Risk and Return: An Overview of Capital Market Theory

Prepared by: Chhaya Patel

Discuss the concepts of average and expected rates of return.

Define and measure risk for individual assets.Show the steps in the calculation of standard

deviation and variance of returns.Explain the concept of normal distribution and the

importance of standard deviation.Compute historical average return of securities and

market premium.Determine the relationship between risk and return.Highlight the difference between relevant and

irrelevant risks.

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Return on a Single Asset Total return

= Dividend + Capital gain

Year-to-Year Total Returns on HLL Share

149.70

70.54

16.52 22.71

49.52

92.33

36.13

52.64

7.29 12.95

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Year

Tota

l Retu

rn (%

)

3

1 1 01 011

0 0 0

Rate of return Dividend yield Capital gain yield

DIVDIV

P PP PR

P P P

Average Rate of ReturnThe average rate of return is the sum of

the various one-period rates of return divided by the number of period.

Formula for the average rate of return is as follows:

4

1 2=1

1 1 = [ ]

n

n tt

R R R R Rn n

Risk of Rates of Return: Variance and Standard Deviation

Formulae for calculating variance and standard deviation:

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Standard deviation = Variance

2

2

1

1

1

n

tt

R Rn

Investment Worth of Different Portfolios, 1969–70 to 1997–98

57.16

13.9910.3610.20

4.41

1

10

100

1969

-70

1970

-71

1971

-72

1972

-73

1973

-74

1974

-75

1975

-76

1976

-77

1977

-78

1978

-79

1979

-80

1980

-81

1981

-82

1982

-83

1983

-84

1984

-85

1985

-86

1986

-87

1987

-88

1988

-89

1989

-90

1990

-91

1991

-92

1992

-93

1993

-94

1994

-95

1995

-96

1996

-97

1997

-98 Year

Index

Stock Market Return

Call Money Market

Long-term Govt. Bonds

Inflation

91-day TB

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Averages and Standard Deviations, 1970–71 to 1997–98

Securities

Arithmetic mean

Standard deviation

Risk premium*

Risk premium#

Ordinary shares (RBI Index) 17.50 22.34 12.04 8.76 Call money market 9.93 3.49 4.47 1.19 Long-term government bonds 8.74 2.59 3.28 91-Day treasury bills 5.46 2.05 Inflation 8.80 5.82

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Relative to 91-Days T-bills. # Relative to long-term government bonds.

Expected Return : Incorporating Probabilities in EstimatesThe expected

rate of return [E (R)] is the sum of the product of each outcome (return) and its associated probability:

RETURNS UNDER VARIOUS ECONOMIC CONDITIONS

Economic Conditions Share Price Dividend Dividend Yield Capital Gain Return (1) (2) (3) (4) (5) (6) = (4) + (5)

High growth 305.50 4.00 0.015 0.169 0.185 Expansion 285.50 3.25 0.012 0.093 0.105 Stagnation 261.25 2.50 0.010 0.000 0.010 Decline 243.50 2.00 0.008 – 0.068 – 0.060

RETURNS AND PROBABILITIES

Economic Conditions Rate of Return (%) Probability Expected Rate of Return (%) (1) (2) (3) (4) = (2) (3)

Growth 18.5 0.25 4.63 Expansion 10.5 0.25 2.62 Stagnation 1.0 0.25 0.25 Decline – 6.0 0.25 – 1.50 1.00 6.00

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Expected Risk and PreferenceThe following formula can be used to

calculate the variance of returns:

9

2 2 2 21 1 2 2

2

1

... n n

n

iii

R E R P R E R P R E R P

R E R P

Expected Risk and PreferenceA risk-averse investor will choose among

investments with the equal rates of return, the investment with lowest standard deviation. Similarly, if investments have equal risk (standard deviations), the investor would prefer the one with higher return.

A risk-neutral investor does not consider risk, and would always prefer investments with higher returns.

A risk-seeking investor likes investments with higher risk irrespective of the rates of return. In reality, most (if not all) investors are risk-averse.

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Normal Distribution Normal distribution is an important concept

in statistics and finance. In explaining the risk-return relationship, we assume that returns are normally distributed.

Normal distribution is a population-based, theoretical distribution.

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