Risk and Return

What is Return?

“Income received on an investment plus
any change in market price, usually
expressed as a percent of the beginning
market price of the investment “

Return

Capital
Yield
Gain

Components of Return
 Yield
The most common form of return for
investors is the periodic cash flows (income)
on the investment, either interest from bonds
or dividends from stocks.
 Capital Gain
The appreciation (or depreciation)
in the price of the asset,
commonly called the
Capital Gain (Loss).

Total Return
Total Return = Yield + Price Change

where,
TR = Total Return
Dt = cash dividend at the end of
the time period t
Pt = price of stock at time period t
Pt-1 = price of stock at time period t-1

Ali purchased a stock for Rs. 6,000. At
the end of the year the stock is worth
Rs. 7,500. Ali was paid dividends of Rs.
260. Calculate the total return received
by Ali.

Solution

Total Return = Rs.[260+(7,500 - 6,000)]
Rs. 6,000
= 0.293
= 29.3%

 The investor cannot be sure of the amount of
return he/she is going to receive.

 There can be many possibilities.

 Expected return is the weighted average of
possible returns, with the weights being the
probabilities of occurrence

Formula:

E ( R ) = S X* P(X)

where X will represent the various values of
return, P(X) shows the probability of various
return

Example
Suppose, if you knew a given
investment had a 50% chance of
earning return of Rs.10, a 25% chance
of earning a return of Rs. 20 and there
is a 25% chance of bearing a loss of
Rs.10.
What is your expected return?

Solution

Return (X) P(X) E(X) =X * P(X)

10 0.50 5
20 0.25 5
-10 0.25 -2.5
TOTAL 7.5

The relative return is the difference between
absolute return achieved by the investment
and the return achieved by the benchmark

For example, the return on a stock may be 8% over
a given period of time. This may sound rather high,
BUT,
If the return on the designated benchmark is 20%
over the same period of time, then the relative
return on that stock is in fact -12%.

 Also called real rate of return
 Inflation-adjusted return reveals the return
on an investment after removing the effects
of inflation.
 Formula:

 Return on Investment = R = 7%
 Inflation rate = IR = 3%
 Inflation Adjusted Return =?

Solution:

Inflation Adjusted Return = [(1+ R)/(1+IR)] – 1
= [(1+0.07)/(1+0.03)]-1
= 1.03883 – 1
= 0.0388
= 4% approximately

 A simple approximation for inflation-adjusted
return is given by simply subtracting the inflation
rate from the rate of return

 Inflation Adjusted Return = R – IR
= 7% - 3%
= 4%

So far we’ve discussed……

– Basic concept of return

– Components of Return

– Expected Return

– Relative Return

– Real Rate of Return

What is Risk?

Risk is the variability between the
expected and actual returns.

Interest Rate Risk
It is the risk that an
investment’s value will
change as a result of
change in interest
rates. This risk affects
the value of bonds
more directly than
stocks.

Market Risk

Market Risk refers to the variability in
returns resulting from fluctuations in
the overall market conditions

Financial Risk

It is the risk associated
with the use of debt
financing. The larger
proportion of assets
financed by debt, the
larger variability in
returns, other things
remaining equal.

Liquidity Risk
An investment that can be bought or sold
quickly without significant price concession is
considered liquid.
The more uncertainty about time element and
the price concession, the greater the liquidity
risk.

Foreign Exchange Risk
When investing in foreign countries one must consider
the fact that currency exchange rates can change the
price of the asset as well. This risk applies to all financial
instruments that are in a currency other than your
domestic currency.

Country Risk
This is also termed political risk,
because it is the risk of investing
funds in another country
whereby a major change in the
political or economic
environment could occur. This
could devalue your investment
and reduce its overall return. This
type of risk is usually restricted
to emerging or developing
countries that do not have stable
economic or political arenas.

SENSITIVITY ANALYSIS
 Sensitivity analysis is an approach
for assessing risk that uses several
possible return estimates to obtain a
sense of variability among outcomes

 One of the tools used to perform
this analysis is “RANGE”

Range is calculated by subtracting the
pessimistic (worst) outcome from the
optimistic (best) outcome.

Formula:
RANGE = Maximum Value – Minimum Value

Example
Suppose that you expect to receive the following
returns on a particular asset.

Min
Return

Max
Return

Solution

Range = Max Value – Min Value
= Rs.635 – Rs.600
= 35 rupees

Higher the range,
the more risky the asset is.

Standard Deviation
* Standard deviation is a tool for assessing risk
associated with a particular investment.

* Standard deviation measures the dispersion or
variability around a mean/expected value.

Formula:
s = S X2 * P(X) – [S X*P(X)]2

Example

Outcomes Return on Probability Return on Probability
Stock A P(X) Stock B P(Y)
(X) (Y)

Outcome 1 13 0.25 7 0.25

Outcome 2 15 0.50 15 0.50

Outcome 3 17 0.25 23 0.25

Solution - (S.D for Stock A)
X P(X) X * P(X) X2 * P (X)

13 0.25 3.25 42.25
15 0.50 7.50 112.50
17 0.25 4.25 72.25
Total 1.00 15.00 227

S.D = S X2 * P(X) – [S X*P(X)]2

S.D = 227 – (15) 2 = 1.41 rupees

Solution - (S.D for Stock B)
Y P(Y) Y* P(Y) Y 2 * P (Y)

7 0.25 1.75 12.25
15 0.50 7.50 112.50
23 0.25 5.75 132.25
Total 1.00 15.00 257

S.D = S Y2 * P(Y) – [S Y*P(Y)]2

S.D = 257 – (15) 2 = 5.66 rupees

Solution
STOCK A STOCK B

Expected Return 15 rupees 15 rupees

Standard Deviation stocks, we see that both 5.66 rupees
Comparing the two 1.41 rupees stocks have
the same expected returns. But the SD or risk is different.

The S.D of stock B > S.D of stock A

We can say that the return of stock B is prone to higher
fluctuation as compared to stock A

Coefficient of Variation

 CV is a measure of relative risk.
 It tells us the risk associated with each unit
of money invested.
 Formula:
CV = s (x) / E(X)

Example
 Stock A has an expected return of Rs. 15 and an
expected variation (S.D) of Rs. 4

 Stock B has an expected return of Rs. 20 and an
expected variation (S.D) of Rs. 5.

 Which stock is riskier?

Solution

• The CV of Stock A is 0.27 which means that against every
rupee invested, there is a risk of 27 paisas.

• The CV of Stock B is 0.25 which means that against every
rupee invested, there is a risk of 25 paisas.

• Since CV(A) > CV(B), so Stock A has more risk.

Risk and Return
of Portfolio

PORTFOLIO

 Portfolio: A grouping of financial assets such
as stocks, bonds, etc

 A good portfolio consists of financial assets
that are not strongly positively correlated

Portfolio Return
STOCK RETURN S. D Weightage of
(R) (s) Investment (W)

A 16% 15% 0.50
Assume that the correlation coefficient between A and B is 0.4
B 14% 12% 0.50

What is the expected return of the portfolio comprising of stock A
and B?

The formula for expected return of a portfolio is:
E (RP) = S Wi*Ri
Hence, in the expected return of the portfolio in this case is:
= (0.5)(0.16) + (0.5)(0.14) = 0.08 + 0.07 = 0.15 = 15%

Portfolio Risk
n n
sP = S S WA WB s AB
A=1 B=1

Where,

sP = Risk of a portfolio
WA is the weight (investment proportion) for the Stock A in the
portfolio,
WB is the weight (investment proportion) for the Stock B in the
portfolio,
sAB is the covariance between returns of Stock A and Stock B

STOCK – A STOCK – B
(col 1) (col 2)

1/2

STOCK A (row1) WA WA s A.A WA WB s A.B

STOCK B (row2) WB WA s B.A WB WB s B.B

How to calculate covariance…?
Formula:

covAB = rA.B* sA*sB
Where,
rA.B = correlation between A and B
sA = standard deviation of Stock A
sB = standard deviation of Stock B

CovA.A = sAA =rA.A*s A*sA
= (1.00)(0.15)(0.15) = 0.0225

CovA.B = sAB=rA.B* sA*sB
= (0.4)(0.15)(0.12) = 0.0072

CovB.A = sBA = rB.A*sB* sA
= (0.4)(0.12)(0.15) = 0.0072

CovB.B = sB.B=rB.B*sB*sB
= (1.00)(0.12)(0.12) = 0.0144

1/2

WA WA s A.A WA WB s A.B
sP =
WB WA s B.A WB WB s B.B

1/2

sP =
(0.5)(0.5)(0.0025) (0.5)(0.5)(0.0072)

(0.5)(0.5)(0.0072) (0.5)(0.5)(0.0144)

1/2

sP = 0.000625 0.001800

0.00180 0.003600

Adding the rows and columns, we get 0.01345. Hence, the risk of
the portfolio is:
s = (0.01345)1/2
s = 11.597% = 11.6% approx.
This value of S.D (11.6) is a measure of the risk associated with the
portfolio consisting of Stock A and Stock B.
Note that the amount of portfolio risk is lesser than the individual
risk of stock A and B.

CV – A better representation of risk
EXPECTED STANDARD Coefficient of
STOCK RETURN DEVIATION Variation
(R) (s) = s/ E(R)

A 16% 15% = 15/16 = 0.93

Hence ifBthe investor make an investment only in Stock A, the risk
14% 12% = 12/14 = 0.85
against each rupee invested would be 93 paisas. For stock B alone,
it would be almost 85 paisas but if half of the money is invested in
stock A and half of it is 15%
Portfolio of A & B invested in stock B then for=each rupee the
11.6% 11.6/15 = 0.77
investor shall have to bear a risk of only 77 paisas. Hence one can
reduce the risk by means of a portfolio.

DIVERSIFICATION

Diversification is basically used as a tool to
spread the risk across the number of assets or
investments.

A diversified portfolio should consist of securities that are not
perfectly positively correlated.

A portfolio should contain some high-risk and some low-risk
securities

How much risk reduction is possible?

How many different securities are required in
order to minimize the risk factor?

For a company, a portfolio containing 20-25
securities is suitable.

For an individual, a portfolio of almost 7
different securities is considered good.

KINDS OF

Systematic
Risk

Unsystematic
Risk

Systematic Risk
Systematic risk is the one
that affects the overall
market such as change in
the country's economic
position, tax reforms or a
change in the world energy
situation.

Unsystematic Risk

The risk which is independent of economic,
political and all other such factors. It is
associated with a particular
company or industry.

 The investor can
only reduce the
“unsystematic
risk” by means of
a diversified
portfolio.
 The “systematic
risk” cannot be
avoided.

 Since the investor takes systematic risk, therefore he should
be compensated for it.
 Return/Compensation depends on level of risk To measure
the risk, we use the Capital Asset Pricing Model.

CAPM
CAPM was developed in 1960s by
William Sharpe's.

This model states the relationship
between expected return, the
systematic return and the valuation of
securities.

CAPM
Sharpe found that the return on an individual
stock or a portfolio of stocks should equal its
cost of capital.
R = Rf + (Rm – Rf)b
Where,
R = required rate of return of security
Rf = risk free rate
Rm = expected market return
B = beta of the security
Rm – Rf = equity market premium

A characteristic line is a regression line that
shows the relationship between an individual’s
security returns and returns on market
portfolio. In order to draw this line we will
have to find the returns that an investor is
getting in excess of the risk free rate.

Y Excess Excess Y Excess Excess Return
e Return on Return on e Return on on
a Stock ABC Market a Stock ABC Market
r Portfolio r Portfolio

1 4 5 11 7 13

2 5 10 12 -1 4

3 -4 -6 13 -6 -1

4 -5 -10 14 -6 9

5 2 2 15 -2 -14

6 0 -3 16 7 -4

7 2 7 17 2 15

8 -1 -1 18 4 6

9 -2 -8 19 3 11

10 4 0 20 1 5

β The slope of characteristic
line is called beta.
β Beta represents the
systematic risk.
β Beta measures the change
in excess return on the
stock over the change in
the excess return on the
market portfolio.

 For beta = 1: The risk associated with the
individual stock is the same as the risk
associated with the market portfolio.

 For beta > 1: It shows that the stock has
more unavoidable risk as compared to the
market as a whole. This kind of stock is
known as aggressive investment.

 For beta < 1: The stock is less risky as
compared to the stocks in the market
portfolio. This kind of stock is known as
defensive investment.

As mentioned earlier, according to CAPM,
return is calculated by:

R = Rf + ( Rm – Rf )*b

Suppose the risk free rate of the security is 6%.
The market rate is 12% and the beta is 1.25,
Then the required rate of return for the security would be
R = 6 + (12 – 6) * 1.25
R = 6 + 7.5
R = 13.5%
Reconsider the above example but suppose that the value of B = 1.60.
Then the return would be:
R= 6 + (12 – 6)*1.60
R= 6 + 9.6
R= 15.6%
So, we see that greater the value of beta, the greater the systematic risk
and in turn the greater the required rate of return.

A security market line
describes the linear
relationship between
the expected return
and the systematic risk
as measured by beta.

What if the expected and
required rate of return are not
the same??

Then there is disequilibrium.

Bibliography
 Principles of Managerial Finance by Lawrence.
G. Gitman
 Investments by Charles P Jones
 Financial Management by Van Horne
 www.investopedia.com


Risk and Return

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Risk and Return