CAPM Guide: Calculate Expected Returns Using the Capital Asset Pricing Model

Capital Asset Pricing Model
(CAPM)
W.Sharpe and J. Tobin
It specifies the manner in which Expected return and Beta are related
CAPM = RISK + RETURN
ingleyogeshh@gmail.com

Uses of CAPM
• To determine interest rates for corporate investments
• To estimate the required returns
• To evaluate the performance

Inputs required for applying CAPM
• Risk free rate of return
• Beta coefficient of security
• Return on security
• Return on market portfolio

Ki=Rf +β (Km – Rf)
• Ki= Required or Expected rate of return on security
• Rf= Risk free rate of return
• β= Coefficient of a security
• Km= Expected rate of return on market portfolio

A security is purchased for Rs 80. The investor gets
dividend of Rs 2 per share and market price after
one year is Rs 90.
What is the Rate of return?

The rate of return= Total Return / Investment
• Total Return = Dividend + Capital Appreciation
= 2 + 10
= Rs 12
The rate of return= Total Return / Investment
=(12/80)*100
=15%

Expected Rate of Return (Probability)
K=∑Pi Ki
• K= Expected rate of return on security
• Pi= Probability associated with the security return
• Ki= Possible outcome

For example, the rate of return and
probabilities on HPCL ltd are given below:
State of economy Probability of Occurrence Rate of return K
Boom 0.30 25% 7.5
Normal 0.50 20% 10
Recession 0.20 15% 3
∑ 20.5%

Risk= σ or S
• Calculation of standard deviation of rates of return of HPCL ltd. in the
previous example is as follows
• Expected rate of return (K): 20.5%
• σ = 3.5%
State of
economy
Rate of
return (Ki )
Rate of return
– Expected
Rate of return
(K)
(Ki –K) 2 Probability (Pi ) Pi * (Ki –K) 2
Boom 25% 4.5 20.25 0.30 6.075
Normal 20% 0.5 .25 0.50 0.125
Recession 15% - 5.5 30.25 0.20 6.050
∑ 12.25

Calculation of Expected Returns using CAPM
• Returns on ICICI bank were 12%, 13%, 12% and 11% in the last four
years.
• Returns on HDFC bank were 12%, 13%, 9% and 10% in the last four
years.
• While average market returns were 14%, 15%, 14% and 13% in the
last four years.
• Return on L&T Infrastructure bond was 6.5%.
You are required to compute beta factors and expected returns for ICICI
bank and HDFC bank by using CAPM and offer your comments.

Beta (β):
• β= COV (R i * R m ) / (σ 2 * m )
• COV (R i * R m ) = ∑ [(R i - Mean R i )*(R m - Mean R m ) ]/ (n -1)
• (σ 2 * m ) = ∑ (R m - Mean R m ) 2 / (n-1)

Calculation of beta factors
Year ICICI (%) HDFC (%) Market return (%)
2012-2013 12 12 14
2013-2014 13 13 15
2014-2015 12 09 14
2015-2016 11 10 13
12 11 14

• Beta factor of ICICI BANK
Year ICICI Ri
(%)
Ri - Mean
Ri
Market
return (%)
Rm
Rm - Mean Rm (Ri - Mean Ri ) * (Rm - Mean Rm ) (Rm -
Mean Rm )2
2012-2013 12 0 14 0 0 0
2013-2014 13 1 15 1 1 1
2014-2015 12 0 14 0 0 0
2015-2016 11 -1 13 1 1 1
12 14 2 2

Beta factor of HDFC BANK
Year HDFC
Ri (%)
Ri - Mean
Ri
Market
return (%)
Rm
Rm - Mean Rm (Ri - Mean Ri ) * (Rm - Mean Rm ) (Rm -
Mean Rm )2
2012-2013 12 1 14 0 0 0
2013-2014 13 2 15 1 2 1
2014-2015 09 -2 14 0 0 0
2015-2016 10 -1 13 1 1 1
11 14 3 2

• β= COV (R i * R m ) / (σ 2 * m )
• ICICI Bank β= (2/3)/(2/3) =1
• HDFC Bank β= (3/3)/(2/3) =1.5

Calculation of Expected Returns using CAPM
Expected Return on ICICI bank
Ki=Rf +β (Rm – Rf)
=6.5 + 1(14-6.5)
=14%
Expected Return on HDFC bank
Ki=Rf +β (Rm – Rf)
=6.5 + 1.5(14-6.5)
=17.75%

Comments:
• In this case, ICICI bank provides low returns of 14% and its beta is 1.0.
However, HDFC bank provides higher expected return of 17.55%
while its beta is 1.5%. Thus, there is a higher risk with HDFC bank due
to higher beta factor.

Risk free return may be taken at 14%
You are required to calculate:
Expected rate of return of portfolio in each using CAPM
Average return of portfolio
Investments in
Equity shares
Face value Dividend/Interest Market price Beta risk factor
ACC LTD 25 2 50 0.8
Tata steel ltd 35 2 60 0.7
UB LTD 45 2 135 0.5
Indian Railways
bonds
1000 140 1005 0.99

Calculation of Expected Rate of Return:
Investments in
Equity shares
Face value Dividend/Interest Market price Capital gain
ACC LTD 25 2 50 25
Tata steel ltd 35 2 60 25
UB LTD 45 2 135 90
Indian Railways
bonds
1000 140 1005 5
1105 146 145

• Expected rate of return on market portfolio:
(Total Return / Investment) * 100
• Total Return = Dividend + Capital Appreciation
= 146 + 145
= 291
Expected rate of return on market portfolio:
= (291/1105)*100
=26.33%

Applying CAPM, we get,
Ki= Rf +β (Rm – Rf)
• ACC Ltd = 14 + 0.8 (26.33-14) = 23.86%
• Tata Steel ltd = 14 + 0.7 (26.33-14) = 22.63%
• U B ltd = 14 + 0.5 (26.33-14) = 20.17%
• Tata Steel ltd = 14 + 0.99 (26.33-14) = 26.21%

• Average return on portfolio: (23.86 + 22.63+20.17+26.21)/4 =23.22%

The expected returns and beta of three securities are as above:
if the risk free rate is 9% and market returns are 14%, which of
the above securities are over, under or correctly valued in the
market?
What should be your strategy?
Securities HPCL ONGC RELIANCE
Expected Return (%) 18 11 15
Beta Factor 1.7 0.6 1.2

Applying CAPM, we get,
Ki= Rf +β (Rm – Rf)
• HPCL = 9 + 1.7 (14-9) = 17.5%
• ONGC = 9 + 0.6 (14-9) = 12%
• Reliance = 9 + 1.2 (14-9) = 15%

• Comparison of securities:
Security Expected Return Market Return
HPCL 17.5% 14%
ONGC 12% 14%
Reliance 15% 14%

Analysis:
Strategy should be to buy undervalued security
and sell the convertible security.
HPCL Undervalued because its return is higher than the market
ONGC Overvalued because its return is lower than market
Reliance Undervalued because its return is higher than the market

For practice:
• Returns on TATA ltd were 11%, 13%, 12% and 10% in the past four
years.
• Returns on M&M ltd were 12%, 14%, 9% and 10% in the last four
years.
• While average market rate of return were 12%, 14%, 14% and 13% in
the last four years.
• Return on government securities is 8%
You are required to compute beta factors and expected returns of both
the companies using CAPM and offer comments.

CAPM Guide: Calculate Expected Returns Using the Capital Asset Pricing Model

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