Lecture_5_Risk and Return.pptx

RISK AND RETURN High Return Comes
Only with High Risk

WHAT IS RETURN?
Return is the amount of gain or loss of an
Investment for a particular period of time.
 It is usually quoted as a percentage.

MEASURING RETURN
Holding Period Return
Annual Return
 Current Yield + Capital Gains
Current Yield = Cash Received During The
Year/Initial Price
Capital Gains = (Year-end Price – Initial
Price)/Initial Price

RETURN EXAMPLE
 The stock price for Stock A was 10 tk
per share 1 year ago. The stock is
currently trading at 9.50 tk per share
and shareholders just received 1 tk
dividend. What return was earned over
the past year?
1.00 + (9.50 - 10.00 )
10.00
K = =
5%

EXPECTED RETURN
The future is uncertain. When we are dealing
with future, we assign probabilities to future
returns.
The Expected rate of return on an
investment represents the mean probability
distribution of possible future returns.



n
i
i
i K
p
K
E
1
)
(

CALCULATION OF EXPECTED
RETURN
(FOR HAMID COMPANY)
Probability to
Economic Scenario Probable Return(ki) happen (pi)
Recession -5% 25%
Normal 18% 50%
Boom 35% 25%
Expected Return = E(k) =
= (-5*.25)+(18*.5)+(35*.25)
= 16.50%


n
1
i
i
i P
k

RISK
Risk reflects the chance that the actual return on an
investment may be different than the expected
return.
One way to measure risk is to calculate the variance
and standard deviation of the distribution of returns.
We will once again use a probability distribution in
our calculations.

CALCULATION OF RISK
(FOR HAMID COMPANY)
Economic Scenario Return(ki) (pi) E(k) ki-E(k) [ki-E(k)]2
[ki-E(k)]2*pi
Recession -5% .25 16.5 - 21.5 462.25
115.5625
Normal 18% .50 16.5 1.5 2.25
1.125
Boom 35% .25 16.5 18.5 342.25 85.5625
σ2 = 202.25
σ = 14.22 %
Here Expected return is 16.5%




n
1
i
i
2
^
i P
)
k
(k

2
Variance 
 


RISK RETURN TRADE-OFF
If you want higher return, you must be
prepared to take a bigger loss (higher risk)
If you want to reduce your risk of loss, you
must sacrifice profit.

RISK-RETURN TRADE-OFF ON
GRAPH
0
10
20
30
40
0 0.5 1 1.5 2 2.5
Return
Return
RISK
 Findings:
Higher the risk higher the profit
Lower the risk lower the profit

COEFFICIENT OF VARIATION
Most investors are Risk Averse, meaning that
they don’t like risk and demand a higher
return for bearing more risk.
The Coefficient of Variation (CV) is
standardized measure of dispersion about the
expected value, that shows the risk per unit of
return.
For Hamid Company CV = 14.22/16.50 =
.8618
^
k
Mean
dev
Std
CV




12
EXAMPLE: EXPECTED
RETURNS
Suppose you have predicted the following
returns for stocks C and T in three possible
states of nature. What are the expected
returns?
 State Probability C
T
 Boom 0.3 0.15 0.25
 Normal 0.5 0.10 0.20
 Recession 0.2 0.02 0.01
RC = .3(.15) + .5(.10) + .2(.02) = .099 = 9.99%
RT = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7%

13
EXAMPLE: VARIANCE AND
STANDARD DEVIATION
Consider the previous example. What
are the variance and standard deviation
for each stock?
Stock C
 2 = .3(.15-.099)2 + .5(.1-.099)2 + .2(.02-.099)2 = .002029
  = .045
 CV= .4545
Stock T
 2 = .3(.25-.177)2 + .5(.2-.177)2 + .2(.01-.177)2 = .007441
  = .0863
 CV= .4876




n
i
i
i R
E
R
p
1
2
2
))
(
(
σ

TOTAL RISK
Portfolio of
U.S. stocks
By diversifying the portfolio, the variance of the portfolio’s return relative to the variance of the
market’s return (beta) is reduced to the level of systematic risk -- the risk of the market itself.
Systematic
risk
Total
risk
Total Risk = Diversifiable Risk + Market Risk
(unsystematic) (systematic)
Percent
risk =
Variance of portfolio return
Variance of market return
20
40
60
80
Number of stocks in portfolio
10 20 30 40 50
1
100

15
SYSTEMATIC RISK
Risk factors that affect a large number of assets
Also known as non-diversifiable risk or market risk
Includes such things as changes in GDP, inflation,
interest rates, etc.

16
UNSYSTEMATIC RISK
Risk factors that affect a limited number of
assets
Also known as unique risk and asset-specific
risk
Includes such things as labor strikes, part
shortages, etc.

17
DIVERSIFICATION
Portfolio diversification is the investment in several
different asset classes or sectors
Diversification is not just holding a lot of assets
For example, if you own 50 internet stocks, you are not
diversified
However, if you own 50 stocks that span 20 different
industries, then you are diversified

18
THE PRINCIPLE OF
DIVERSIFICATION
Diversification can substantially reduce the variability of
returns without an equivalent reduction in expected
returns
This reduction in risk arises because worse than
expected returns from one asset are offset by better than
expected returns from another
However, there is a minimum level of risk that cannot be

19
DIVERSIFIABLE RISK
The risk that can be eliminated by combining assets into
a portfolio
Often considered the same as unsystematic, unique or
asset-specific risk
If we hold only one asset, or assets in the same
industry, then we are exposing ourselves to risk that we
could diversify away

20
PORTFOLIOS
A portfolio is a collection of assets
An asset’s risk and return is important in how it affects
the risk and return of the portfolio
The risk-return trade-off for a portfolio is measured by
the portfolio expected return and standard deviation,
just as with individual assets

21
PORTFOLIO DIVERSIFICATION
A strategy employed by investors to reduce risk
Holding many different securities rather than just one

22
PORTFOLIO EXPECTED
RETURNS
The expected return of a portfolio is the
weighted average of the expected returns
for each asset in the portfolio
You can also find the expected return by
finding the portfolio return in each possible
state and computing the expected value as
we did with individual securities



m
j
j
j
P R
E
w
R
E
1
)
(
)
(

FORMING TWO ASSET
PORTFOLIO
Weight Stock Expected
Standard
Return
Deviation
40% A 18% 20%
60% B 22% 25%
Correlation between Returns of A and B, ρAB = .6.
The general equation for expected return of a portfolio of n assets
:
E(kA..N) = wAkA + wBkB + …. + Wnkn = ∑ wiki
The expected return of this portfolio:
E(kAB) = wAkA + wBkB = .40x18 + .60x22 = 20.4%.

PORTFOLIO RISK
Two Asset Portfolio St. Dev
σAB = √wA
2σA
2
+WB
2σB
2
+ 2WAWBσAσBρAB
=√.42*202 +.62*252 + 2*.4*.6*20*25*.4
= √.16*400 + .36 * 484 + 2*.24*500*.4
= 19.62%

CAPITAL ASSET PRICING MODEL
(CAPM)
Model based upon concept that a stock’s
required rate of return is equal to the risk-
free rate of return plus a risk premium that
reflects the riskiness of the stock after
diversification.
Primary conclusion: The relevant riskiness
of a stock is its contribution to the
riskiness of a well-diversified portfolio.

BETA
Measures a stock’s market risk, and shows a stock’s
volatility relative to the market.
Indicates how risky a stock is if the stock is held in a
well-diversified portfolio.

CALCULATING BETAS
Run a regression of past returns of a security against
past returns on the market.
The slope of the regression line (sometimes called the
security’s characteristic line) is defined as the beta
coefficient for the security.

ILLUSTRATING THE
CALCULATION OF BETA
.
.
.
ki
_
kM
_
-5 0 5 10 15 20
20
15
10
5
-5
-10
Regression line:
ki = -2.59 + 1.44 kM
^ ^
Year kM ki
1 15% 18%
2 -5 -10
3 12 16

COMMENTS ON BETA
If beta = 1.0, the security is just as risky
as the average stock.
If beta > 1.0, the security is riskier than
average.
If beta < 1.0, the security is less risky than
average.
Most stocks have betas in the range of 0.5

THE SECURITY MARKET LINE (SML):
CALCULATING REQUIRED RATES OF
RETURN
SML: ki = kRF + (kM – kRF) βi
Assume kRF = 8% and kM = 15%, βi = 1.2 , ki = ?
The market (or equity) risk premium is RPM = kM – kRF =
15% – 8% = 7%.
ki = 8 +[ (15-8) x 1.2] =16.4

PRACTICE MATH:
Stock P and Q have the following probability distribution of returns:
Returns R
Economic Scenario Probabilities Stock P Stock Q
Recession 25% -1% -4%
Normal 55% 13% 18%
Boom 20% 20% 26%
Required:
a) Calculate expected return of each stock.
b) Calculate the expected return of a portfolio consisting of 55% of stock P and 45% of
stock Q.
c) Assume the correlation of two stocks is 0.55. Calculate the standard deviation of returns
for each stock and for the portfolio.

Lecture_5_Risk and Return.pptx

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