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erage Geom etric443214?????????????????ggrrrrrr? So, our investor made % on his money for four years, realizing a holding period return of % 4)( ?McGrawHill/Irwin Copyright 169。 2023 by The McGrawHill Companies, Inc. All rights reserved. 95 HoldingPeriod Returns ? The holding period return is the return that an investor would get when holding an investment over a period of n periods, when the return during period i is given as ri: ??holdi ng peri od ret urn ?? ( 1 ? r1) ? ( 1 ? r2) ? ? ( 1 ? rn) ? 1s om e ti m es cal le d buy and hold r et ur nfor the 4 ? ye ar perio dMcGrawHill/Irwin Copyright 169。 2023 by The McGrawHill Companies, Inc. All rights reserved. 93 Returns: Example ? Suppose you bought 100 shares of WalMart (WMT) one year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share 100 shares). At the end of the year, the stock sells for $30. How did you do? ? Quite well. You invested $25 * 100 = $2,500. At the end of the year, you have stock worth $3,000 and cash dividends of $20. Your dollar gain was $520 = $20 + ($3,000 – $2,500). ? Your percentage gain for the year is 500,2$520$% ?McGrawHill/Irwin Copyright 169。 2023 by The McGrawHill Companies, Inc. All rights reserved. 91 Returns: Very Important ? Dollar Returns – the sum of the cash received and the change in value of the asset, in dollars. Time 0 1 Initial investment Ending market value Dividends ?Percentage Returns: the sum of the cash received and the change in value of the asset divided by the original investment. Frequently: rt = ln(1 + (pt pt1+dt)/pt1) is better for modeling. Fechner’s Law: response is proportional to stimulus McGrawHill/Irwin Copyright 169。McGrawHill/Irwin Copyright 169。 2023 by The McGrawHill Companies, Inc. All rights reserved. 90 Chapter Outline Returns HoldingPeriod Returns Return Statistics Average Stock Returns and RiskFree Returns Risk Statistics Summary and Conclusions McGrawHill/Irwin Copyright 169。 2023 by The McGrawHill Companies, Inc. All rights reserved. 92 Dollar Return = Dividend + Change in Market Value Returns ??perc e n ta g e ret urn ?doll a r ret urnbeg inn ing ma rke t v a lue?div ide nd ? c hang e in ma rket v a luebeg inn ing ma rke t v a lue? div ide nd y ie ld ? c a pit a l g a ins y ie l dThi s i s not s ta tut o ry (ta x la w ) ca pit a l g a insMcGrawHill/Irwin Copyright 169。 2023 by The McGrawHill Companies, Inc. All rights reserved. 94 Returns: Example ? Dollar Returns – $520 gain Time 0 1 $2,500 $3,000 $20 ?Percentage Returns 500,2$520$% ?McGrawHill/Irwin Copyright 169。 2023 by The McGrawHill Companies, Inc. All rights reserved. 9