risk and returns- fin society-iiu business school 29-11-08

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


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


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%


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%


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


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%


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%


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


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


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


Total Risk of Individual Security

Total Risk of Individual Security (Var)=

Portfolio Risk (Cov) or Systematic Risk +

Unsystematic or Diversifiable Risk (Var – Cov)


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)


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

risk and returns- fin society-iiu business school 29-11-08

Documents

total return

dividend of rs

average return

price of rs

expected return var

expected return rbt

rate of return deviation

rate of return rbt