8/11/2019 Risk Return Diversification
1/10
Risk and Return - IIDiversifcation:What happens to the riskiness o an average 1-stockportolio as more stocks are added?
Risk would decrease because the added stocks wouldnot be perectly correlated but Return would remainrelatively constant
Market risk is that part o a security!s stand-alone risk thacannotbe eliminated by diversifcationFirm-specifc risk is that part o a security!s stand-alonerisk which can be eliminated by proper diversifcation
"s more stocks are added# each new stock has a smalle
risk-reducing impact $y orming portolios# we can eliminate about hal the
riskiness o individual stocks %&'( vs 1)(*
# Stocks in Portfolio10 20 30 40 2000+
Company Specific Risk
MarketRisk
35
18
0
Stand!lone Risk"
p
p$%
8/11/2019 Risk Return Diversification
2/10
spalls very slowly ater about +, stocks are included
he lower limit or spis about s./ 1)(
0 you choose to hold a one-stock portolio and thus ar
eposed to more risk than diversifed investors# woul
you be compensated or the total risk you bear? 234 5ou can get rid o diversifable risk easily#
cheaply 0 you choose not to diversiy# you won!t be
compensated with a higher epected return or risk youcould eliminate so easily
5ou will only receive a higher return or risk that you
can!t diversiy away 6 market risk
Beta = Cov (X,Y)/Var (X)
Where X = Market Returns
Y = Security Returns
Total Risk = Variance o Security
Syste!atic Risk = Beta X Variance o Market
"nsyste!atic Risk = Total Risk # Syste!atic Risk
8/11/2019 Risk Return Diversification
3/10
Markowitz Model
Harry M. Markowitz is credited with introducing new
concepts of risk measurement and their application to thselection of portfolios.
Started idea with risk aversion of average investors andesire to maximize return with given risk or vice versa
He used statistical analysis for selection of assets in th
portfolio in an efficient manner.
Markowitz generated a number of portfolios within a give
amount of money
Combined risk of two assets taken separately is not thsame risk of two assets together, thus two securities likata Motors !nd "#$%!&C# don't have same risk class
he "isk index is measured by the variance or th
distribution around the mean, its range etc. ()ariance anCovariance*
his led to what is called the Modern +ortfolio heory Combination of securities called +ortfolio
!ssumption of Markowitz heory. %nvestors are rational-. ree access to fair and correct information/. Markets are efficient and absorb information 0uickly
1. %nvestors are risk averse and try to minimize risk2. %nvestors' decision based on return and S.3.4. %nvestors prefer higher returns to lower for given leve
of risk
8/11/2019 Risk Return Diversification
4/10
What is the CAPM?"n e7uilibrium model speciying the relationship
betweenrisk and re7uired return on assets held indiversifedportolios
Assumptions o the CAPM 0nvestors all think in terms o a single period
"ll investors have the same epectations
0nvestors can borrow or lend unlimited amounts at the
risk ree rate "ll assets are perectly divisible
here are no taes or transactions costs
"ll investors are price takers# ie# can!t in8uence thestock prices 9uantities o all assets are given and fed
&fficient Portfolio
'
rf
Risk (reeRet)rn *
Market Ret)rn * rm
&,!1'0
SM$5 ri6 r
f7 8
i(r
M 9 r
f*
8/11/2019 Risk Return Diversification
5/10
8/11/2019 Risk Return Diversification
6/10
0ndi=erence curve / investor!s attitude toward risk as
re8ected in risk>return tradeo= unction 3ptimal portolio / tangency point between the e
8/11/2019 Risk Return Diversification
7/10
;
8/11/2019 Risk Return Diversification
8/10
The CM* '+uation
What does the CML tell us?hat any investor can achieve a portolio with a total
risk>return tradeo= on the G. easily /H mi themarket portolio and treasury bills
he epected rate o return on any ereturn
tradeo= o any portolioThis tells us aout portolios! "hat aout indi#idual
securities??? 0t turns out# that i you Jump %mathematically* on the
G. long enough# you get the K. 6 the Kecurity .arkeine
0nvestors like r and dislike L
"s number o securities increases# only covariance
matter
he L o a well diversifed portolio depends only on.arket Risk
Gontribution o a security to mkt portolio relative to
the average / M$eta and .arket Risk
kp* k
R(+
Slope
/ntercept
7
p'
kM k
R(
7
M
8/11/2019 Risk Return Diversification
9/10
$ecurit% Market Line
0 beta / 1,# stock is average risk
0 beta H 1,# stock is riskier than average
0 beta N 1,# stock is less risky than average
Covariance ith the!arket
-
m
im
iB
=
Variance o the !arket
&fficient
Portfolio
'
rf
Risk (ree
Ret)rn *
Market Ret)rn * rm
&,!1'0
SM$5 ri6 r
f7 8
i(r
M 9 r
f*
8/11/2019 Risk Return Diversification
10/10
.ost stocks have betas in the range o ,' to 1'
G. and K.
Cse G. to value portolios
Cse K. to value securities %portolios* that will be heldin a well diversifed portolio
CM*.
K.: ri / r I Mi%r. - r*
P
M
fM
fP
rrrr
=
+