Risk & Return
In which security will you invest?
•
Security A gives annual expected return of 12% p.a.
•
Security B gives annual expected return of 18% p.a.
Option 1: Security A
Option 2: Security B
Option 3: Can not say
Elements in Return
Return on a typical investment consists of two components:
•
(1) Periodic cash receipts(or income) on investment in the form of
interest or dividends
•
(2) Change in price of asset called capital gain/loss
•
Total return = Income + Price change(+/)
RETURN OF A SINGLE ASSET
Rate of Return =
Annual income
+
Ending priceBeginning price
Beginning price
Beginning price
Current yield
Capital gains /loss
yield
Return
Year
Dividend
(Rs.)
Share Price
(Rs.)
Return
(%)
2007
2
100

2008
2.5
108
=[2.5+(108100)]/100 = 0.105 = 10.5%
2009
3
115
=[3+(115108)]/108 = 0.0925 = 9.25%
2010
3
104
??
2011
4
120
??
6
1
1
0
1
0
1
1
0
0
0
Rate of return
Dividend yield
Capital gain yield
DIV
DIV
P
P
P
P
R
P
P
P
AVERAGE ANNUAL RETURNS
The arithmetic mean is defined as:
n
R
i
R
=
i=1
n
The arithmetic mean return for stock A is: (19+14+2212+5)/5 =
9.6%
Year
Total return (%)
1
19
2
14
3
22
4
12
5
5
Can you Calculate Average Return?
Year
Price (Rs)
Return
2013
50
2014
100
100%
2015
50
50%
Geometric Average Return
•
Geometric average return measures compound , cumulative returns over time
. It
is used in investments to reflect the realized change in wealth over multiple
periods.
•
Geometric Return = [(1+0.19)(1+0.14)(1+0.22)(10.12)(1+0.05)]
1/5
1 =
8.86%
DATA ON THE NIFTY INDEX
The return for the year ended 1991 is 559/331 1 =
68.88 percent. The returns for other years have been calculated
the same way. The means of the returns are calculated as under:
Arithmetic Mean
= ( 68.84 + 36.28 ++ 6.76 + 31.41)/ 24 =
19.57 %
Geometric Mean
=(1.6884x1.3628x1.0676x1.3141)
1/24
–1 = (25.0378)1/241 =
14.36 %
Year ending
NIFTY
Annual return
(%)
Year ending
NIFTY
Annual return
(%)
1990
331

2002
1094
3.25
1991
559
68.84
2003
1880
71.90
1992
761
36.28
2004
2081
10.68
1993
1043
36.95
2005
2837
36.34
1994
1182
13.40
2006
3966
39.83
1995
909
23.15
2007
6139
54.77
1996
899
1.04
2008
2959
51.79
1997
1079
20.05
2009
5201
75.76
1998
884
18.08
2010
6135
17.95
1999
1480
67.42
2011
4624
24.62
2000
1264
14.65
2012
5905
27.70
2001
1059
16.18
2013
6304
6.76
2014
8284
31.41
Expected Return based on
Probability
Scenario
Probability(P)
Return(R)
Expected return=
PxR
Boom
0.30
16%
0.30X16 =4.8%
Normal
0.50
12%
0.50x12 = 6%
Recession
0.20
8%
0.20x8 = 1.6%
TOTAL EXPECTED
RETURN = 4.8%
+6%+1.6% =
12.4%
11
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 Capital Asset Pricing Model, Corporate Finance, Rjt