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STAC70H3 (1)

Lecture 1 STAC70.docx

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Michael Evans

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Return: Change in price of an asset as a proportion of the initial price R =( P – P )/P = (P /P ) -1 > -1 t t t-1 t-1 t t-1 (where R = the return in the T’th period) t whereas the gross return = (P /P ) = 1 + R t t-1 t (P tP )t-kgross return in the k closest period = 1 + R (k) t Note: P /P t P t-kx P tP .t-1 P t-1 t-2 t-k+1/P t-k1+R )(1+Rt)....(1t-1 t-k+1) Def: r = ln (P /P ) = ln P – ln P = P P t t t-1 t t-1 t – t-1 k k k 2 3 Note: r = tn(1+R ) = ∑ tx-0) /k! d /dx (ln(x+x)) = x – x /2 + x /3 +.... ~x Eg: 1) ln(1+.1)=.0953~0.1 2) ln(1+.01)=.00995~0.01 3)ln(1+0.5)=.405 ~ 0.05 (P tP )t-k∏ (1+R t-i+1 ln (P tP )t-k∑ ln(1+R t-i+1 Dividends R t P D t + /tP = Pt-1/ P t-1 t + t t-1 ........................................................................................
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