3. Risk
The main concern while making investment in any area
is risk.
Risk is defined as variation of actual return from the
expected return.
Any individual while investing his fund tries to
estimate the risk associated with his investment and
make final decision of investment only if its falls
within the level of risk which he can afford to take.
Risk and expected return of an investment are related.
Theoretically, the higher the risk, higher is the expected
returned. The higher return is a compensation expected
by investors for their willingness to bear the higher
risk.
4. It is therefore important for an individual to estimate
the amount of risk being undertaken by him while
making investment decisions.
There are two important issues relating to calculation
of risk:
A. Factor which leads to creation of risk i.e. which are
likely to deviate the actual return from the expected
return.
B. Methods of calculating risk
5. Factors Causing risk
The factors causing risk can be broadly divided in two parts:
A. Systematic Risk
B. Unsystematic Risk
Systematic Risk : It arises due to factors like economic,
sociological, political etc. which have bearing on the entire
market. This is also called uncontrollable or non-diversifiable
risk.
Market risk
Interest rate Risk
Purchasing power Risk
Exchange rate Risk
6. Market risk
• Market risk is caused by the herd mentality of
investors, i.e. the tendency of investors to follow
the direction of the market. Hence, market risk is
the tendency of security prices to move together. If
the market is declining, then even the share prices
of good-performing companies fall.
• Market risk constitutes almost two-thirds of total
systematic risk. Therefore, sometimes the
systematic risk is also referred to as market risk.
Market price changes are the most prominent
source of risk in securities.
7. Interest rate risk
• Interest rate risk arises due to changes in market interest rates.
In the stock market, this primarily affects fixed income securities
because bond prices are inversely related to the market interest
rate.
• In fact, interest rate risks include two opposite components:
Price Risk and Reinvestment Risk. Both of these risks work in
opposite directions. Price risk is associated with changes in the
price of a security due to changes in interest rate.
• Reinvestment risk is associated with reinvesting interest/
dividend income. If price risk is negative (i.e., fall in price),
reinvestment risk would be positive (i.e., increase in earnings on
reinvested money). Interest rate changes are the main source of
risk for fixed income securities such as bonds and debentures.
8. Purchasing Power Risk (or Inflation Risk)
• Purchasing power risk arises due to inflation. Inflation is
the persistent and sustained increase in the general
price level. Inflation erodes the purchasing power of
money.
• Therefore, if an investor’s income does not increase in
times of rising inflation, then the investor is actually
getting lower income in real terms.
• Fixed income securities are subject to a high level of
purchasing power risk because income from such
securities is fixed in nominal terms.
• It is often said that equity shares are good hedges
against inflation and hence subject to lower purchasing
power risk.
9. Exchange Rate Risk
• In a globalized economy, most companies have
exposure to foreign currency.
• Exchange rate risk is the uncertainty associated
with changes in the value of foreign currencies.
• Therefore, this type of risk affects only the
securities of companies with foreign exchange
transactions or exposures such as export
companies, MNCs, or companies that use imported
raw materials or products.
10. Unsystematic Risk
• Unsystematic risk is the risk that is unique to a specific company
or industry.
• It's also known as nonsystematic risk, specific risk, diversifiable
risk, or residual risk.
• It arises due to factors peculiar to an given firms such as labour
strike, change in management, change in demand of product etc.
• This is also known as Controllable and diversifiable risk.
• There are two kinds of risk which are normally covered under
unsystematic Risk :
• Business Risk
• Financial Risk
11. Business Risk
• Both internal and external issues may cause business
risk.
• Internal risks are tied to operational efficiencies,
such as management failing to take out a patent to
protect a new product would be an internal risk, as it
may result in the loss of competitive advantage.
• The Food and Drug Administration (FDA) banning a
specific drug that a company sells is an example of
external business risk.
12. Financial Risk
• Financial risk relates to the capital structure
of a company.
• A company needs to have an optimal level
of debt and equity to continue to grow and
meet its financial obligations.
• A weak capital structure may lead to
inconsistent earnings and cash flow that
could prevent a company from trading.
13. Return
• Return can be defined as the actual income from a project
as well as appreciation in the value of capital.
• Thus, there are two components in return—the basic
component or the periodic cash flows from the
investment, either in the form of interest or dividends; and
the change in the price of the asset, com
monly called as
the capital gain or loss.
• The term yield is often used in connection to return,
which refers to the income component in relation to
some price for the asset.
• The total return of an asset for the holding period
relates to all the cash flows received by an investor
during any designated time period to the amount of
money invested in the asset.
14. Calculation of risk
Example:-1 Consider a company ABC Ltd. Having record of
following dividend and average price per share during last six
years:
Find Return and Risk associated with the share of the company.
Year Average Market Price (Rs.) Dividend per Share
(Rs.)
1 35 5
2 42 5
3 49 10
4 55 12
5 52 15
6 60 12
15. Solution:- Calculation of Return
Average Return ()= =34.36%
Year Average market
price
Dividend per
share
Capital yield
%
Dividend yield
%
Total return for a year
%
1 35 5 --- --- ---
2 42 5 20.00 14.29 34.29
3 49 10 16.67 23.81 40.48
4 55 12 12.24 24.49 36.73
5 52 15 -5.45 27.27 21.82
6 60 12 15.38 23.08 38.46
Sum of the Returns (Year Wise) for given Period 171.78
16. Solution: Calculation of Risk
= = 43.43
σ = 6.59
Year Total Return (R) % Deviation of R from Average Return
% (R-)
Square of Deviation
1 34.29 -0.07
2 40.48 6.12 3
3 36.73 2.37
4 21.82 -12.54 1
5 38.46 4.1
17. Standard deviation looks at how spread out a group of
numbers is from the mean by looking at the square root of
variance, while variance measures the average degree to
which each point differs from the mean – average of all data.
Standard deviation is much easier to interpret as it is in the
same unit of measurement as that of original data. In case of
variance the unit of measurement changes due to squaring,
which get restored to the original unit while taking square
root of the variance.
19. • In Finance, Co-efficient of Variation allows investors to
determine how much volatility or risk is assumed in
comparison to the amount of return expected from
the investment. Ideally, if the co-efficient of variation
result in a lower ratio of the standard deviation to
mean return, then there is better risk return trade-off.
• If the expected return or denominator is zero or
negative, co-efficient of variation could be misleading.
20. Calculation of risk: By coefficient of variation
Example:-2 There are two alternatives A and B
offering same Return say 20% But A is having Standard Deviation of
15% and B is having Standard Deviation of 13%.
Then, B is considered superior than A as it is inherited with low risk
than A for a given level of Return.
Security A Security B
Expected Return E (R) 20% 20%
Standard Deviation 15% 13%
21. Calculation of risk: By coefficient of variation
Example:-2 There are two alternatives A and B. However, the appraisal
technique would be different if A is offering rate of Return of 20% and B
is offering rate of Return of 17%.
In this case, since the expected rate of return for the two proposal are
different therefore one cannot make correct decision simply by
referring to Standard Deviation of the two proposal.
In this case, one should calculate coefficient of variation for the two
proposal as shown below:
Now, it is observed that the risk, measured by coefficient of variation, is
higher in case of proposal B. therefore, a risk averse investor should opt
security A for investment.
Security A Security B
Expected Return E(R)
Standard Deviation
20%
15%
17%
13%
Co-efficient of Variation 75 76.47
22. Calculation of risk: from expected return
Example:-3 Consider the following return under five
year different situations and the probability of
occurrence of situations is also given for the
corresponding return.
Situations Return (R) % Probability
(P)
Deviation R-
E(R)
1 22 0.15 -3.2 10.24 1.536
2 26 0.20 0.80 0.64 0.128
3 24 0.10 -1.2 1.44 0.144
4 30 0.25 4.8 23.04 5.76
5 24 0.30 -1.2 1.44 0.432
126
E(R) = 25.20
24. What Is a Characteristic Line?
A characteristic line is a straight line formed using regression
analysis that summarizes a particular security's systematic risk
and rate of return. The characteristic line is also known as the
security characteristic line (SCL).
The characteristic line is created by plotting a security's return
at various points in time. The y-axis on the chart measures the
excess return of the security. Excess return is measured
against the risk-free rate of return. The x-axis on the chart
measures the market's return in excess of the risk free rate.
25. The security's plots reveal how the security performed relative to the
market in general. The regression line formed from the plots will
show the security's excess return over the measured period of time
as well as the amount of systematic risk the security demonstrates.
The y-intercept is the security's alpha, which represents its rate of
return in excess of the risk-free rate, which cannot be accounted for
by that market’s specific risks.
The alpha stands for the asset’s rate of return above and beyond its
risk-free return, adjusted for the asset’s relative riskiness. The slope of
the characteristic line is the security's systematic risk, or beta, which
measures the correlated variability of the specific asset’s price when
compared to that of the market as a whole.
26. What the Characteristic Line Shows
The characteristic line presents a visual
representation of how a specific security or other
asset performs when compared to the
performance of the market as a whole. The return,
and correlated risk, of a specific asset, relative to
the market in general, are represented by both the
slope of the characteristic line and its standard
deviation.
28. Bifurcating total risk: Systematic and unsystematic
Example:- 4 Consider the data for six days of the
stock ABC Ltd. And market index as shown below:
Day 1 2 3 4 5 6
Market Index 5000 5150 5350 5400 5325 5250
Price of Stock 95 98 102 110 106 101
29. Solution:-
Market index Price of Stock ABC Ltd. Return on Market index
Rm (X)
Return on Security
Ri (Y)
5000 95 - --- -
5150 98 3.00 3.16
5350 102 3.88 4.08 15.0
5400 110 0.93 7.84 0.87
5325 106 -1.39 -3.64 1.92
5250 101 -1.41 -4.72 1.98
=28.87
30. =
=
We Have:
= = = 1
= = = 1.35
-
= 1.35-1.577(1) = -0.23
Thus the systematic Risk of the stock is 1.577 and unsystematic
Risk is -0.23
32. Measurement of Beta
Characteristic line is used for bifurcating total Risk into systematic
Risk and unsystematic risk of the stocks. As beta of the stock
measures volatility of the stock relative to the movement of the
market, it can also be computed using the following formula:
Beta of Stock =
Beta of Stock =
Example:-4 consider the following data relating to
return on stock and market index: Compute beta of
the stock.
33. Period Return on Stock % Return on Market %
1 10 15
2 18 12
3 14 18
4 20 16
5 11 19
35. Covariance =
Covariance = = - 4.2
Variance of Market =
Variance of Market= = 6
Beta of Stock =
= = -0.7
36. Portfolio Management
• Portfolios are combinations of assets. Portfolios consist
of collections of securities.
• Portfolio management means selection of securities and
constant shifting of the portfolio in the light of varying
attractiveness of the constituents of the portfolio.
• It is a choice of selecting and revising spectrum of
securities to it in with the characteristics of an investor.
• Portfolio management includes portfolio planning,
selection and construction, review and evaluation of
securities. The skill in portfolio management lies in
achieving a sound balance between the objectives of
safety, liquidity and profitability.
37. Illustration 2: Consider three different security A, B, and C having following
expected return. if one combine them to form the portfolio, the expected
return would depend upon their respective weights.
For example, if an individual makes a portfolio by combining 50% of A, 30%
of B and 20% of C, the expected return of the portfolio would be given as:
E(Rp)= .12 x .50 + .14 x .30 + .18 x .20 = 13.80%
If the above weight are changed to 20% of A, 40% of B and 40% of C, then
the portfolio return would be as:
E(Rp) = .12 x .20 + .14 x .40 + .18 x .40 = 15.20%
Thus, the expected return of portfolio is calculated by aggregating the
product of expected return of individual security with its corresponding
weight in the portfolio.
Security A B C
E (R) Expected Return 12% 14% 18%
39. Relationship between the returns of Securities X and Y
• Positive covariance: X’s and Y’s return could be above their
average returns at the same time. Alternatively, X’s and Y’s
returns could be below their average returns at the same
time. In either situation, this implies positive relation
between two returns. The covariance would be positive.
• Negative Covariance: X’s return could be above its average
return while Y’s return could be below its average return
and vice versa. This denotes a negative relationship
between returns of X and Y. The covariance would be
negative.
• Zero Covariance: Returns on X and Y could show no pattern;
that is, there is no relationship. In this situation there is no
covariance.
40. Relationship between coefficient of correlation and total risk of
portfolio formed by Securities X andY
• When the coefficient of correlation is +1 between the two securities i.e.
perfectly positive correlated, the total risk of portfolio is maximum.
• Further, When the coefficient of correlation is in range of 0 to +1, it tends
to increase total risk of portfolio. This is due to the fact that whenever,
there is any movement in the market, both the securities would move in
the same direction, therefore, as long as there is positive correlation
between the two securities, the risk of portfolio is not reduced.
• When the coefficient of correlation is -1 between the two securities i.e.
perfectly negative correlated, the total risk of portfolio is minimum.
• Further, When the coefficient of correlation is in range of 0 to -1, it tends to
decrease total risk of portfolio. This is due to the fact that whenever, there
is any movement in the market, both the securities would move in the
opposite directions to each other. As a result of this, the loss in one
security gets nullified due to gain in other security.
41. Example:-1 Mr. A has Rs. 90,000 for investment. He invested
30% of his funds in securities of X Ltd. Which are likely to
provide return 14% and the remaining in securities of Y Ltd.
Which is likely to provide return of 19%. Find the expected
return on the total investment.
Solution: Total Return of the investment .
Total return from the portfolio of X Ltd and Y Ltd =
(15,750/90,000) X 100
Securities Weight Return (A) Amount of
Investment (B)
Return from
investment (A X B)
X Ltd. 0.30 0.14 27,000 3,780
Y Ltd. 0.70 0.19 63,000 11,970
90,000 15,750
