die van bates in plek. Die resultate van opsie teorie kan egter nie direk toegepas word op groei-opsies nie, aangesien sekere van die aannames nie geldig mag wees in die geval van groei-opsies nie. Die teenwoordigheid van hierdie groei-opsies het tot gevolg dat dit feitlik onmoontlik is om gewone aandeel-duur teoreties te bereken. Die studie toets empiries die verhouding tussen groei-geleenthede en gewone aandeel-duur deur te fokus op die rentekoers sensitiwiteit van Suid Afrikaanse groei-ondernemings. Die volgende hipoteses met betrekking tot die gewone aandele duur en groei-ondernemings word gestel: • Daar is 'n betekenisvolle verskil in rentekoers sensitiwiteit tussen groei-ondernemings en lae groei-ondernemings. • Daar is 'n betekenisvolle verskil tussen duur van groei-ondernemings gemeet deur gebruik te maak van nominale rentekoerse en duur van groei-ondernemings deur gebruik te maak van reële rentekoerse. Alle nie-myn ondernemings op die Johannesburg Sekuriteite Beurs SA, vir die periode 1980 tot 2000, is ontleed. Hierdie ondernemings is gesorteer in verskillende portefeuljes wat hulle groei geleenthede reflekteer. Markkapitalisasie, boek-tot-markwaarde en prysverdienste verhoudings is gebruik as maatstawwe om ondernemings te rangskik volgens groeigeleenthede. Die resultate van enkel veranderlike regressies dui positiewe duur aan vir gewone aandele. Die negatiewe verhouding tussen aandeelopbrengs en verandering in nominale rentekoerse is onafhanklik van grootte, boek-tot-markwaarde of prysverdienste verhoudings vir die getoetste ondernemings. Indien die markfaktor ingesluit word, as 'n onafhanklike veranderlike, lei dit tot opvallend verskillende gewone aandeel-duur. Die duur is gekorreleer met grootte, met beide koëffisiënte en t-statistieke wat styg wanneer beweeg word van klein ondernemings tot groter ondernemings. Addisioneel, die klein ondernemings het negatiewe, nie positiewe duur, anders as in die geval van eenvoudige enkel veranderlike regressies. Daar is ook bewyse dat hoë groei portefeuljes, soos gemeet deur lae boek-tot-markwaarde en hoë prysverdienste verhoudings, minder sensitief is vir rentekoers veranderings as lae groei portefeuljes. Met die aanwending van al drie Fama en French se faktore is daar nie meer kruis-selektiewe afhanklikheid (cross-selectional dependence) op ondernemingsgrootte aanwesig nie, met die gemiddelde duur wat naby nul is en statisties onbedeidend in feitlik all gevalle is. Wanneer die verandering in die nominale rentekoers verdeel word in veranderings in reële koerse en veranderings in inflasie, beïnvloed dit ook nie betekenisvol die bepaalde gewone aandeel duur nie. Die outeur het met die gebruik van die Fama & French drie faktor model geen bewyse gevind wat die vermelde hipoteses staaf nie. Dit mag beteken dat die rente-risiko verwantskappe in die Fama en French risiko faktore vervat is.

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