Risk And Returns- Fin Society-iiu Business School 29-11-08
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Risk and Returns Mazhar Hussain Consultant/ Assistant Professor FMS, IIU-Business School November 29, 2008
Capital Market Theory: An Overview Returns: Dividend and Capital Gain
Purchased 100 shares of Tele Computers Public Limited Company at a price of Rs.37 per share
Suppose Company paid dividend of Rs.1.85 per share
Total Investment = Rs.37 * 100=Rs.3700
Div = Rs.1.85 * 100= Rs.185
After one week later, if the market price of the share is Rs.40 per share
Capital Gain = (Rs.40 – Rs.37) * 100 = Rs.300 Capital Loss = (Rs.35 – Rs.37) * 100 = - Rs.200
Capital Market Theory: An Overview Returns: Dividend and Capital Gain
Total Rupee Return = Dividend income + Capital Gain (or loss) Total Rupee Return = Rs.185 + Rs.300 = Rs.485 Total Cash if shares are sold = Initial Investment + Total Rupee Return = Rs.3700 + Rs.485 = Rs.4185 = Proceeds from Share sale + Dividends =Rs.40 * 100 + Rs.185 =Rs.4000 + Rs.185 = Rs.4185
Capital Market Theory: An Overview Returns: Dividend and Capital Gain Dividend Yield = Divt+1 / Pt = Rs.1.85/Rs.37 =5%
Capital Gain = (Pt+1 – Pt) / Pt =(Rs.40 – Rs.37)/Rs.37 = Rs.3/Rs.37 = 8.10 %
Total Return on Investment= Rt+1
Rt+1= Divt+1 / Pt + (Pt+1 – Pt) / Pt
= 5% + 8.10% = 13.10%
Capital Market Theory: An Overview Holding- Period Returns (HPR)
(1+ R1) * (1+ R2) *…*(1+Rt)*…* (1+RT) If the returns were 11%, -5% and 9% in a three years period (1+ R1) * (1+ R2)*(1+ R3)= (Rs.1+0.11) * (Rs.1- 0.05) * (Rs.1+ 0.09) = Rs.1.11* Rs.0.95 * Rs.1.09 = Rs.1.15 Therefore the Total Return at the end of three years = 15%
Capital Market Theory: An Overview Return Statistics
Mean = R = (R1 +…..+RT)/ T If the returns on common stock from 2000 to 2003 are 0.1370, 0.3580, 0.4514 and – 0.0888 respectively, than return over these four years is R = 0.1370 + 0.3580+ 0.4514 – 0.0888/4= 0.2144
Capital Market Theory: An Overview Average Stock Returns and Risk-Free
Returns Excess Return on the Risky Asset =Risk Premium = Risky Returns – Risk-Free Returns If
Average Risky Return = 13.3% and Average Risk-Free Return = 3.8% than Average Excess Return= (13.3% - 3.8%) = 9.5%
Capital Market Theory: An Overview Risk Statistics: How the risk can be measured
Variance:
is a measure of the squared deviations of a security’s return from its expected return Var = 1/T-1 { (R1 – R)2 + (R2 – R)2 + (R3 – R)2 + (R4 – R)2}
Standard Deviation:
the square root of the variance SD = σ = √ Var
Risk and Return :Capital Asset Pricing Model (CAPM) Expected Return, Variance and Covariance
Expected Return : the average return per period a security has earned in the past
Covariance: is a statistic measuring the interrelationship between two securities
Correlation: the alternative approach, to determine the correlation between the two securities
Risk and Return :Capital Asset Pricing Model (CAPM) Expected Return:
States of Economy
RAT
RBT
Depression
-20% 5%
Recession
10% 20%
Normal
30% -12%
Boom
50% 9%
RA = 17.5% and RB = 5.5%
Risk and Return :Capital Asset Pricing Model (CAPM) State of Eco.
Rate of Return RAT
Depression
-0.20
Recession
Deviation from Squared Expected Return Value of Deviation (RAT - RA) (RAT - RA)2
0.10
(-0.20 – 0.175)= -0.375 -0.075
(-0.375)2= 0.140625 0.005625
Normal
0.30
0.125
0.015625
Boom
0.50
0.325
0.105625
Total
0.267500
Risk and Return :Capital Asset Pricing Model (CAPM) State of Eco.
Depression
RBT 0.05
Recession Normal
0.20 -0.12
Deviation from Squared Expected Return Value of Deviation (RBT - RB) (RBT - RB)2 (0.05 – 0.055)= (-0.005)2= -0.005 0.000025 0.145 0.021025 -0.175 0.030625
Boom
0.09
0.035
Total
Rate of Return
0.001225 0.052900
Risk and Return :Capital Asset Pricing Model (CAPM) Var (R )= 0.2675/4 = 0.066875 A
SD (R )= √ 0.066875 = 0.2586= 25.86% A
Var (R )= 0.0529/4 = 0.013225 B
SD (R )= √ 0.013225 = 0.1150 = 11.50% B
Risk and Return :Capital Asset Pricing Model (CAPM) State of Eco.
Rate of Return
Deviation from Expected Return
Rate Deviation of from Return Expected Return
Product of Deviation
RAT
(RAT - RA)
RBT
(RBT - RB)
(RAT - RA) * (RBT - RB)
Depression
-0.20
-0.375
0.05
-0.005
0.001875
Recession
0.10
-0.075
0.20
0.145
-0.010875
Normal
0.30
0.125
-0.12
-0.175
-0.021875
Boom
0.50
0.325
0.09
0.035
0.011375
Total
- 0.0195
Risk and Return :Capital Asset Pricing Model (CAPM) Covariance
σ = Cov (R , R )= (R
σ = Cov (R , R )= - 0.0195 = - 0.004875
Interpretation of Results
AB
AB
A
A
B
AT
- R ) *(R A
B
Positive relationship Negative relationship No relation = Zero Covariance
BT
-R) B
Risk and Return :Capital Asset Pricing Model (CAPM) Correlation ρ = Corr (R ,R ) = Cov (R , R )/ σ * σ = - 0.004875/ 0.2586 * 0.1150 = - 0.1639 AB
A
B
A
B
A
B
Interpretation of Results
Positively Correlated,+1= Perfect Positive Correlation Negatively Correlated,-1= Perfect Negatively Correlation Uncorrelated, 0 = No correlation
Risk and Return :Capital Asset Pricing Model (CAPM) Total Risk of Individual Security Total Risk of Individual Security (Var)= Portfolio Risk (Cov) or Systematic Risk + Unsystematic or Diversifiable Risk (Var – Cov)
Risk and Return :Capital Asset Pricing Model (CAPM) Definition of Risk When Investor Hold the
Market Portfolio Researchers argue that the best measure of the risk of a security in large portfolio is the Beta of the security Beta measures the responsiveness of a security to the movement in the market portfolio. β = Cov (R ,R ) / Var (R )
i
i
M
M
Risk and Return :Capital Asset Pricing Model (CAPM) Sate
Type of Eco.
Return on Market %
Return on Jelco, Inc. %
I
Bull
15
25
II
Bull
15
15
II
Bear
-5
-5
IV
Bear
-5
-15
Type of Eco.
Return on Market %
Return on Jelco, Inc. %
Bull
15%
20% = 25%½+ 15%½
Bear
-5%
-10% = -5%½ + (-15%½)
The Capital Asset Pricing Model: The Relationship b/w Risk and Expected Return (CAPM) Expected Return on Market RM = RF + Risk Premium Expected Return on Individual Security CAPM : R = RF + β * ( RM – RF ) R = Expected return on a security RF = Risk- free rate β = Beta of the Security ( RM – RF ) = Difference b/w expected return on market and risk-free rate
The Capital Asset Pricing Model: The Relationship b/w Risk and Expected Return (CAPM) Expected Return on Individual Security
CAPM :
R=R +β*(R –R )
If β = 0 , R = R
If β = 1 , R = R
F
M
F
M
F
In Diagram Form: SECURITIES MARKET LINE E ( Rm )
Rf
1
βi
Capital Market Theory: An Overview Returns: Dividend and Capital Gain
Purchased 100 shares of Tele Computers Public Limited Company at a price of Rs.37 per share
Suppose Company paid dividend of Rs.1.85 per share
Total Investment = Rs.37 * 100=Rs.3700
Div = Rs.1.85 * 100= Rs.185
After one week later, if the market price of the share is Rs.40 per share
Capital Gain = (Rs.40 – Rs.37) * 100 = Rs.300 Capital Loss = (Rs.35 – Rs.37) * 100 = - Rs.200
Capital Market Theory: An Overview Returns: Dividend and Capital Gain
Total Rupee Return = Dividend income + Capital Gain (or loss) Total Rupee Return = Rs.185 + Rs.300 = Rs.485 Total Cash if shares are sold = Initial Investment + Total Rupee Return = Rs.3700 + Rs.485 = Rs.4185 = Proceeds from Share sale + Dividends =Rs.40 * 100 + Rs.185 =Rs.4000 + Rs.185 = Rs.4185
Capital Market Theory: An Overview Returns: Dividend and Capital Gain Dividend Yield = Divt+1 / Pt = Rs.1.85/Rs.37 =5%
Capital Gain = (Pt+1 – Pt) / Pt =(Rs.40 – Rs.37)/Rs.37 = Rs.3/Rs.37 = 8.10 %
Total Return on Investment= Rt+1
Rt+1= Divt+1 / Pt + (Pt+1 – Pt) / Pt
= 5% + 8.10% = 13.10%
Capital Market Theory: An Overview Holding- Period Returns (HPR)
(1+ R1) * (1+ R2) *…*(1+Rt)*…* (1+RT) If the returns were 11%, -5% and 9% in a three years period (1+ R1) * (1+ R2)*(1+ R3)= (Rs.1+0.11) * (Rs.1- 0.05) * (Rs.1+ 0.09) = Rs.1.11* Rs.0.95 * Rs.1.09 = Rs.1.15 Therefore the Total Return at the end of three years = 15%
Capital Market Theory: An Overview Return Statistics
Mean = R = (R1 +…..+RT)/ T If the returns on common stock from 2000 to 2003 are 0.1370, 0.3580, 0.4514 and – 0.0888 respectively, than return over these four years is R = 0.1370 + 0.3580+ 0.4514 – 0.0888/4= 0.2144
Capital Market Theory: An Overview Average Stock Returns and Risk-Free
Returns Excess Return on the Risky Asset =Risk Premium = Risky Returns – Risk-Free Returns If
Average Risky Return = 13.3% and Average Risk-Free Return = 3.8% than Average Excess Return= (13.3% - 3.8%) = 9.5%
Capital Market Theory: An Overview Risk Statistics: How the risk can be measured
Variance:
is a measure of the squared deviations of a security’s return from its expected return Var = 1/T-1 { (R1 – R)2 + (R2 – R)2 + (R3 – R)2 + (R4 – R)2}
Standard Deviation:
the square root of the variance SD = σ = √ Var
Risk and Return :Capital Asset Pricing Model (CAPM) Expected Return, Variance and Covariance
Expected Return : the average return per period a security has earned in the past
Covariance: is a statistic measuring the interrelationship between two securities
Correlation: the alternative approach, to determine the correlation between the two securities
Risk and Return :Capital Asset Pricing Model (CAPM) Expected Return:
States of Economy
RAT
RBT
Depression
-20% 5%
Recession
10% 20%
Normal
30% -12%
Boom
50% 9%
RA = 17.5% and RB = 5.5%
Risk and Return :Capital Asset Pricing Model (CAPM) State of Eco.
Rate of Return RAT
Depression
-0.20
Recession
Deviation from Squared Expected Return Value of Deviation (RAT - RA) (RAT - RA)2
0.10
(-0.20 – 0.175)= -0.375 -0.075
(-0.375)2= 0.140625 0.005625
Normal
0.30
0.125
0.015625
Boom
0.50
0.325
0.105625
Total
0.267500
Risk and Return :Capital Asset Pricing Model (CAPM) State of Eco.
Depression
RBT 0.05
Recession Normal
0.20 -0.12
Deviation from Squared Expected Return Value of Deviation (RBT - RB) (RBT - RB)2 (0.05 – 0.055)= (-0.005)2= -0.005 0.000025 0.145 0.021025 -0.175 0.030625
Boom
0.09
0.035
Total
Rate of Return
0.001225 0.052900
Risk and Return :Capital Asset Pricing Model (CAPM) Var (R )= 0.2675/4 = 0.066875 A
SD (R )= √ 0.066875 = 0.2586= 25.86% A
Var (R )= 0.0529/4 = 0.013225 B
SD (R )= √ 0.013225 = 0.1150 = 11.50% B
Risk and Return :Capital Asset Pricing Model (CAPM) State of Eco.
Rate of Return
Deviation from Expected Return
Rate Deviation of from Return Expected Return
Product of Deviation
RAT
(RAT - RA)
RBT
(RBT - RB)
(RAT - RA) * (RBT - RB)
Depression
-0.20
-0.375
0.05
-0.005
0.001875
Recession
0.10
-0.075
0.20
0.145
-0.010875
Normal
0.30
0.125
-0.12
-0.175
-0.021875
Boom
0.50
0.325
0.09
0.035
0.011375
Total
- 0.0195
Risk and Return :Capital Asset Pricing Model (CAPM) Covariance
σ = Cov (R , R )= (R
σ = Cov (R , R )= - 0.0195 = - 0.004875
Interpretation of Results
AB
AB
A
A
B
AT
- R ) *(R A
B
Positive relationship Negative relationship No relation = Zero Covariance
BT
-R) B
Risk and Return :Capital Asset Pricing Model (CAPM) Correlation ρ = Corr (R ,R ) = Cov (R , R )/ σ * σ = - 0.004875/ 0.2586 * 0.1150 = - 0.1639 AB
A
B
A
B
A
B
Interpretation of Results
Positively Correlated,+1= Perfect Positive Correlation Negatively Correlated,-1= Perfect Negatively Correlation Uncorrelated, 0 = No correlation
Risk and Return :Capital Asset Pricing Model (CAPM) Total Risk of Individual Security Total Risk of Individual Security (Var)= Portfolio Risk (Cov) or Systematic Risk + Unsystematic or Diversifiable Risk (Var – Cov)
Risk and Return :Capital Asset Pricing Model (CAPM) Definition of Risk When Investor Hold the
Market Portfolio Researchers argue that the best measure of the risk of a security in large portfolio is the Beta of the security Beta measures the responsiveness of a security to the movement in the market portfolio. β = Cov (R ,R ) / Var (R )
i
i
M
M
Risk and Return :Capital Asset Pricing Model (CAPM) Sate
Type of Eco.
Return on Market %
Return on Jelco, Inc. %
I
Bull
15
25
II
Bull
15
15
II
Bear
-5
-5
IV
Bear
-5
-15
Type of Eco.
Return on Market %
Return on Jelco, Inc. %
Bull
15%
20% = 25%½+ 15%½
Bear
-5%
-10% = -5%½ + (-15%½)
The Capital Asset Pricing Model: The Relationship b/w Risk and Expected Return (CAPM) Expected Return on Market RM = RF + Risk Premium Expected Return on Individual Security CAPM : R = RF + β * ( RM – RF ) R = Expected return on a security RF = Risk- free rate β = Beta of the Security ( RM – RF ) = Difference b/w expected return on market and risk-free rate
The Capital Asset Pricing Model: The Relationship b/w Risk and Expected Return (CAPM) Expected Return on Individual Security
CAPM :
R=R +β*(R –R )
If β = 0 , R = R
If β = 1 , R = R
F
M
F
M
F
In Diagram Form: SECURITIES MARKET LINE E ( Rm )
Rf
1
βi
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