Post on 04-Jun-2018
transcript
8/13/2019 Risk in Return for Basic Finance
1/62
Chapter 7-8: Risk and Return
8/13/2019 Risk in Return for Basic Finance
2/62
Objectives
Inflation and rates of return How to measure risk
(variance, standard deviation, beta) How to reduce risk
(diversification)
How to price risk(security market line, Capital AssetPricing Model)
8/13/2019 Risk in Return for Basic Finance
3/62
Inflation, Rates of Return,and the Fisher Effect
8/13/2019 Risk in Return for Basic Finance
4/62
Conceptually:
Nominalrisk-freeInterest
Ratek rf
=
Realrisk-freeInterest
Ratek*
+
Inflation-risk
premium
IRP
Mathematically:
(1 + k rf ) = (1 + k*) (1 + IRP)
This is known as the Fisher Effect
Interest Rates
8/13/2019 Risk in Return for Basic Finance
5/62
Suppose the real rate is 3%, and the nominal rate is8%. What is the inflation rate premium?
(1 + k rf ) = (1 + k*) (1 + IRP)(1.08) = (1.03) (1 + IRP)
(1.08) = (1.03 + 1.03 IRP)(1.03 IRP) = (0.05), so
IRP = 4.85%
Interest Rates
8/13/2019 Risk in Return for Basic Finance
6/62
Term Structure of Interest Rates
The pattern of rates of return for debtsecurities that differ only in the lengthof time to maturity.
yieldtomaturity
time to maturity (years)
8/13/2019 Risk in Return for Basic Finance
7/62
Term Structure of Interest Rates
yieldto
maturity
time to maturity (years)
The yield curve may be downwardsloping or inverted if rates areexpected to fall.
8/13/2019 Risk in Return for Basic Finance
8/62
For a Treasury security, what isthe required rate of return?
Since Treasuries are essentially free ofdefault risk , the rate of return on aTreasury security is considered the
risk-free rate of return.
Required
rate ofreturn =
Risk-free
rate ofreturn
8/13/2019 Risk in Return for Basic Finance
9/62
For a corporate stock or bond ,what is the required rate of return?
How large of a risk premium should werequire to buy a corporate security?
Required
rate ofreturn
= +Risk-free
rate ofreturn
Risk
premium
8/13/2019 Risk in Return for Basic Finance
10/62
Returns
Expected Return - the return that aninvestor expects to earn on an asset,
given its price, growth potential, etc.
Required Return - the return that aninvestor requires on an asset given its risk and market interest rates.
8/13/2019 Risk in Return for Basic Finance
11/62
State of Probability ReturnEconomy (P) Orl. Utility Orl. Tech
Recession .20 4% -10%
Normal .50 10% 14%Boom .30 14% 30%
For each firm, the expected return on thestock is just a weighted average :
k = P(k 1)*k 1 + P(k 2)*k 2 + ...+ P(k n )*kn
Expected Return
8/13/2019 Risk in Return for Basic Finance
12/62
Expected Return
State of Probability ReturnEconomy (P) Orl. Utility Orl. Tech
Recession .20 4% -10%
Normal .50 10% 14%Boom .30 14% 30%
k = P(k 1)*k 1 + P(k 2)*k 2 + ...+ P(k n )*knk (OU ) = .2 (4%) + .5 (10%) + .3 (14%) = 10%
k (OT ) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%
8/13/2019 Risk in Return for Basic Finance
13/62
Based only on yourexpected return
calculations, whichstock would you
prefer?
8/13/2019 Risk in Return for Basic Finance
14/62
RISK?
Have you considered
8/13/2019 Risk in Return for Basic Finance
15/62
What is Risk?
The possibility that an actual returnwill differ from our expected return.
Uncertainty in the distribution ofpossible outcomes.
8/13/2019 Risk in Return for Basic Finance
16/62
What is Risk?
Uncertainty in the distribution ofpossible outcomes.
8/13/2019 Risk in Return for Basic Finance
17/62
How do We Measure Risk?
A more scientific approach is toexamine the stocks standard
deviation of returns. Standard deviation is a measure of
the dispersion of possible outcomes .
The greater the standard deviation,the greater the uncertainty, and,therefore, the greater the risk.
8/13/2019 Risk in Return for Basic Finance
18/62
Standard Deviation
= (k i - k) 2 P(k i )n
i =1
8/13/2019 Risk in Return for Basic Finance
19/62
Orlando Util i ty, I nc.
( 4% - 10%) 2 (.2) = 7.2(10% - 10%) 2 (.5) = 0(14% - 10%) 2 (.3) = 4.8Variance = 12Stand. dev. = 12 = 3.46%
= (k i - k) 2 P(k i)n
i =1
8/13/2019 Risk in Return for Basic Finance
20/62
Orlando Technology, I nc.
(-10% - 14%) 2 (.2) = 115.2(14% - 14%) 2 (.5) = 0
(30% - 14%)2
(.3) = 76.8Variance = 192Stand. dev. = 192 = 13.86%
= (k i - k) 2 P(k i)n
i =1
8/13/2019 Risk in Return for Basic Finance
21/62
Which stock would you prefer?
How would you decide?
8/13/2019 Risk in Return for Basic Finance
22/62
Orlando Orlando
Utility Technology
Expected Return 10% 14%
Standard Deviation 3.46% 13.86%
Summary
8/13/2019 Risk in Return for Basic Finance
23/62
It depends on your tolerance for risk!
Remember, theres a tradeoff between
risk and return.
Return
Risk
8/13/2019 Risk in Return for Basic Finance
24/62
Portfolios
Combining several securitiesin a portfolio can actuallyreduce overall risk .
How does this work?
8/13/2019 Risk in Return for Basic Finance
25/62
Suppose we have stock A and stock B.The returns on these stocks do not tendto move together over time (they arenot perfectly correlated).
rateof
return
time
k A
k B
Wh h h d h
8/13/2019 Risk in Return for Basic Finance
26/62
rateof
return
time
k pk A
k B
What has happened to thevariability of returns for the
portfolio?
8/13/2019 Risk in Return for Basic Finance
27/62
Diversification
Investing in more than one securityto reduce risk .
If two stocks are perfectly positively correlated , diversification has noeffect on risk.
If two stocks are perfectly negatively correlated , the portfolio is perfectly diversified.
8/13/2019 Risk in Return for Basic Finance
28/62
If you owned a share of every stock
traded on the NYSE and NASDAQ,would you be diversified?YES!
Would you have eliminated all ofyour risk?NO! Common stock portfolios stillhave risk.
8/13/2019 Risk in Return for Basic Finance
29/62
Some risk can be diversifiedaway and some cannot.
Market risk (systematic r isk) isnondiversifiable. This type of risk
cannot be diversified away. Company-unique risk (unsystematic
risk) is diversifiable . This type of riskcan be reduced throughdiversification.
8/13/2019 Risk in Return for Basic Finance
30/62
Market Risk
Unexpected changes in interestrates.
Unexpected changes in cash flowsdue to tax rate changes, foreign
competition, and the overallbusiness cycle.
8/13/2019 Risk in Return for Basic Finance
31/62
Company-unique Risk
A companys labor force goes onstrike.
A companys top management diesin a plane crash.
A huge oil tank bursts and floods a
companys production area.
8/13/2019 Risk in Return for Basic Finance
32/62
As you add stocks to your portfolio,company-unique risk is reduced.
portfoliorisk
number of stocks
Market risk
company-unique
risk
8/13/2019 Risk in Return for Basic Finance
33/62
Do some firms have moremarket risk than others?
Yes. For example:Interest rate changes affect all firms, but
which would be more affected:
a) Retail food chainb) Commercial bank
8/13/2019 Risk in Return for Basic Finance
34/62
Yes. For example:Interest rate changes affect all firms, but
which would be more affected:
a) Retail food chainb) Commercial bank
Do some firms have moremarket risk than others?
8/13/2019 Risk in Return for Basic Finance
35/62
Note
As we know, the market compensatesinvestors for accepting risk - butonly for market risk . Company-
unique risk can and should bediversified away.
So - we need to be able to measure market risk.
8/13/2019 Risk in Return for Basic Finance
36/62
This is why we have Beta.
Beta: a measure of market risk. Specifically, beta is a measure of how
an individual stocks returns varywith market returns.
Its a measure of the sensitivity ofan individual stocks returns tochanges in the market.
8/13/2019 Risk in Return for Basic Finance
37/62
A firm that has a beta = 1 has averagemarket risk . The stock is no more or lessvolatile than the market.
A firm with a beta > 1 is more volatile thanthe market. (ex: technology firms)
A firm with a beta < 1 is less volatile thanthe market. (ex: utilities)
The markets beta is 1
Ch t i ti li
8/13/2019 Risk in Return for Basic Finance
38/62
Characteristic line
-5-15 5 10 15
-15
-10
-10
-5
5
10
15
XYZ Co. returns
S&P 500returns
. . . .
. . . .. . . .
. . . .. . . .
. . . .
. . . .. . . .
. . .. . . .
. . .
Beta = slope= 1.20
The line of best fit
through a series of
returns for a firmsstock relative to themarket returns.
Calculating Beta
8/13/2019 Risk in Return for Basic Finance
39/62
Calculating Beta
-5-15 5 10 15
-15
-10
-10
-5
5
10
15
XYZ Co. returns
S&P 500returns
. . . .
. . . .. . . .
. . . .. . . .
. . . .
. . . .. . . .
. . .. . . .
. . . .
Beta = slope= 1.20
8/13/2019 Risk in Return for Basic Finance
40/62
Measuring a Portfolio Beta
Portfolio beta
The relationship between a portfolios returnsand the markets different returns A measure of the portfolios nondiversifiable
risk portfolio =(% invested in stock j) x ( of stock j)
8/13/2019 Risk in Return for Basic Finance
41/62
Summary:
We know how to measure risk, usingstandard deviation for overall riskand beta for market risk.
We know how to reduce overall riskto only market risk throughdiversification .
We need to know how to price risk sowe will know how much extra returnwe should require for accepting extrarisk.
8/13/2019 Risk in Return for Basic Finance
42/62
What is the Required Rate ofReturn?
The return on an investment
required by an investor givenmarket interest rates and theinvestments risk .
8/13/2019 Risk in Return for Basic Finance
43/62
market
riskcompany-
unique risk
can be diversified
away
Requiredrate ofreturn = +
Risk-freerate ofreturn
Riskpremium
8/13/2019 Risk in Return for Basic Finance
44/62
Required
rate ofreturn
Beta
Lets try to graph this relationship!
8/13/2019 Risk in Return for Basic Finance
45/62
Required
rate ofreturn
.
Risk-free
rate ofreturn(6%)
Beta
12%
1
The return line that reflects theattitudes of investors regardingthe minimal acceptable returnfor a given level of systematicrisk.
Security MarketLine (SML)
8/13/2019 Risk in Return for Basic Finance
46/62
This linear relationship between
risk and required return isknown as the Capital Asset
Pricing Model (CAPM).
Required SML
8/13/2019 Risk in Return for Basic Finance
47/62
Required
rate of
return
.
Risk-free
rate ofreturn(6%)
Beta
12%
1
SML
0
Is there a riskless(zero beta) security?
Required SML
8/13/2019 Risk in Return for Basic Finance
48/62
Required
rate of
return
Beta
.12%
1
SML
0
Is there a riskless(zero beta) security?
Treasurysecurities are
as close to risklessas possible.Risk-free
rate ofreturn(6%)
Required SML
8/13/2019 Risk in Return for Basic Finance
49/62
Required
rate of
return
.
Beta
12%
1
SMLWhere does the S&P 500fall on the SML?
Risk-free
rate ofreturn(6%)
0
Required SML
8/13/2019 Risk in Return for Basic Finance
50/62
Required
rate of
return
.
Beta
12%
1
SMLWhere does the S&P 500fall on the SML?
The S&P 500 isa good
approximation
for the market
Risk-free
rate ofreturn(6%)
0
8/13/2019 Risk in Return for Basic Finance
51/62
Required SMLHi h t h
8/13/2019 Risk in Return for Basic Finance
52/62
Required
rate of
return
.
Beta
12%
1
SMLHigh-techstocks
Risk-free
rate ofreturn(6%)
0
8/13/2019 Risk in Return for Basic Finance
53/62
k j = k rf + j (k m - k rf )
where:
k j = the required return on security j,
k rf = the risk-free rate of interest, j = the beta of security j, and
k m = the return on the market index.
The CAPM equation:
b
b
8/13/2019 Risk in Return for Basic Finance
54/62
Example:
Suppose the Treasury bond rate is6% , the average return on the
S&P 500 index is 12% , and WaltDisney has a beta of 1.2 . According to the CAPM , what
should be the required rate ofreturn on Disney stock?
8/13/2019 Risk in Return for Basic Finance
55/62
k j = k rf + (k m - k rf )
k j = .06 + 1.2 (.12 - .06)k j = .132 = 13.2%
According to the CAPM, Disney
stock should be priced to give a13.2% return.
b
Required SML
8/13/2019 Risk in Return for Basic Finance
56/62
Required
rate of
return
.
Beta
12%
1
SML
0
Risk-free
rate ofreturn(6%)
Required SML
8/13/2019 Risk in Return for Basic Finance
57/62
equ ed
rate of
return
.
Beta
12%
1
SML
0
Theoretically, everysecurity should lie
on the SML
Risk-free
rate ofreturn(6%)
Required SML
8/13/2019 Risk in Return for Basic Finance
58/62
q
rate of
return
.
Beta
12%
1
SML
0
Theoretically, everysecurity should lie
on the SML
If every stockis on the SML,
investors are being fullycompensated for risk.Risk-free
rate ofreturn(6%)
Required SML
8/13/2019 Risk in Return for Basic Finance
59/62
q
rate of
return
.
Beta
12%
1
SML
0
If a security is abovethe SML, it is
underpriced.
Risk-free
rate ofreturn(6%)
Required SML
8/13/2019 Risk in Return for Basic Finance
60/62
q
rate of
return
.
Beta
12%
1
SML
0
If a security is abovethe SML, it is
underpriced.
If a security isbelow the SML, it
is overpriced.Risk-freerate ofreturn(6%)
Si l R C l l i
8/13/2019 Risk in Return for Basic Finance
61/62
P t+1 60
P t 50
Simple Return Calculations
= = 20%Pt+1 - P t 60 - 50
P t 50
- 1 = -1 = 20%
t t+1
$50 $60
(a) (b)
8/13/2019 Risk in Return for Basic Finance
62/62
monthly expected month price return return (a - b) 2
Dec $50.00 Jan $58.00 0.160 0.049 0.012321 Feb $63.80 0.100 0.049 0.002601 Mar $59.00 -0.075 0.049 0.015376 Apr $62.00 0.051 0.049 0.000004
May $64.50 0.040 0.049 0.000081 Jun $69.00 0.070 0.049 0.000441 Jul $69.00 0.000 0.049 0.002401 Aug $75.00 0.087 0.049 0.001444
Sep $82.50 0.100 0.049 0.002601 Oct $73.00 -0.115 0.049 0.028960 Nov $80.00 0.096 0.049 0.002090 Dec $86.00 0.075 0.049 0.000676