CHAPTER 8
Investors like returns and dislike risk; hence, they will invest in
risky assets only if those assets offer higher expected returns.
While doing ‘risk analysis’ it can help if we keep in mind that:
1.
2.
All business assets are expected to produce cash flows, and the
riskiness of an asset is based on the riskiness of its cash flows. The
riskier the cash flows, the riskier the asset.
Assets can be categorized as financial assets, especially stocks and
bonds, and as real assets, such as trucks, machines, and whole
businesses. Our focus in this chapter is to carry out risk analysis for
financial assets, especially stocks.
A stock’s risk can be considered in two ways: (a) on a stand-alone, or
single-stock, basis, or (b) in a portfolio context, where a number of
stocks are combined and their consolidated cash flows are analyzed.
1.
2.
3.
▪
▪
There is an important difference between stand-alone and portfolio risk,
and a stock that has a great deal of risk held by itself may be much less
risky when held as part of a larger portfolio.
Stand-alone risk, is important in stock analysis primarily because it serves
as a lead-in to portfolio analysis.
4.
In a portfolio context, a stock’s risk can be divided into
two components:


5.
Diversifiable risk: Diversifiable risk can be diversified away
and is thus of little concern to diversified investors.
Market risk: Market risk reflects the risk of a general stock
market decline and cannot be eliminated by diversification
(hence, does concern investors). Only market risk is relevant to
rational investors because diversifiable risk can and will be
eliminated.
A stock with high market risk must offer a relatively high
expected rate of return to attract investors. Investors in
general are averse to risk, so they will not buy risky
assets unless they are compensated with high expected
returns.



Whenever an individual makes an investment
he does so with the expectation of earning
more money in the future.
Return can be defined as ‘something over and
above my basic investment’.
Return can be expressed both in dollar terms
and percentage return terms.

In dollar or rupees terms, return can simply be stated as the
total amount of dollar or rupees received from an
investment less the original invested amount.
 Dollar return = Amount received – Amount invested

Two main problems arise when expressing returns in
dollar/rupee terms:
 Size/scale of investment: If returns are expressed in dollar terms
one cannot make a meaningful judgment about the value of return
unless and until we compare it with the size/scale of investment.
For e.g. a $100 return on $1000 investment is a good return, but a
$100 return on $100,000 investment is not.
 Timing of return: Furthermore, making a meaningful judgment
about dollar return also requires us to know about timing of return.
For e.g. a $100 return on $1000 investment 1 year from now is a
good return, but the same return received after 20 years is not.


The scale of investment and timing of return problem
associated with expressing returns in $ form can be resolved
if we express investment result in rate of return or
percentage return form.
ROR in % form can be calculated as:
ROR = Amount received – Amount invested
Amount invested
 ROR solves the problem of knowing scale of investment for forming a
meaningful judgment about value of return as it takes into account
the size of investment. For example a $10 return on $100 investment
produces a 10% ROR while a $10 return on $1000 investment
produces only 1% ROR.
 ROR solves timing of return problem as returns normally are
expressed on an annual basis.

Risk is defined as:
 A hazard, exposure to loss or injury.
 Chance of occurrence of an unfavorable event.
 Risk is the dispersion of returns around mean, or expected
mean.
 In the last chapter (Interest rate) we studied how risk premiums
were paid to cover the risk associated with investment in
treasury or corporate securities. For a treasury security, for
example, investment comes with the risk of decrease in
purchasing power in the future (inflation risk) or increase in
interest rates (interest rate risk). The risk premiums (inflation
risk premium and maturity risk premium) thus paid on the
treasury security reflects these two risks.
 In this chapter our focus will be to carry out risk analysis for
stocks.
Individuals and firms invest funds today with the
expectation of receiving additional funds in the future.
 Bonds offer relatively low returns, but with relatively
little risk—at least if you stick to Treasury and highgrade corporate bonds.
 Stocks offer the chance of higher returns, but stocks
are generally riskier than bonds. If you invest in
speculative stocks (or, really, any stock), you are taking
a significant risk in the hope of making an appreciable
return.




It is important to remember that,
“No investment should be undertaken unless the
expected rate of return is high enough to
compensate for the perceived risk.”
Investment in risky assets generally results in returns
that is less or more than what was originally
expected of them, rarely if ever do they produce
their expected returns.
Investment risk, then, is related to the probability of
earning a low or negative actual return on an
investment. The greater the chance of earning lower
than expected or negative returns, the riskier the
investment.
1. Stand-alone Risk and Returns
Calculation of the expected rate of return and
volatility for a single stock.

An asset’s risk can be analyzed in two ways:
 Stand-alone basis: On a stand alone basis the
riskiness of the asset is considered all by itself.
 Portfolio basis: When analyzing the riskiness of a
stock on a portfolio basis the riskiness of the asset
is considered in relation to other assets held in the
portfolio.

We’ll first analyze how to measure a stock’s
risk on a stand-alone basis.
• Risk is the dispersion of returns around mean, or
expected mean.
• Risk is measured by variance or standard deviation.
• For standard deviation calculation we need to know
expected rate of return or k, thus before calculating
standard deviation we calculate expected rate of
return.
• For performing these calculations we will use the
data given (in the next slide).
Economy
Pi
HT
USR
Recession
0.1
-60%
-8%
Below avg
0.2
-20%
-2%
Average
0.4
30%
5%
Above avg
0.2
60%
12%
Boom
0.1
90%
20%

In order to see how a stock’s stand-alone risk and
return are calculated let’s proceed with an example
where we calculate stand-alone return and risk of
two stocks, HT and USR.
^
k HT  expected rate of return on HT stock
^
N
k   ri Pi
i 1
^
k HT  (-60%) (0.1)  (-20%) (0.2)  (30%) (0.4)  (60%) (0.2)  (90%) (0.1)
^
k HT  23%
^
k USR  expected rate of return on USR stock
^
N
k   ri Pi
i 1
^
k USR  (-8%) (0.1)  (-2%) (0.2)  (5%) (0.4)  (12%) (0.2)  (20%) (0.1)
^
k USR  5.20%
Expected return
HT
23%
USR
5.20%




HT has the highest expected return, and appears to be the
better investment alternative than USR, but is it really?
Looking at this data only investment should be made in
USR’s stock only.
Have we failed to take account of risk? Yes.
Let’s now calculate take into account riskiness of these
stocks.
• Risk is the dispersion of returns around mean.
• Standard deviation (si) measures stand-alone
risk.
• The larger the si , the lower the probability that
actual returns will be close to the expected return.
s  Standard deviation
s  Variance  s
2
σ
N
 (K
i 1
 k̂ ) Pi
2
i
Economy
Pi
HT
USR
Recession
0.1
-60%
-8%
Below avg
0.2
-20%
-2%
Average
0.4
30%
5%
Above avg
0.2
60%
12%
Boom
0.1
90%
20%
s
N

i 1
(K i  K̂) 2 Pi
(-60 - 23) (0.1)  (-20 - 23) (0.2)

  (30 - 23) 2 (0.4)  (60 - 23) 2 (0.2)
 (90 - 23) 2 (0.1)

2
s HT
s HT
 42%
2





1
2
s
N

i 1
(K i  K)2 Pi
(-8 - 5.20) (0.1)  (-2 - 5.20) (0.2)

sUSR   (5 - 5.20) 2 (0.4)  (12 - 5.20) 2 (0.2)
 (20 - 5.20) 2 (0.1)

2
sUSR  10.49%
2





1
2
Standard Deviation
HT
42%
USR
10.49%
Standard deviation (si) measures stand-alone, risk.
The larger the si , the lower the probability that actual returns will
be close to the expected return.
 From the data above, HT has a higher standard deviation than
USR which means HT’s stock is riskier than HT’s and is not as safe
a investment as HT.
 Looking at this data only investment should be made in USR’s
stock only.
 On the other hand, if investment was made looking solely at
expected return, HT was a better choice as it returned 23%
against USR’s 5.20%.







Most investors are Risk Averse, meaning they don’t like risk
and demand a higher return for bearing more risk.
The Coefficient of Variation (CV) measures risk per unit of
expected return.
CV is a standardized measure of dispersion about the
expected return.
In simple words, CV tells how risky a stock is in relation to its
expected rate of return.
The higher the expected rate of return as compared to
standard deviation of a stock, lower is the riskiness of the
stock and vice versa.
σ
CV =
k
24
CV =
CV (HT)
σ/k
42/23
1.83
σ
k
CV (USR)
σ/k
10.49/5.20
2.00
Decision: Investment in HT stock is a safer option as its
risk per unit of return is relatively less than that of USR
stock.
25
HT Company
 K= 23%
 s= 42%
 CV = 1.83
USR Co.
 K = 5.20%
 s= 10.49%
 CV = 2.00
26

Discussion will focus on:
1.
Portfolio Returns and Portfolio Risk
 Calculate the expected rate of return and volatility for a
portfolio of investments and describe how diversification
affects the returns of a portfolio of investments.
2.
Types of Risk
 A stock’s risk consists of diversifiable and market risk. The only
relevant risk that a stock in a portfolio faces is its market risk.
Beta coefficient is a measure of stock’s market risk and it is
measured by the extent to which the return on a stock moves
with the overall stock market.
3.
The CAPM
 Estimate an investor’s required rate of return using capital asset
pricing model.
27
Assume a two-stock portfolio, total investment
capital of $100,000 with $50,000 investment in
HT and $50,000 in USR.
^
Calculate kp and sp.
^
^
^
kp is a weighted average of the expected return of each asset in the
portfolio :
n
kp = S wiki
^
^
i=1
From our example the expected return of HT was KHT = 23%
and the expected return of USR was KUSR = 5.20%
^
kp = 0.5(23%) + 0.5(5.20%) = 14.1%.
^
^
^
kp is between kHT and kUSR.
A stock’s risk consists of diversifiable and market risk.
1. Diversifiable risk
•
Firm-specific risk is that part of a security’s
stand-alone risk that can be eliminated by
proper diversification.
2. Market risk.
•
Market risk is that part of a security’s standalone risk that cannot be eliminated by
diversification, and is measured by beta.



As more and more assets are added to a
portfolio, risk measured by s decreases.
However, we could put every conceivable
asset in the world into our portfolio and still
have risk remaining.
This remaining risk is called Market Risk and
is measured by Beta.
31


It is important to remember that whenever
we hold stock in a portfolio we eliminate its
diversifiable risk with the help of efficient
diversification. The only relevant risk then a
stock in a portfolio faces is its market risk.
Beta coefficient is a measure of stock’s
market risk and it is measured by the extent
to which the return on a stock moves with the
overall stock market.
Figure: Effect of Portfolio Size on Portfolio Risk for Average Stocks


As more stocks are added, each new stock
has a smaller risk-reducing impact.
sp falls very slowly after about 10 stocks are
included, and after 40 stocks, there is little, if
any, effect.



Beta is a key element of the CAPM theory.
Stand-alone risk as measured by a stock’s s
or CV is not important to a well-diversified
investor.
The only relevant risk that a stock in a
portfolio faces is its market risk. Beta
coefficient is a measure of stock’s market risk
and it is measured by the extent to which the
return on a stock moves with the overall
stock market.



Rational, risk averse investors are concerned
with sp , which is based on market risk.
Market stock beta is always equal to 1.
For a stock having a beta of 1 it means it is as
risky as market. If market moves up by 10%
stock also moves up by 10% similarly if
market moves down by 10% stock also moves
down by 10%.


For a stock having a beta of 2 it means it is
more volatile than the market. If market
moves up by 10% stock moves up by 20%
similarly if market moves down by 10% stock
moves down by 20%.
For a stock having a beta of 0.5 it means it is
only half as volatile as the market. If market
moves up by 10% stock moves up by 5%
similarly if market moves down by 10% stock
moves down by 5%.




If beta = 1.0, average stock.
If beta > 1.0, stock riskier than average.
If beta < 1.0, stock less risky than average.
Most stocks have betas in the range of
0.5 to 1.5.

Beta measures a stock’s market risk. It shows
a stock’s volatility relative to the market.

Beta shows how risky a stock is if the stock is
held in a well-diversified portfolio.


Suppose there are two companies, AA and
BB. The beta coefficient for company AA is
0.85 and the beta coefficient for company BB
is 1.50.
Keeping this data in mind we can calculate
the required returns on the stocks of AA and
BB with the help of SML equation.
Security
Beta
AA
0.85
BB
1.50



RPM = market risk premium = kM - kRF
RPi = stock risk premium = (RPM)bi
ki = kRF + (kM - kRF )bi
= kRF + (RPM)bi
42
SML: ki = kRF + (kM – kRF)bi .




Assume :
kRF = 8%.
kM = 15%.
RPM = kM – kRF = 15% – 8% = 7%.
SML: ki = kRF + (kM – kRF)bi .



ki = kRF + (kM – kRF)bi
kAA = 8% + (7 * 0.85)
kAA = 13.95%



ki = kRF + (kM – kRF)bi
kBB = 8% + (7 * 1.50)
kBB= 18.5%
SML: ki = 8% + (15% – 8%) bi
ki (%)
SML
.
BB
kM = 15
.
. .
AA
kRF = 8 T-bills
-1
0
1
2
Risk, bi

What is Intel’s required return if its B = 1.2
(from ValueLine Investment Survey), the
current 3-mo. T-bill rate is 5%, and the
historical US market risk premium of 8.6% is
expected?
46
bp= Weighted average
= 0.5(bAA) + 0.5(bBB)
= 0.5(0.85) + 0.5(1.50)
= 1.175

What happens if inflation increases?

What happens if investors become more risk
averse about the stock market?

What happens if beta increases?
48






If investors raise inflation expectations by 3%, what would happen to the
SML?
As the expected rate of inflation increases, a premium must be added to
the real risk-free rate of return to compensate investors for the loss of
purchasing power that results from inflation.
The risk-free rate as measured by the rate on U.S. Treasury securities is
called the nominal, or quoted, rate; and it consists of two elements: (1) a
real inflation-free rate of return, k* and (2) an inflation premium, IP,
equal to the anticipated rate of inflation. Thus, kRF = k* + IP.
Therefore, the 6% kRF mentioned in the previous equation (ki = 6% + (5%)
bi ) might be thought of as consisting of a 3% real risk-free rate of return
plus a 3% inflation premium:
kRF = k* + IP = 3% + 3%
However, now assume that expected inflation rate rose by 2% i.e.
IP = 3% + 2% = 5%
Because of increase in inflation premium, risk free rate increases to 8%.
kRF = k* + IP = 3% + 5% = 8%

In simple words,
 As inflation increases, kRF increases.

ki = kRF + (kM – kRF)bi
kRF = k* + IP

Under CAPM an increase in kRF leads to an
equal increase in ROR of all risky assets.

An increase in investor’s risk aversion means
they now require a greater return for buying
riskier assets (stocks) which leads to
increased kM as kRF (risk free rate) remains
constant.

An increase in beta means an increase in
market riskiness of the stock which leads to
increased required rate of return on stocks.