Learning Objectives

• understand the risk and return characteristics

of a portfolio
• explain how diversification reduces risk.
 Introduction to return and risk
• The return on an investment and the risk of
an investment are basic concepts in finance.
• A financial decision typically involves risk.
For example,
– a company that borrows money faces the risk
that interest rates may change, and
– a company that builds a new factory faces the risk
that product sales may be lower than expected.
– These and many other decisions involve future
cash flows that are risky.
• To make effective financial decisions,
managers need to understand what causes
risk,

• how it should be measured and the effect of

risk on the rate of return required by
investors.
 Return
• The return is the total gain or loss experienced on
an investment over a given period of time.
• Total Return = Income received on an investment
plus any change in market price,

1. Income component of return: Investor may

receive some cash directly while investor own the
investment.
2.Capital gain or capital loss: The value of the asset
investor purchase will often change.
 Return on Financial Assets

Total Return

Periodic Capital Gain or

Income Loss
Example : At the beginning of the year, the stock was selling for
Rs.37 per share. If you had bought 100 shares, you would have had
a total outlay of Rs.3, 700. Suppose that, over the year, the stock
paid a dividend of Rs.1.85 per share. By the end of the year, then,
you would have received income of:
Dividend = Rs.1.85 x 100 = Rs.185

Also, the value of the stock has risen to Rs.40.33 per share by the
end of the year. Your 100 shares are now worth Rs.4, 033, so you
have a capital gain of:

Capital gain = (Rs.40.33 - 37) x 100 = Rs.333.

Total return on investment = 185 + 333 = Rs.518
On the other hand, if the price had dropped to say, Rs.34.78, you
would have a capital loss of:
Capital Loss = (Rs.34.78 - 37) x 100 = -Rs.222

Total return on investment = 185 + (222) = Rs. – 37.00

 Risk
• Risk is the chance of financial loss.

• Risk defined as the variability of returns those

that are expected.

• Assets having greater chances of loss are

viewed as more risky than those with lesser
chances of loss.

• Therefore, risk is the potential for

divergence between the actual outcome and
what is expected.
 Elements of Risk
• External Factors: Factors which are external to a
company and affect a large number of securities
simultaneously. These are mostly uncontrollable
in nature.

• Internal Factors: which are internal to companies

and affect only those particular companies.
These are controllable to a great extent.
 Systematic Risk
• The impact of economic, political and social
changes is system-wide and that portion of total
variability in security returns caused by such
system-wide factors is referred to as Systematic
Risk .
•Uncertainties about general economic conditions:
GDP, interest rate or inflation are examples of
systematic risks.
• These conditions affect nearly all companies to
some degree.
•Systematic risk is further subdivided: interest rate
risk, market risk, and purchasing power risk.
• Interest rate risk : Variation in bond prices
caused due to the variations in interest rate is
known as interest rate risk.
• Market risk : The variations in returns caused by
the volatility of the stock market is referred to as
the market risk. (Ups and downs in the Mkt price,
polical, economical, social, change in monetary
policy, change in investor expectations)
• Purchasing power risk: It refers to the variation
in investor returns caused by inflation. (Inflation
– prices of goods and services – purchasing power
of investor’s investment)
 Unsystematic Risk
• Variability of returns occurs because of firm
specific factors known as unsystematic risk.
• Examples for firm specific factors: raw material
scarcity, labour strike, management inefficiency.
• This risk is unique or peculiar to a company or
industry and affects it in addition to the systematic
risk affecting all securities.
• Announcement of an oil strike by a company will
primarily affect that company and, perhaps a few
others (such as primary competitors and suppliers).
It is unlikely to have much of an effect on the world
oil market, this is an unsystematic event.
Unsystematic risk can be eliminated by
combining assets into a portfolio.
The unsystematic or unique risk affecting
specific securities arises from two sources:
a) the operating environment of the company
– Business Risk
b) the financing pattern adopted by
the company – Finance Risk
• Business risk : Business risk is a function of
the operating conditions faced by a company
and is the variability in operating income
caused by the operating conditions of the
company.
• Financial risk: Variability in EPS due to the
presence of debt in the capital structure of a
company is referred to as financial risk.
What rate of return do you expect on
your investment (savings) this
year?

What rate will you actually earn?

Example 2:
•Robin, a high -traffic video arcade, wishes to
determine the return on two of its video machines,
C and D. C was purchased 1 year ago for Rs.20,000
and currently has a market value of Rs.21,500.
During the year, it generated Rs.800 of after tax cash
receipts. D was purchased 4 years ago, its value in
the year just completed declined from Rs.12,000 to
Rs.11,800. During the year, it generated Rs.1,700 of
after tax cash receipts.
•Calculate the annual rate of return for each video
machines.
Example 2
• Return expressed as a percent of the beginning
market price of the investment.
Rt = Dt + ( Pt - Pt-1)
Pt-1
• (C): RC = Rs.800 + Rs.21, 500 - Rs.20, 000
Rs.20, 000
= Rs. 2,300 = 11.5%
Rs.20, 000

• (D): RD = Rs.1, 700 + Rs.11, 800 - Rs.12, 000

Rs.12, 000
Rs 1,500 = 12.5%
Rs.12, 000
• Conclusion: Although the market value of D
declined during the year, its cash flow caused
it to earn a higher rate of return than C
earned during the same period. Clearly, the
combined impact of cash flow and changes
in value, measured by the rate of return, is
important.
 RISK OF A SINGLE ASSET
Risk Assessment
•Sensitivity analysis uses several possible return
estimates to obtain a sense of the variability among
outcomes. One common method involves making
pessimistic (worst),
most likely (expected) and
optimistic (best) estimates of the returns associated
with a given asset.
•In this case, the asset's risk can be measured by the
range of returns. The range is found by subtracting the
pessimistic outcome from the optimistic outcome.
•The greater the range, the more variability, or risk, the
asset is said to have.
 Asset A Asset B
Initial Investment Rs.10,000 Rs.10,000
Annual rate of return
Pessimistic 13% 7%
Most likely 15% 15%
Optimistic 17% 23%
Range 4% 16%
Asset A appears to be less risky than asset B. It is range of
4% is less than the range of 16% for asset B
 Expected Rate of Return E(R)
• For an individual asset, the expected rate of
return is sum of the potential returns multiplied
with the corresponding probability of the
returns. It is the weighted average of the various
possible outcomes
 Risk measurement
• Standard deviation and coefficient of variation
can be used to measure the variability of asset
return.

Variance and Standard Deviation

• Variance and standard deviation measure the
volatility of returns.
• The most common statistical indication of an
asset's risk is the standard deviation σR , which
measures the dispersion around the expected
value.
 Determining Standard
Deviation (Risk Measure)
n
 =  ( Ri - R )2( Pi )
i=1
Standard Deviation, , is a statistical measure of
the variability of a distribution around its mean.
It is the square root of variance.
 How to Determine the
Expected Return and Standard
Deviation
Stock BW
Ri Pi (Ri)(Pi) (Ri - R )2(Pi)
-.15 .10 -.015 .00576
-.03 .20 -.006 .00288
.09 .40 .036 .00000
.21 .20 .042 .00288
.33 .10 .033 .00576
Sum 1.00 .090 .01728
 Determining Standard
Deviation (Risk Measure)
n
 =  ( Ri - R )2( Pi )
i=1

 = .01728

 = .1315 or 13.15%
 Coefficient of Variation
The ratio of the standard deviation of a distribution
to the mean of that distribution.
It is a measure of RELATIVE risk.
CV = s / R
CV of BW= .1315 / .09 = 1.46

CV is useful in comparing the risks of assets with

differing expected returns.
The CV shows the risk per unit of return, and it
provides a more meaningful basis for
comparison, when the ER on two alternatives
are not the same.
 Rate of
ScenarioProbabili Return
ty Stock fund
Bond fund
Recession 33.3% -7% 17%
Normal 33.3% 12% 7%
Boom 33.3% 28% -3%
Consider the following two risky asset
worlds. There is a 1/3 chance of each state of
the economy and the only assets are a stock
fund and a bond fund.
 Expected Return, Variance, and Covariance
Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%

E(rS ) = 13  (−7%) + 13  (12%) + 13  (28%)

E(rS ) = 11%
Expected Return, Variance, and Covariance

Stock fund Bond Fund

Rate of Rate of
Scenario Squared Squared
Return Return
Deviation Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
E(rB ) = 13  (17%) + 13  (7%) + 13  (−3%)
E(rB ) = 7%
Expected Return, Variance, and Covariance
Stoc k fund Bond Fund
Rate Squared Rate of
Scenario of Deviation Squared
Retu Return
rn Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%

(11% − −7%) = 3.24% 2

Expected Return, Variance, and Covariance
Stoc k fund Bond Fund
Rate Squared Rate of
Scenario of Deviation Squared
Retu Return
rn Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%

(11% −12%)2 = .01%

Expected Return, Variance, and Covariance
Stoc k fund Bond Fund
Rate Squared Rate of
Scenario of Deviation Squared
Retu Return
rn Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%

(11% − 28%)2 = 2.89%

 Stock fund Bond F u n d
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%

1
2.05% = (3.24% + 0.01% + 2.89%)
3
 Stock fund Bond Fund
Rate of Rate of
Scenario Squared Squared Return
Return Deviation
Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%

14.3% = 0.0205
 MEASUREMENT OF RISK OF A
PORTFOLIO.
• Portfolio is a selection of securities for investment
purposes. It is a common approach that investors
invest in portfolios of securities rather than in
individual securities.
• Portfolio selection is one of the main issues in the
investment theory and it refers to the process of
selecting securities to include into portfolios of
investments
• Given that there is a trade-off between risk and
returns, the attitude of an investor towards risk is
pivotal in his/her investment behaviour and in
particular the selection of securities to include into
his/her portfolio.
 The expected return on a portfolio
• It is a weighted average of the expected returns on the
individual assets/securities in the portfolio with the
weights being the fraction of the total portfolio
invested in each asset.
 Determining Portfolio
Expected Return
n
RP =  ( Wj )( Rj )
j=1
RP is the expected return for the portfolio,
Wj is the weight (investment proportion) for the jth
asset in the portfolio,
Rj is the expected return of the jth asset,
n is the total number of assets in the portfolio.
 Calculation of the expected return
on a portfolio
Assume that there are only two securities (1 and
2) in a portfolio and E(R1) = 0.08 and E(R2) =
0.12. Also assume that the current market value
of Security 1 is 60 per cent of the total current
market value of the portfolio (that is, w1 = 0.6
and w2 = 0.4).
• Then: E(Rp) = (0.6)(0.08) + (0.4)(0.12)
= 0.096 or 9.6%
•
 Two risky securities and are included in a portfolio,
with proportions 0.30 and 0.70 respectively. The
expected returns and the associated risks of these
securities are: = 28%; = 18% and = 74%; = 52%.
The correlation coefficient of the returns is = -65%.
• What are the expected returns and the risk of this
portfolio?
Answer:
Returns: = 0.30*(0.28)+0.70*(0.18) = 21.0%
Risk: (0.3)2 (0.74)2 +(0.7) 2(0.52) 2+2(0.3)(0.7)(0.74) (0.52)(-0.65)
= 0.07673
Variance =0.07673 and
SD= 27.7%
 DIVERSIFICATION AND RISK RETURNS PORTFOLIO
SELECTION

Diversification is the process by which the

invested wealth is spread among different
individual securities included in a portfolio. The
aim of this process is to minimise portfolio risk
with the minimum sacrifice on returns.

The level of the risk reduction depends on the risk

of the included securities but also on the degree
of the correlation of those individual returns with
each other.
Diversification
 Diversification and Portfolio Risk
• Principle of diversification tells us that
spreadin an investment across many asset
gwill eliminate some of the risk, but not all of
s the
risk.
•Diversification can substantially reduce the
variability of returns without an equivalent
reduction in expected returns.
• This reduction in risk arises because worse
than expected returns from one asset are offset
by better than expected returns from another.
•However, there is a minimum level of risk that
cannot be diversified away, and that is the
systematic portion.
 Systematic Risk

• A systematic risk is one that influences a large

number of assets, each to a greater or lesser
extent.
• Because systematic risks have market wide
effects, they are sometimes called market risks.
• Uncertainties about general economic
conditions such as GDP, interest rate or inflation
are examples of systematic risks. These
conditions affect nearly all companies to some
degree.
 Unsystematic (diversifiable) Risk

• An unsystematic risk is one that affects a single asset or

a small group of assets.
• Because these risks are unique to individual companies
or assets, they are sometimes called unique or asset
specific risks.
• Announcement of an oil strike by a company will
primarily affect that company and, perhaps a few others
(such as primary competitors and suppliers).
• It is unlikely to have much of an effect on the world oil
market, this is an unsystematic event. This risk can be
eliminated by combining assets into a portfolio.
Total Risk
•Total Risk = Systematic Risk + Unsystematic
(diversifiable) Risk.
•The standard deviation of returns is a measure of
total risk.
• For well-diversified portfolios, unsystematic
risk is very small.
•Consequently, the total risk for a diversified
portfolio is essentially equivalent to the
systematic risk
 Total Risk = Systematic Risk
STD DEV OF PORTFOLIO RETURN + Unsystematic Risk

Unsystematic risk
Total Risk
Systematic risk

NUMBER OF SECURITIES IN THE PORTFOLIO

 Measurement of Systematic
Risk
• Systematic risk of a security is measured by a
statistical measure called Beta.
• The input data required for the calculation
of beta are the historical data returns of
individual security as well as the returns of a
representative stock market index.
• The statistical methods may be used for
the calculation of beta, namely the
correlation method or the regression method.
Using correlation method, beta can be calculated from the historical data of return:
Calculating beta by using the regression method
• Example 6: With the given data in example 5,
calculate the beta of ITC stock using the
regression model.
• Dependent Variable Y = Ri
• Independent Variable X = Rm
• ƸXY = 2160.49
• ƸX = 49.82
• ƸY = 111.69
• ƸX2 = 1432.75
• n = 12