risk & return pp
TRANSCRIPT
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1/405.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Chap ter 11
Risk andReturn
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2/405.2 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Defining Return
Income received on an investmentplus any change in market price,
usually expressed as a percent ofthe beginning market price of the
investment.
Dt+ (PtPt - 1)
Pt - 1R =
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3/405.3 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Return Example
The stock price for Stock A was $10pershare 1 year ago. The stock is currently
trading at $9.50per share and shareholdersjust received a $1 dividend. What return
was earned over the past year?
$1.00 + ($9.50$10.00)
$10.00R== 5%
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4/405.4 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Defining Risk
What rate of return do you expect on yourinvestment (savings) this year?
What rate will you actually earn?
The var iab i li ty o f returns from
those that are expected .
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5/405.5 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Determ ining Expected
Retu rn (Discrete Dist .)
R= ( Ri)( Pi)
Ris the expected return for the asset,Riis the return for the i
thpossibility,
Piis the probability of that returnoccurring,
nis the total number of possibilities.
n
I = 1
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6/405.6 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
How to Determ ine the Expected
Return and Standard Deviat ion
Stock BW
Ri Pi (Ri)(Pi)
-0.15 0.10 0.015
-0.03 0.20 0.006
0.09 0.40 0.036
0.21 0.20 0.042
0.33 0.10 0.033
Sum 1.00 0.090
Theexpectedreturn, R,for Stock
BW is .09or 9%
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7/405.7 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Determ ining Standard
Dev iation (Risk Measure)
s= ( RiR)2( Pi)Standard Deviation, s, is a statistical
measure of the variability of a distributionaround its mean.
It is the square root of variance.
Note, this is for a disc rete distr ibut ion.
n
i = 1
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8/405.8 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
How to Determ ine the Expected
Return and Standard Deviat ion
Stock BW
Ri Pi (Ri)(Pi) (Ri - R )2(Pi)
0.15 0.10 0.015 0.005760.03 0.20 0.006 0.00288
0.09 0.40 0.036 0.00000
0.21 0.20 0.042 0.002880.33 0.10 0.033 0.00576
Sum 1.00 0.090 0.01728
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9/405.9 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Determ ining Standard
Dev iation (Risk Measure)
n
i=1s= ( RiR)2( Pi)
s= .01728s = 0.1315or 13.15%
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10/405.10 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Coeff ic ient o f Variat ion
The ratio of the standard deviat ion ofa distribution to the mean of that
distribution.
It is a measure of RELATIVErisk.
CV = s/RCV of BW = 0.1315/ 0.09= 1.46
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5.11 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Disc rete versus . Con t inuous
Dist r ibut ions
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.15 0.03 9% 21% 33%
Discrete Cont inuous
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
-50%
-41%
-32%
-23%
-14%
-5%
4%
13%
22%
31%
40%
49%
58%
67%
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5.12 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Cont inuous
Distr ibut ion Prob lem
Assume that the following list represents thecontinuous distribution of population returnsfor a particular investment (even thoughthere are only 10 returns).
9.6%,15.4%, 26.7%,0.2%, 20.9%,28.3%,5.9%, 3.3%, 12.2%, 10.5%
Calculate the Expected ReturnandStandard Deviat ionfor the populat ion.
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5.13 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Lets Use the Calculator!Enter Data first. Press:
2nd Data
2nd CLR Work
9.6 ENTER
15.4 ENTER
26.7 ENTER
Note, we are inputting dataonly for the X variable andignoring entries for the Yvariable in this case.
Source: Courtesy of Texas Instruments
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5.14 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Lets Use the Calculator!
Enter Data first. Press:
0.2 ENTER
20.9 ENTER
28.3 ENTER
5.9 ENTER
3.3 ENTER
12.2 ENTER
10.5 ENTER
Source: Courtesy of Texas Instruments
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5.15 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Lets Use the Calculator!
Examine Resu lts! Press:
2nd Stat
through the results.
Expected return is 9% forthe 10 observations.Population standard
deviation is 13.32%. This canbe much quicker
than calculating by hand,but slower than using aspreadsheet.
Source: Courtesy of Texas Instruments
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5.16 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Certainty Equ ivalen t(CE) is theamount of cash someone would
require with certainty at a point intime to make the individual
indifferent between that certain
amount and an amount expected tobe received with risk at the same
point in time.
Risk A tt itudes
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5.17 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Certainty equivalent > Expected value
Risk Preference
Certainty equivalent = Expected value
Risk Indifference
Certainty equivalent < Expected valueRisk Aversion
Mostindividuals are Risk Averse.
Risk A tt itudes
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5.18 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
You have the choice between (1) a guaranteeddollar reward or (2) a coin-flip gamble of
$100,000 (50% chance) or $0 (50% chance).The expected value of the gamble is $50,000.
Maryrequires a guaranteed $25,000, or more, tocall off the gamble.
Raleighis just as happy to take $50,000 or takethe risky gamble.
Shannonrequires at least $52,000 to call off thegamble.
Risk A tt itude Examp le
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5.19 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
What are the Risk Attitude tendencies of each?
Risk A tt itude Examp le
Maryshows risk aversionbecause her
certainty equivalent < the expected value ofthe gamble.
Raleighexhibits risk indifferencebecause hercertainty equivalent equals the expected value
of the gamble.
Shannonreveals a risk preferencebecause hercertainty equivalent > the expected value ofthe gamble.
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5.20 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
RP= ( Wj)( Rj)
RPis the expected return for the portfolio,
Wjis the weight (investment proportion)for thejthasset in the portfolio,
Rjis the expected return of the jthasset,
mis the total number of assets in the
portfolio.
Determ ining Port fo l io
Expected Return
m
J = 1
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5.21 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Determ ining Port fo l io
Standard Deviat ion
m
J=1
m
K=1sP= WjWk jk
Wjis the weight (investment proportion)for thejthasset in the portfolio,
Wkis the weight (investment proportion)
for the kthasset in the portfolio,
jkis the covariance between returns forthejthand kthassets in the portfolio.
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5.22 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
You are creating a portfolio of Stock D and StockBW (from earlier). You are investing $2,000in
Stock BW and $3,000in Stock D. Remember that
the expected return and standard deviation ofStock BWis 9%and 13.15%respectively. The
expected return and standard deviation ofStock Dis 8%and 10.65%respectively. The correlation
coefficient between BW and D is 0.75.
What is the expected return and standarddeviation of the portfolio?
Port fo l io Risk and
Expected Return Examp le
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5.23 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
WBW= $2,000/$5,000 = 0.4
WD= $3,000/$5,000 =0.6RP= (WBW)(RBW) + (WD)(RD)
RP= (0.4)(9%) + (0.6)(8%)
RP= (3.6%) + (4.8%) = 8.4%
Determ ining Port fo l io
Expected Return
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5.24 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Portfolio variance = xBWBW + xDD
+ 2 (xBWxDBWDBWD)
Portfolio standard deviation =
xBWBW + xDD+2 (xBWxDBWDBWD)
Determ ining Port fo l io
Standard Deviat ion
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5.25 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
sP= (0.4)(8%) + (0.6)( 10.65%) +2 (0.4)(0.6)(0.75)(8%)(10.65%)
sP= 0.008174
= 9.04%
Determ ining Port fo l io
Standard Deviat ion
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5.26 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Systematic Risk is the variability of returnon stocks or portfolios associated with
changes in return on the market as a whole.
Unsys tematic Risk is the variability of returnon stocks or portfolios not explained by
general market movements. It is avoidablethrough diversification.
Total Risk = SystematicRisk+Unsystemat icRisk
Total Risk = Sys tematic
Risk + Unsys tematic Risk
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5.27 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Total
Risk
Unsystematic risk
Systematic risk
STD
DEVO
FPORTFOLIO
RETURN
NUMBER OF SECURITIES IN THE PORTFOLIO
Factors such as changes in the nations
economy, tax reform by the Congress,or a change in the world situation.
Total Risk = Sys tematic
Risk + Unsys tematic Risk
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5.28 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Total
Risk
Unsystematic risk
Systematic risk
STD
DEVO
FPORTFOLIO
RETURN
NUMBER OF SECURITIES IN THE PORTFOLIO
Factors unique to a particular companyor industry. For example, the death of akey executive or loss of a governmental
defense contract.
Total Risk = Sys tematic
Risk + Unsys tematic Risk
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5.29 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
CAPM is a model that describes therelat ionshipbetween r iskand
expected (required) return; in thismodel, a securitys expected
(required) return is the risk-free rateplus a premium based on thesystemat ic r isk of the security.
Cap ital Asset
Pricing Model (CAPM)
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5.30 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
1. Capital markets are efficient.
2. Homogeneous investor expectations
over a given period.3. Risk-freeasset return is certain
(use short- to intermediate-termTreasuries as a proxy).
4. Market portfolio contains onlysystemat ic r isk (use S&P 500 Indexor similar as a proxy).
CAPM Assumpt ions
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5.31 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
An index of systemat ic r isk.
It measures the sensi t iv i tyof astocks returns to changes inreturns on the market portfolio.
The betafor a portfolio is simply aweighted average of the individual
stock betas in the portfolio.
What is Beta?
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5.32 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
EXCESS RETURNON STOCK
EXCESS RETURNON MARKET PORTFOLIO
Beta < 1(defensive)
Beta = 1
Beta > 1(aggressive)
Each characteristicline has a
different slope.
Charac ter ist ic L ines
and Dif feren t Betas
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5.33 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Rjis the required rate of return for stock j,Rfis the risk-free rate of return,
bjis the beta of stock j (measuressystematic risk of stock j),
RMis the expected return for the market
portfolio.
Rj= Rf+ bj(RMRf)Securi ty Market Line
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5.34 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Rj= Rf+ bj(RMRf)
bM= 1.0Systematic Risk (Beta)
Rf
RM
RequiredReturn
RiskPremium
Risk-freeReturn
Securi ty Market Line
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5.35 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Obtaining Betas
Can use histor ica l dataif past best represents theexpectations of the future
Can also utilize services like Value Line, IbbotsonAssociates, etc.
Ad justed Beta
Betas have a tendency to revert to the mean of 1.0
Can utilize combination of recent betaand mean
2.22(0.7) + 1.00(0.3) = 1.554 + 0.300 = 1.854 est imate
Securi ty Market Line
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5.36 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Lisa Miller at Basket Wondersis attemptingto determine the rate of return required by
their stock investors. Lisa is using a 6% Rfand a long-term market expected rate of
return of 10%. A stock analyst following the
firm has calculated that the firm betais 1.2.What is the requ ired rate of returnon the
stock of Basket Wonders?
Determ inat ion o f the
Requ ired Rate of Return
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5.37 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
RBW= Rf+ bj(RMRf)RBW= 6%+ 1.2(10%6%)
RBW= 10.8%
The required rate of return exceedsthe market rate of return as BWs
beta exceeds the market beta (1.0).
BWs Required
Rate o f Retu rn
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5.38 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
REVISION QUESTIONS1) Define a risk and return.
2)What is the definition of diversification.
3) Distinguish between systematic and unsystematic
risks. Give examples for each risk.
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5.39 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
4) Calculate the expected returns and standarddeviations of a two-stock portfolio. The following
data for Stock X and Stock Y as follows:
Out of a portfolio valuing RM 100,000, RM40,000 is invested in stock X and RM 60,000 in
stock Y.Stock X Stock Y
ExpectedReturn 11%
25%
Standard
Deviation15% 20%
Correlation
0.3
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5) Calculate the expected returns and standarddeviations of a two-stock portfolio. The following
data for Stock C and Stock D as follows:
Out of a portfolio valuing RM 100,000, RM60,000 is invested in stock C and RM 40,000
in stock D.
Stock C Stock DExpectedReturn 12% 20%Standard
Deviation14% 25%
C l ti 0 5