Risk and Return

◼Risk and Return concepts

◼Risk in a portfolio context
◼Relationship between risk and return
 Introduction

◼ While making the decisions regarding investment and financing, the finance
manager seeks to achieve the right balance between risk and return, in order to
optimize the value of the firm.

◼ Risk and return go together in investments.

◼ Everything an investor does it tied directly or indirectly to the return and risk.
The concepts of Return
◼ The objective of any investor is to maximize expected returns from
his investment, subject to various constraints, primarily risk.
◼ Return is the motivating force inspiring the investor in the form of
rewards for undertaking the investment.
◼ The importance of return in any investment can be traced to the
following factors:
1. It enables the investors to compare alternative investments in terms
of what they have to offer to the investors.
2. Measurement of historical (past) returns enables the investor to
assess how well they have done.
3. Measurement of historical returns helps in estimation of future
returns.
◼ This reveals that they are there are two types of return-Realized or
Historical Return and Expected Return.
◼ Realized Return :this is ex-post (after the fact) return, or the return that was
or could have been earned. For example, a deposit of Rs.1,000 in a bank on
1st Jan, at a stated annual interest rate of 10% will be worth Rs.1,100 exactly
in a year. The historical or realized return in this case is 10%

◼ Expected Return: this is the return from an asset that the investors
anticipate or expect to earn over some future period. The expected return is
subject to uncertainty, or risk and may or may not occur. The investor
compensates for the uncertainty in returns and the timing of those returns by
requiring an expected return that is sufficiently high to offset the risk or
uncertainty.

◼ Components of Return: return is basically made up of 2 components:

1. The periodic cash receipts or income on investment in the form of interest,
dividends etc. The term yield is often used in connection with return. Yield
refers to the income derived from a security in relation to its price, usually its
purchase price. Ex: yield on a 10% bond at a purchase price of Rs.900 is
11.11%.
2. The appreciation (depreciation) in the price of an asset is referred to as
capital gain (loss). This is the difference between the purchase price and the
time at which the asset can be sold.
 Measuring the rate of return
◼ The rate of return is the total return the investor receives during the
holding period ( the period when the security is owned or held by the
investor) stated as a percentage of the purchase price of the
investment at the beginning of the holding period. In other words, it is
the income from the security in the form of cash flows and the
difference in price of the security between the beginning and end of the
holding period expressed as a percentage of the purchase price of the
security at the beginning of the holding period.

◼ General equation: k = Dt + (Pt- Pt-1)

Pt-1
Where k = rate of return
Pt = price of the security at time ‘t’ i.e. at the end of the holding period
Pt-1 = price of the security at time ‘t-1’ , i.e. at the beginning of the holding period
Dt = income or cash flow receivable from the security at time ‘t’.
◼ Illustration 1: if a share of ACC is purchased for Rs.3,580 on February 8th of
last year, and sold for Rs.3,800 on Feb 9th of this year and the company paid
a dividend of Rs.35 for the year, calculate the rate of return?

◼ Answer : k = Dt + (Pt- Pt-1) = 35+ (3,800-3,580)

Pt-1 3,580

=7.12%

❑ Illustration 2: if a 14%, Rs.1,000 ICICI debenture was purchased for

Rs.1,350 and the price of this security rises to Rs.1,500 by the end of an
year. Calculate rate of return for this debenture.

❑ Answer: 140+ (1500-1350) = 21.48%

1350
Probabilities and Rate of Return
◼ A probability is a number that describes the chances of an event
taking place . Probabilities are governed by 5 rules and range from 0
to 1.
1. A probability can never be larger than 1 (i.e. maximum probability that
an event taking place is 100%)
2. The sum total of probabilities must be equal to 1.
3. A probability can never be a negative no.
4. If an outcome is certain to occur, it is assigned a probability of 1,
while an impossible outcomes are assigned a probability of 0.
5. The possible outcomes must be mutually exclusive and collectively
exhaustive.
◼ How does probability affect the rate of return? In a world of uncertainty, the
expected return may or may not materialize. In such a situation, the
expected rate of return for any asset is the weighted average rate of return
using the probability of each rate of return as the weight. The expected rate
of return “k” is calculated by summing up the probabilities.

◼ Illustration:3 the probability distributions and corresponding rates of return

for Alpha Co. are shown below: what is the expected rate of return?

Possible outcomes (i) Probability of Rate of return (%)

occurrence (Pi) (Ki)
1 0.10 50

2 0.20 30

3 0.40 10

4 0.20 -10

5 0.10 -30

1.00
◼ k = (0.10) (0.50) +(0.20) (0.30) + (0.40) (0.10)+ (0.20) (-0.10)+ (0.10) (-0.30)
= 10%

Risk:
◼ Risk and return go hand- in hand in investments and finance.
◼ Risk can be defined as the chance that the actual outcome from an
investment will differ from the expected outcome.

◼ Sources of risk:
➢ Interest Rate Risk: is the variability in a security’s return resulting from
changes in level of interest rates. This risk affects bondholders more directly
than equity shareholders.
➢ Market risk: refers to the variability in returns due to the fluctuations in the
securities market. All securities are exposed to the market risk but equity
shares get most affected. This risk includes a wide range of factors
exogenous to securities themselves like depressions, wars, politics etc.
➢ Inflation risk: with rise in inflation there is reduction in purchasing power hence
this is also referred as purchasing power risk and affects all securities. This
risk is also directly related to interest rate risk, as interest rate go up with
inflation.
◼ Business Risk: risk of doing business in a particular industry or environment
and it gets transferred to the investors who invest in the business of the
company.
◼ Financial risk: arises when companies resort to financial leverage or the use
of debt financing. The more the company resorts to debt financing the
greater is the financial risk.
◼ Liquidity risk: associated with the secondary market in which the particular
security is traded. A security which can be bought or sold quickly without
significant price concession is considered liquid. The greater the uncertainty
about the time element and the price concession, the greater the liquidity
risk. Securities which have ready markets like T-bills have lesser liquidity
risk.

◼ Measurement of total Risk: risk is associated with the dispersion in the

likely outcomes. If an asset’s return has no variability, it has no risk. An
investor analyzing a series of returns on investment over a period of years
needs to know something about the variability of its returns or in other words
the asset’s total risk.
◼ There are different ways to measure variability of returns. The range of the
returns, i.e. the difference between the highest possible rate of return and
the lowest possible rate of return is one measure, but the range is based on
only two extreme values.
 n
◼ VAR (k) =  Pi(ki − k )2
i =1
Where Var (k)= variance of returns
Pi = probability associated with the ith possible outcome
ki = rate of return from the ith possible outcome
k = expected rate of return
n = no. of years

❑Another popular way of measuring variability is standard deviation.

S.D = VAR
Portfolios and Risk
◼ An investment portfolio refers to the group of assets that is owned by
an investor. It is possible to construct a portfolio in such a way that the
total risk of the portfolio is less than the sum of the risk of the individual
assets taken together. Generally investing in a single security is riskier
than investing in a portfolio, because the returns to the investor are
based on the future of a single asset. Hence, in order to reduce risk,
investors hold a diversified portfolio which might contain equity capital,
bonds, real estate, savings accounts, bullion, collectibles and various
other assets.
◼ Illustration 4: assume that you put your money equally into the stocks of 2
companies Banlight Ltd, a manufacturer of sunglasses and Varsha Ltd, a
manufacturer of raincoats. If the monsoons are above average in a
particular year, the earnings of Varsha Ltd would be up leading to an
increase in its share price and returns to the share holders. On the other
hand, the earnings of Banlight would be on a decline leading to a
corresponding decline in the share prices and investor’s returns. If there is a
prolonged summer the situation would be just the opposite.

◼ While the return on each individual stock might vary quite a bit depending
on the weather, the return on your portfolio (50% Banlight and 50% Varsha
stocks) could be quite stable because the decline in one will be offset by the
increase in the other.
◼The table below gives the returns on the 2 stocks on the assumption that
rainy, normal and sunny weather are equally likely events (1/3 probability
each). Calculate the expected return and standard deviation of the two stocks
individually and of the portfolio of 50% Banlight and 50% Varsha stocks

Weather Return on B Return on V Return on

conditions stock stock portfolio

RB(%) RV(%) RP (%)

Rainy 0 20 10
Normal 10 10 10
Sunny 20 0 10

Possible Probabilities RB RV RP
outcomes
Rainy 1/3 0 20 10
Normal 1/3 10 10 10
Sunny 1/3 20 0 10
Expected rate of 10% 10%
return k
S.D 66.67 = 8.16% 66.67 = 8.16% 0 = 0%
◼ The portfolio earns 10% no matter what the weather is. Hence through
diversification, 2 risky stocks have been combined to make a risk less
portfolio.

◼ The returns on Banlight and Varsha are said to be perfectly negatively

correlated since they always move in opposite directions in exactly the
same manner. On the other hand 2 stocks which go up and down together
in the same manner are said to be perfectly positively correlated. Both these
types of correlation rarely happen in practice. In general all stocks have
some degree of positive correlation because certain variables like economic
factors, political climate etc. tend to affect all stocks.

◼ We need not have stocks which are perfectly negatively correlated in a

portfolio in order to achieve the benefit of risk reduction through
diversification. As long as the assets in a portfolio are not perfectly positively
correlated, diversification does not result in risk reduction.
◼ Diversifiable and non diversifiable risk: the fact that returns on stocks do not
move in perfect tandem means that risk can be reduced by diversification. But
the fact that there is some positive correlation means that in practice risk can
never be reduced to zero. So there is a limit on the amount of risk that can be
reduced to zero. So there is a limit on the amount of risk that can be reduced
through diversification. This can be traced through 2 major reasons.
◼ Degree of correlation: the amount of risk reduction depends on the degree of
positive correlation between the stocks. The lower the degree of positive
correlation the greater is the amount of risk reduction that is possible.
◼ The no. of stocks in the portfolio: as the no. of stocks increases, the
diversifying effect of each additional stock diminishes.
◼ Non diversifiable risk is that part of total risk ( from various sources like
interest rate risk, inflation risk, financial risk, etc. ) that is related to the general
economy or the stock market as a whole and hence cannot be eliminated by
diversification. Non diversifiable risk is also referred to as market risk or
systematic risk.
◼ Diversifiable risk on the other hand, is that part of total risk that that is specific
to the company or industry and hence can be eliminated by diversification.
Diversifiable risk is also called unsystematic risk or specific risk.
◼ Non-diversifiable or market risk factors:
➢ Major changes in tax rates
➢ War and other calamities
➢ An increase or decrease in inflation rates
➢ A change in economic policy
➢ Industrial recession
➢ An increase in international oil prices, etc.

❑ Diversifiable or specific risk factors:

➢ Company strike
➢ Bankruptcy of a major supplier
➢ Death of a key company officer
➢ Unexpected entry of a new competitor in the market etc.
Risk of stocks in a portfolio

◼ For a diversified investor, the risk of the stock is only that portion of the total
risk that cannot be diversified away or its non-diversifiable risk.
◼ How is non diversifiable risk or market risk measured?. it is generally
measured by Beta (β) coefficient. Beta measures the relative risk
associated with any individual portfolio as measured in relation to the risk of
the market portfolio. The market portfolio represents the most diversified
portfolio of risky assets an investor could buy since it includes all risky
assets. This relative risk can be expressed as:

βj = non diversifiable risk of asset or portfolio

Risk of market portfolio

◼ Thus, the beta coefficient is a measure of the non-diversifiable or systematic
risk of an asset relative to that of the market portfolio. A beta of 1.0 indicates
an asset of average risk. A beta coefficient greater than 1.0 indicates above
average risk stocks whose returns tend to be more risky than the market.
Stocks with beta coefficient less than 1.0 are of below average risk i.e. less
riskier than the market portfolio.

◼ In case of market portfolio , all the possible diversification is done- thus the
risk of the market portfolio is non-diversifiable which an investor cannot
avoid. Similarly as long as the asset’s return are not positively correlated
with returns from other assets, there will be some way to diversify away its
unsystematic risk. As a result beta depends only on non-diversifiable risks.

◼ The beta of a portfolio is the weighted average of the betas of the securities
that constitute the portfolio, the weights being the proportions of
investments in the respective securities. Ex: beta of security A is 1.5 and
that of security B is 0.9 and 60% and 40% of our portfolio is invested in the
2 securities respectively, the beta of our portfolio will be 1.26
(1.5*.60+0.9*0.40)
 Measurement of Beta
◼ The systematic relationship between the return on security or a portfolio
and the return on the market can be described using a linear regression,
identifying the return on a security or portfolio as the dependent variable kj
and the return on market portfolio as the independent variable km, in the
single index model developed by William Sharpe.
kj = αj + βj km+ ej ------Characteristic Regression Line

◼ The beta parameter βj in the model represents the slope of the above
regression relationship and measures the responsiveness of the security
or portfolio or security will vary with changes in market return. The beta
coefficient of a security is defined as the ratio of the security’s covariance
of return with the market to the variance of the market.
βj = Cov (kj km)
Var (km)
◼ The alpha parameter is the intercept of the fitted line and indicates what the
security or portfolio will be when the market return is zero. Ex: if a security with
an α of +2 percent would earn 2 percent even when the market return was
zero and would earn an additional 2 percent at all levels of market return. The
converse is true if a security has α of -2 percent. The positive α thus
represents a sort of bonus return and would be highly desirable aspect of a
portfolio or security while a negative α represents a penalty to the investor.

◼ The third term ej is the unexpected return resulting from influences not
identified by the model. Frequently referred to as random or residual return, it
may take on any value but its generally found to average out to zero.

◼ What do the figures of β and α imply? When we say that the security has a β
of 1.54 we mean that if the return on the market portfolio rises by 10%, the
return on the security ‘j’ will rise by 15.4%. An α of 4.6% implies that the
security earns 4.6% over and above the market rate of return.
 The Capital Asset Pricing Model
◼ The CAPM developed by William F Sharpe, John Lintner and Jan Mossin is
one of the major developments in financial theory. The CAPM establishes a
linear relationship between the required rate of return of a security and its
systematic or un diversifiable risk or beta.
◼ The CAPM is represented mathematically by

kj = Rf +Bj (km -Rf)

Where,
kj = expected or required rate of return on security j
Rf = risk- free rate of return
Bj = beta coefficient of security j
km = return on market portfolio
◼ Assumptions:
➢ Investors are risk-averse and use the expected rate of return and standard
deviation of return as appropriate measures of risk and return for their
portfolio. In other words, the greater the perceived risk of a portfolio, the
higher return a risk-averse investor expects to compensate the risk.
➢ Investors make their investment decisions based on a single period horizon,
i.e. the next immediate time period.
➢ Transaction costs in financial markets are low enough to ignore and assets
can be bought and sold in any unit desired. The investor is limited only by his
wealth and the price of the asset.
➢ Taxes do not affect the choice of buying assets.
➢ All individuals assume that they can buy assets at the going market price
and they all agree on the nature of the return and the risk associated with
investment.
❑ CAPM enables us to be much more precise about how trade-offs between
risk and return are determined in financial markets.
❑ In the CAPM, the expected rate of return can also be thought of as a
required rate of return because the market is assumed to be in equilibrium.
❑ Expected rate of return is the return from an asset that investors anticipate
or expect to earn over some future period. ROR for a security is defined as
the minimum expected rate of return needed to induce an investor to
purchase it.
◼ Required rate of return = risk free rate + risk premium
◼ Risk premium= βj (km -Rf)

◼ This beta coefficient ‘Bj ‘ is the non-diversifiable risk of the asset relative to
the risk of the market. If the risk of the asset is greater than the market risk,
i.e. β exceeds 1.0, the investor assigns a higher risk premium to asset j than
to the market. Ex: suppose a fertilizer co. had a βj of 1.5 that is ROR on a
market (km) was 15 percent per year and that its risk free interest rate (Rf)
was 6 percent p.a. using the CAPM calculate the required rate of return.

kj = Rf +Bj (km -Rf)

= 0.06 +1.5 (0.15-0.06)
=19.5%