❖ Sup9po.1se Ryoeu tbuourgnhst 1:0E0 sxhaarmespofleWal-Mart
(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?
Year Return 1 10% 2 -5% 3 20% 4 15%
Arithmaevteircargeeturrn1r2r3r4 4
10%5%20%15%10% 4
Holding Period Returns
Time
0
Initial investment
1
•Percentage Returns: the sum of the cash
received and the change in value of the asset
divided by the original investment. Frequently:
❖ 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$02.8,%500).$520
9.2 Holding-Period 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
Value percentage return
dollar return
beginning market value
dividend change in market value beginning market value
dividend yield capital gains yield This is not statutory (tax law) capital gains
现代企业资本市场理论分析
9.1 Returns: Very Important
❖ Dollar Returns
the sum of the cash received and the change in value of the asset, in dollars.
Dividends
Ending market value
❖ Your percentage gain for the year is $2,500
9.1 Returns: Example
❖ Dollar Returns
$520 gain
$ห้องสมุดไป่ตู้0
$3,000
Time
0
-$2,500
1 •Percentage Returns
20.8% $520 $2,500
❖ Note that the geometric average is not the same thing as the arithmetic average. In finance we use the geometric average. For small changes, the arithmetic average is approximately the same as the geometric.
rt = ln(1 + (pt - pt-1+dt)/pt-1) is better for modeling. Fechner’s Law: response is
proportional to stimulus
Dollar Return9=.D1iviRdeendtu+rCnhsange in Market
periodhi ios glid veninasgri: pe riod return (1r1)(1r2)L(1rn)1 somectiamll"eebsduaynhdo"lrdeturn fotrh4eyeapreriod
Holding Period Return: Example ❖ Suppose your investment provides the following returns over a four-year period. [Note that this is a PV, NOT NPV
• So, our investor made 9.58% on his money for four years, realizing a holding period return of 44.21%
1.4421(1.09584)44
Holding Period Return: Example
Year Return Youhroldinpgeriordeturn
1 2
10% -5%
(1r1)(1r2)(1r3)(1r4)1
3 20% (1.10)(.95)(1.20)(1.15)1
4 15% .442144.21%
Holding Period Return: Example ❖ An investor who held this investment would have actually realized an annual return of 9Y.5ea8r%R: eturn Geomeatrvicerargeeturn 1 10% (1rg)4 (1r1)(1r2)(1r3)(1r4) 2 -5% 3 20% rg 4 (1.10)(.95)(1.20)(1.15)1 4 15% .0958449.58%