SUMMARY
Sometimes it may be necessary to find the first few dominant principal components of a dispersion (covariance) matrix of large order. For many computers such problems could be too big to handle. This paper provides an effective approach to such situations through a series of splitting and merging operations on subsets of variables. An illustration is provided with applications of the suggested technique to stock price data.
The c o n s i s t e n c y of t h e Modigliani-Miller v a l u a t i o n p r o p o s i t i o n and CAPM w a s demonstrated by Hamada. Hamada r e s t r i c t s h i s a n a l y s i s t o change i n l e v e r a g e of a f i r m which i s s u f f i c i e n t l y small s o t h a t t h e d i s t r i b u t i o n of market r e t u r n s w i l l n o t b e a f f e c t e d . c o n s i d e r i n g t h e m u l t i -f i r m case. A n i m p l i c a t i o n of t h i s proof i s t h a t changes i n l e v e r a g e of f i r m s i s a p o t e n t i a l s o u r c e of n o n -s t a t i o n a r i t y i n t h e i n t e rl a c e o f market r e l a t i o n s h i p s t h a t are e x p l a i n e d by t h e CAPM. We show t h a t t h e s y s t e m a t i c r i s k o f a f i r m i s n o t o n l y a f f e c t e d by changes in t h a t f i r m ' s l e v e r a g e , b u t a l s o by changes i n t h e l e v e r a g e of o t h e r f i r m s which p a r t i c ip a t e i n t h e same c a p i t a l market.
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