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Chapter - 4
Risk and Return: An Overview of Capital
Market Theory
2Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
Chapter Objectives 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.
3Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
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 R
etu
rn (%
)
1 1 01 011
0 0 0
Rate of return Dividend yield Capital gain yield
DIVDIV
P PP PR
P P P
4Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
Average Rate of Return The 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:
1 2=1
1 1 = [ ]
n
n tt
R R R R Rn n
5Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
Risk of Rates of Return: Variance and Standard Deviation Formulae for calculating variance and
standard deviation:Standard deviation = Variance
2
2
1
1
1
n
tt
R Rn
6Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
Investment Worth of Different Portfolios, 1969–70 to 1997–98
57.16
13.9910.3610.20
4.41
1
10
100
1969-7
0
1970-7
1
1971-7
2
1972-7
3
1973-7
4
1974-7
5
1975-7
6
1976-7
7
1977-7
8
1978-7
9
1979-8
0
1980-8
1
1981-8
2
1982-8
3
1983-8
4
1984-8
5
1985-8
6
1986-8
7
1987-8
8
1988-8
9
1989-9
0
1990-9
1
1991-9
2
1992-9
3
1993-9
4
1994-9
5
1995-9
6
1996-9
7
1997-9
8 Year
Index
Stock Market Return
Call Money Market
Long-term Govt. Bonds
Inflation
91-day TB
7Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
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
Relative to 91-Days T-bills. # Relative to long-term government bonds.
8Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
Expected Return : Incorporating Probabilities in Estimates The 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
9Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
Expected Risk and Preference The following formula can be used to
calculate the variance of returns:
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
10Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
Expected Risk and Preference A 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.
11Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.
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.