Risk and Returns
Mazhar HussainConsultant/ Assistant Professor
FMS, IIU-Business SchoolNovember 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 Total Investment = Rs.37 * 100=Rs.3700
Suppose Company paid dividend of Rs.1.85 per share
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 = = 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)
States of Economy RAT RBT
Depression -20% 5%
Recession 10% 20%
Normal 30% -12%
Boom 50% 9%
Expected Return: RA = 17.5% and
RB = 5.5%
Risk and Return :Capital Asset Pricing Model (CAPM)State of Eco. Rate of
ReturnDeviation from Expected Return
Squared Value of Deviation
RAT (RAT - RA) (RAT - RA)2
Depression -0.20 (-0.20 – 0.175)=
-0.375
(-0.375)2=
0.140625
Recession 0.10 -0.075 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. Rate of
ReturnDeviation from Expected Return
Squared Value of Deviation
RBT (RBT - RB) (RBT - RB)2
Depression 0.05 (0.05 – 0.055)=
-0.005
(-0.005)2=
0.000025
Recession 0.20 0.145 0.021025
Normal -0.12 -0.175 0.030625
Boom 0.09 0.035 0.001225
Total 0.052900
Risk and Return :Capital Asset Pricing Model (CAPM) Var (RA)= 0.2675/4 = 0.066875
SD (RA )= 0.066875 = 0.2586= 25.86%
Var (RB)= 0.0529/4 = 0.013225
SD (RB )= 0.013225 = 0.1150 = 11.50%
Risk and Return :Capital Asset Pricing Model (CAPM)
State of Eco. Rate of Return
Deviation from Expected Return
Rate of Return
Deviation from 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 AB = Cov (RA, RB)= (RAT - RA) *(RBT - RB)
AB = Cov (RA, RB)= - 0.0195 = - 0.004875
Interpretation of Results Positive relationship Negative relationship No relation = Zero Covariance
Risk and Return :Capital Asset Pricing Model (CAPM)
Correlation AB = Corr (RA,RB) = Cov (RA, RB)/ A * B
= - 0.004875/ 0.2586 * 0.1150 = - 0.1639
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.
i = Cov (Ri ,RM) / Var (RM)
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 + * ( RM – RF ) R = Expected return on a security RF = Risk- free rate = 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 = RF + * ( RM – RF )
If = 0 , R = RF
If = 1 , R = RM
In Diagram Form:
SECURITIES MARKET LINE
i
mRE
1
fR