Ch 06 Show
-
Upload
mohamed-gamal -
Category
Documents
-
view
243 -
download
0
Transcript of Ch 06 Show
-
8/6/2019 Ch 06 Show
1/42
6 - 1
Copyright 2002 by Harcourt, Inc All rights reserved.
CHAPTER 6Risk and Return: The Basics
Basic return concepts
Basic risk concepts
Stand-alone riskPortfolio (market) risk
Risk and return: CAPM/SML
-
8/6/2019 Ch 06 Show
2/42
6 - 2
Copyright 2002 by Harcourt, Inc All rights reserved.
What are investment returns?
Investment returns measure thefinancial results of an investment.
Returns may be historical orprospective (anticipated).
Returns can be expressed in:Dollar terms.
Percentage terms.
-
8/6/2019 Ch 06 Show
3/42
6 - 3
Copyright 2002 by Harcourt, Inc All rights reserved.
What is the return on an investmentthat costs $1,000 and is sold
after 1 year for $1,100?
Dollar return:
Percentage return:
$ Received - $ Invested$1,100 - $1,000 = $100.
$ Return/$ Invested$100/$1,000 = 0.10 = 10%.
-
8/6/2019 Ch 06 Show
4/42
6 - 4
Copyright 2002 by Harcourt, Inc All rights reserved.
What is investment risk?
Typically, investment returns are not
known with certainty. Investment risk pertains to the
probability of earning a return lessthan that expected.
The greater the chance of a return farbelow the expected return, thegreater the risk.
-
8/6/2019 Ch 06 Show
5/42
6 - 5
Copyright 2002 by Harcourt, Inc All rights reserved.
Probability distribution
Rate ofreturn (%)50150-20
Stock X
Stock Y
Which stock is riskier? Why?
-
8/6/2019 Ch 06 Show
6/42
6 - 6
Copyright 2002 by Harcourt, Inc All rights reserved.
Assume the Following
Investment Alternatives
Economy Prob. T-Bill HT Coll USR MP
Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0%
Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0
Average 0.40 8.0 20.0 0.0 7.0 15.0
Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0
Boom 0.10 8.0 50.0 -20.0 30.0 43.0
1.00
-
8/6/2019 Ch 06 Show
7/42
6 - 7
Copyright 2002 by Harcourt, Inc All rights reserved.
What is unique about
the T-bill return?
The T-bill will return 8% regardlessof the state of the economy.
Is the T-bill riskless? Explain.
-
8/6/2019 Ch 06 Show
8/42
6 - 8
Copyright 2002 by Harcourt, Inc All rights reserved.
Do the returns of HT and Collectionsmove with or counter to the economy?
HT moves with the economy, so itis positively correlated with theeconomy. This is the typicalsituation.
Collections moves counter to theeconomy. Such negativecorrelation is unusual.
-
8/6/2019 Ch 06 Show
9/42
6 - 9
Copyright 2002 by Harcourt, Inc All rights reserved.
Calculate the expected rate of returnon each alternative.
.k = k Pi i
i=1
n
k = expected rate of return.
kHT = 0.10(-22%) + 0.20(-2%)+ 0.40(20%) + 0.20(35%)+ 0.10(50%) = 17.4%.
^
^
-
8/6/2019 Ch 06 Show
10/42
6 - 10
Copyright 2002 by Harcourt, Inc All rights reserved.
HT has the highest rate of return. Does that make it best?
k
HT 17.4%
Market 15.0
USR 13.8T-bill 8.0
Collections 1.7
^
-
8/6/2019 Ch 06 Show
11/42
6 - 11
Copyright 2002 by Harcourt, Inc All rights reserved.
What is the standard deviation
of returns for each alternative?
.
V ri
i tit r
iii
!!
W!!W
!W
-
8/6/2019 Ch 06 Show
12/42
6 - 12
Copyright 2002 by Harcourt, Inc All rights reserved.
WT-bills = 0.0%.WHT = 20.0%.
WColl = 13.4%.WUSR= 18.8%.WM = 15.3%.
.1i i2
i!
!W
HT:
W = ((-22 - 17.4)20.10 + (-2 - 17.4)20.20+ (20 - 17.4)20.40 + (35 - 17.4)20.20+ (50 - 17.4)20.10)1/2 = 20.0%.
-
8/6/2019 Ch 06 Show
13/42
6 - 13
Copyright 2002 by Harcourt, Inc All rights reserved.
Prob.
Rate of Return (%)
T-bill
USRHT
0 8 13.8 17.4
-
8/6/2019 Ch 06 Show
14/42
-
8/6/2019 Ch 06 Show
15/42
6 - 15
Copyright 2002 by Harcourt, Inc All rights reserved.
Expected Return versus Risk
Which alternative is best?
Expected
Security return Risk, W
HT 17.4% 20.0%Market 15.0 15.3
USR 13.8 18.8
T-bills 8.0 0.0Collections 1.7 13.4
-
8/6/2019 Ch 06 Show
16/42
6 - 16
Copyright 2002 by Harcourt, Inc All rights reserved.
Portfolio Risk and Return
Assume a two-stock portfolio with
$50,000 in HT and $50,000 inCollections.
Calculate kp and Wp.^
-
8/6/2019 Ch 06 Show
17/42
6 - 17
Copyright 2002 by Harcourt, Inc All rights reserved.
Portfolio Return, kp
kp is a weighted average:
kp = 0.5(17.4%) + 0.5(1.7%) = 9.6%.
kp is between kHT and kColl.
^
^
^
^
^ ^
^ ^
kp = 7wikin
i = 1
-
8/6/2019 Ch 06 Show
18/42
6 - 18
Copyright 2002 by Harcourt, Inc All rights reserved.
Alternative Method
kp = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40+ (12.5%)0.20 + (15.0%)0.10 = 9.6%.
^
Estimated Return
(More...)
Economy Prob. HT Coll. Port.
Recession 0.10 -22.0% 28.0% 3.0%
Below avg. 0.20 -2.0 14.7 6.4
Average 0.40 20.0 0.0 10.0
Above avg. 0.20 35.0 -10.0 12.5
Boom 0.10 50.0 -20.0 15.0
-
8/6/2019 Ch 06 Show
19/42
6 - 19
Copyright 2002 by Harcourt, Inc All rights reserved.
Wp = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20 +(10.0 - 9.6)20.40 + (12.5 - 9.6)20.20+ (15.0 - 9.6)20.10)1/2 = 3.3%.
Wp is much lower than:either stock (20% and 13.4%).
average of HT and Coll (16.7%).
The portfolio provides average returnbut much lower risk. The key here isnegative correlation.
-
8/6/2019 Ch 06 Show
20/42
6 - 20
Copyright 2002 by Harcourt, Inc All rights reserved.
Two-Stock Portfolios
Two stocks can be combined to forma riskless portfolio if r = -1.0.
Risk is not reduced at all if the twostocks have r = +1.0.
In general, stocks have r} 0.65, so
risk is lowered but not eliminated. Investors typically hold many stocks.
What happens when r = 0?
-
8/6/2019 Ch 06 Show
21/42
6 - 21
Copyright 2002 by Harcourt, Inc All rights reserved.
What would happen to the
risk of an average 1-stockportfolio as more randomly
selected stocks were added?
Wp would decrease because the
added stocks would not be
perfectly correlated, but kp would
remain relatively constant.
^
-
8/6/2019 Ch 06 Show
22/42
6 - 22
Copyright 2002 by Harcourt, Inc All rights reserved.
Large
0 15
Prob.
2
1
W1 }35% ; WLarge }20%.
Return
-
8/6/2019 Ch 06 Show
23/42
6 - 23
Copyright 2002 by Harcourt, Inc All rights reserved.
# Stocks in Portfolio
10 20 30 40 2,000+
Company Specific(Diversifiable) Risk
Market Risk
20
0
Stand-Alone Risk, Wp
Wp (%)35
-
8/6/2019 Ch 06 Show
24/42
6 - 24
Copyright 2002 by Harcourt, Inc All rights reserved.
Stand-alone Market Diversifiable
Market risk is that part of a securitys
stand-alone risk that cannotbeeliminated by diversification.
Firm-specific, ordiversifiable, risk is
that part of a securitys stand-alone riskthat can be eliminated bydiversification.
risk risk risk= + .
-
8/6/2019 Ch 06 Show
25/42
6 - 25
Copyright 2002 by Harcourt, Inc All rights reserved.
Conclusions
As more stocks are added, each newstock has a smaller risk-reducing
impact on the portfolio.Wp falls very slowly after about 40
stocks are included. The lower limitforWp is about 20% = WM .
By forming well-diversified portfolios,investors can eliminate about half theriskiness of owning a single stock.
-
8/6/2019 Ch 06 Show
26/42
6 - 26
Copyright 2002 by Harcourt, Inc All rights reserved.
No. Rational investors will minimize
risk by holding portfolios.They bear only market risk, so prices
and returns reflect this lower risk.
The one-stock investor bears higher(stand-alone) risk, so the return is lessthan that required by the risk.
Can an investor holding one stock earn
a return commensurate with its risk?
-
8/6/2019 Ch 06 Show
27/42
6 - 27
Copyright 2002 by Harcourt, Inc All rights reserved.
Market risk, which is relevant for stocksheld in well-diversified portfolios, is
defined as the contribution of a securityto the overall riskiness of the portfolio.
It is measured by a stocks betacoefficient, which measures the stocksvolatility relative to the market.
What is the relevant risk for a stock heldin isolation?
How is market risk measured for
individual securities?
-
8/6/2019 Ch 06 Show
28/42
6 - 28
Copyright 2002 by Harcourt, Inc All rights reserved.
How are betas calculated?
Run a regression with returns on
the stock in question plotted on theY axis and returns on the marketportfolio plotted on the X axis.
The slope of the regression line,which measures relative volatility,is defined as the stocks betacoefficient, orb.
-
8/6/2019 Ch 06 Show
29/42
6 - 29
Copyright 2002 by Harcourt, Inc All rights reserved.
Use the historical stock returns tocalculate the beta for KWE.
Year Market KWE1 25.7% 40.0%2 8.0% -15.0%
3 -11.0% -15.0%4 15.0% 35.0%5 32.5% 10.0%6 13.7% 30.0%
7 40.0% 42.0%8 10.0% -10.0%9 -10.8% -25.0%
10 -13.1% 25.0%
-
8/6/2019 Ch 06 Show
30/42
6 - 30
Copyright 2002 by Harcourt, Inc All rights reserved.
Calculating Beta for KWE
KWE 0. 0.02
0.0%
20%
0%
20%
0%
0% 20% 0% 20% 0%
KWE
-
8/6/2019 Ch 06 Show
31/42
6 - 31
Copyright 2002 by Harcourt, Inc All rights reserved.
How is beta calculated?
The regression line, and hencebeta, can be found using acalculator with a regression
function or a spreadsheet program.In this example, b = 0.83.
Analysts typically use four or five
years of monthly returns toestablish the regression line.Some use 52 weeks of weeklyreturns.
-
8/6/2019 Ch 06 Show
32/42
6 - 32
Copyright 2002 by Harcourt, Inc All rights reserved.
If b = 1.0, stock has average risk.
If b > 1.0, stock is riskier than average.
If b < 1.0, stock is less risky thanaverage.
Most stocks have betas in the range of
0.5 to 1.5.
Can a stock have a negative beta?
How is beta interpreted?
-
8/6/2019 Ch 06 Show
33/42
6 - 33
Copyright 2002 by Harcourt, Inc All rights reserved.
Expected Return versus Market Risk
Which of the alternatives is best?
Expected
Security return Risk, b
HT 17.4% 1.29Market 15.0 1.00
USR 13.8 0.68
T-bills 8.0 0.00Collections 1.7 -0.86
-
8/6/2019 Ch 06 Show
34/42
6 - 34
Copyright 2002 by Harcourt, Inc All rights reserved.
Use the SML to calculate each
alternatives required return.
The Security Market Line (SML) ispart of the Capital Asset PricingModel (CAPM).
SML: ki = kRF + (RPM)bi .
Assume kRF = 8%; kM = kM = 15%.
RPM = (kM - kRF) = 15% - 8% = 7%.
^
-
8/6/2019 Ch 06 Show
35/42
6 - 35
Copyright 2002 by Harcourt, Inc All rights reserved.
Required Rates of Return
kHT = 8.0% + (7%)(1.29)
= 8.0% + 9.0% = 17.0%.kM = 8.0% + (7%)(1.00) =15.0%.
kUSR = 8.0% + (7%)(0.68) =12.8%.
kT-bill = 8.0% + (7%)(0.00) = 8.0%.
kColl = 8.0% + (7%)(-0.86) = 2.0%.
-
8/6/2019 Ch 06 Show
36/42
6 - 36
Copyright 2002 by Harcourt, Inc All rights reserved.
Expected versus Required Returns
k k
HT 17.4% 17.0% Undervalued
Market 15.0 15.0 Fairly valued
USR 13.8 12.8 Undervalued
T-bills 8.0 8.0 Fairly valued
Coll 1.7 2.0 Overvalued
-
8/6/2019 Ch 06 Show
37/42
6 - 37
Copyright 2002 by Harcourt, Inc All rights reserved.
.
.Coll.
.HT
T-bills
.USR
kM = 15
kRF = 8
-1 0 1 2
.
SML: ki = kRF + (RPM) biki = 8% + (7%) bi
ki (%)
Risk, bi
SML and Investment Alternatives
Market
-
8/6/2019 Ch 06 Show
38/42
6 - 38
Copyright 2002 by Harcourt, Inc All rights reserved.
Calculate beta for a portfolio with 50%
HT and 50% Collections
bp = Weighted average= 0.5(bHT) + 0.5(bColl)= 0.5(1.29) + 0.5(-0.86)= 0.22.
-
8/6/2019 Ch 06 Show
39/42
6 - 39
Copyright 2002 by Harcourt, Inc All rights reserved.
What is the required rate of return
on the HT/Collections portfolio?
kp = Weighted average k
= 0.5(17%) + 0.5(2%) = 9.5%.
Or use SML:
kp = kRF + (RPM) bp= 8.0% + 7%(0.22) = 9.5%.
-
8/6/2019 Ch 06 Show
40/42
6 - 40
Copyright 2002 by Harcourt, Inc All rights reserved.
SML1
Original situation
Required Rateof Return k (%)
SML2
0 0.5 1.0 1.5 2.0
18
15
11
8
New SML( I = 3%
Impact of Inflation Change on SML
-
8/6/2019 Ch 06 Show
41/42
6 - 41
Copyright 2002 by Harcourt, Inc All rights reserved.
kM = 18%
kM = 15%SML1
Original situation
Required Rateof Return (%)
SML2
After increasein risk aversion
Risk, bi
18
15
8
1.0
( RPM = 3%
Impact of Risk Aversion Change
-
8/6/2019 Ch 06 Show
42/42
6 - 42
Copyright 2002 by Harcourt, Inc All rights reserved.
Has the CAPM been verified through
empirical tests?
No. The statistical tests have
problems that make empiricalverification virtually impossible.
Investors may be concerned aboutboth stand-alone risk and market risk.
Furthermore, investors requiredreturns are based on future risk, butbetas are based on historical data.