NPTEL Course

Course Title: Security Analysis and Portfolio Management

Instructor: Dr. Chandra Sekhar Mishra

Module-2

Session-3

Risk and Return – I

Outline

● Basic Concepts of Return ● Basic Concepts of Risk ● Sources of Risk ● Measuring Risk of a Single Asset

Basics of Return

The investors invest in any asset in anticipation of return on the same. In case of financial assets, this can also be termed as the financial results of the investment or financial asset. As one of the foremost criteria, an investor can distinguish different financial assets based on return on such financial assets. Returns can be classified as historical or expected i.e. prospective. Returns can be in absolute value i.e. in terms of currency and in relative terms i.e. in terms of %. For example, if an investment purchased one year back at Rs.120 is sold for Rs.132, the absolute return is Rs.12 and the relative return is 10% (i.e.12 / 120). Return in a way represents total gain or loss on investment. The total gain/ loss can comprise of periodic return and change in the value of investment at the end of the holding period.

Hence a basic formula used for calculation of return can be as below:

Where rt is the actual, required or expected return during period t, Pt is the current price, Pt-1 is the price during the previous time period, and Ct is any cash flow accruing from the investment.

Suppose one has bought a share of ABC Limited at Rs.300 one year back. Over the last year ABC has distributed dividend of Rs.5 per share. If the share of ABC sells at Rs.340 today, what is the return?

The total return is Rs.45 that comprises of Rs.5 of dividend and Rs.40 (Rs.340 – Rs.300) in terms of appreciation in the market price of the share. Hence the % return is Rs.45/Rs.300 i.e. 15%.

In case the share of ABC sells at Rs.280 today what is the return?

The absolute return (-ve)Rs.15 (i.e. Rs.5 dividend and loss of Rs.20 in terms of fall in price), which is -5% on origninal ivestment of Rs.300.

Holding Period Returns

The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri:

1

1

t

ttt

P

CPPr

t

Suppose an investment provides the following periodic return over last five years:

Year 1 2 3 4 5

Return (%) 12 15 -8 14 16

The holding period return on the investment is computed as below:

This can be interpreted as 56.70% return over five year holding period. In case an asset does not provide any periodic return – like annual return in the previous example – the holding period return (HPR)can be calculated as below:

1Investment of Value Beginning

Investment of Value Ending HPR

Example: A financial asset was purchased at Rs.300 and it grew to Rs.370 over five year period. The HPR over three year period is

33.33% 0.3333 1300

400

This return can be converted to effective annual return which can also be termed as annual holding period return or yield as below:

Annual HPR = (1+HPR)1/n – 1

Where, n is the number of years the investment is held. In the previous example, the annual HPR is:

(1.3333)1/3 – 1 = 0.1006 = 10.06%

Expected Return

Unlike historical return, in case of expected returns are predicted for the future with relevant values being predicted. The prediction can be for different expected outcomes. In such case probability is associated with possible outcomes and expected return from an investment is estimated.

Suppose there are two shares A and B and rate of returns in different conditions are expected to be as below:

State of the Economy

Probability of occurrence

Rate of Return (%)

A B

1)1()1()1(

returnperiod holding

21

nrrr

%70.565670.

1)16.1()14.1()92.0()15.1()12.1(

1)1()1()1()1()1( 54321

rrrrr

n

i

iirprE1

)(

Boom 0.50 22 24

Normal 0.30 18 18

Recession 0.20 14 12

The expected return on Share A = 0.50 x 22 + 0.30 x 18 + 0.20 x 14 = 19.2%.

Similarly return from Share B = 0.50 x 24 + 0.30 x 18 + 0.20 x 12 = 19.8%.

Risk:

Usually, investment returns are not known with certainty. In the context of investment, risk is defined as the chance of suffering a loss. Assets (real or financial) which have a greater chance of loss are considered more risky than those with a lower chance of loss. Risk may be used interchangeably with the term uncertainty to refer to the variability of returns associated with a given asset. The common sources of risk are as below:

Firm Specific Risks o Business Risk: Investors can be subject to bad performance of business or the firm

due to several reasons like weak demand for the products/ services, technological changes, supply related problems, mismanagement.

o Financial Risk: This emanates from the fact that the particular firm has borrowings as its source of finance. Higher the borrowing, higher is the interest outflow. In good condition, borrowing helps better return on shareholders’ funds – an implication of financial leverage. However in bad condition, borrowing can harm the firm. Borrowings also invite default risk.

Investor-Specific Risks o Interest rate risk: Change in interest rates can affect the value of interest bearing

securities. There is an inverse relationship between interest rate and value of interest bearing securities like bonds, debentures, etc. The equity shares are also affected indirectly by the movement in interest rates.

o Liquidity risk: The investors can have problem in converting the securities into cash because of inadequate market or for the fact that the securities are not listed. Sometimes, irrespective of listing, the securities are not traded in the market.

o Market risk: This is not related to the particular firm’s performance, but depends upon the overall market condition being pessimistic or optimistic because of several underlying factors. During a bullish period, prices of most of the equity shares move up and vice versa in bearish period. Market also moves in cycles.

Firm and Investor Risks o Event Risk: These are the risks caused due to unforeseen events related to the

company or a sector like ad adverse court judgment, regulatory policy change, sudden demise of key people of the organization.

o Exchange Rate Risk: This risk is caused due to change in currency rates. Companies having exports as major source revenue or imports of supplies are vulnerable to this risk. In the present era of globalization, it is difficult for any company to be immune to this risk.

o Purchasing-power risk: These are caused by changes in price level in the country. Inflationary conditions can affect the firms adversely because of decrease in demand.

o Tax risk: Change in tax rates for companies and/ or investors can have adverse impact. Sudden change in tax rules may affect the companies favorably or unfavorably. Tax being a major element of expense for any company, adverse

change in tax rates can be taxing for the company concerned. Investors’ residual income can also be affected by change in personal income tax rules and rates.

Unsystematic vs. Systematic Risk

The risks that can be controlled by diversifying the portfolio of financial assets are known as unsystematic or diversifiable risk. The risks that cannot be controlled by investors are known as systematic risk. Market risks are essentially systematic risk where as investor or firm related risks can be diversified. Systematic risks affect the companies across the system.

Risk Preferences: By default investors are risk averse, the difference among investors is only with respect to the relative risk averseness. However, based on the preferences for risk, investors can be classified into three categories as below:

Risk Neutral

Risk Averse

Risk Seeking

Risk of a Single Asset: Please refer Figure 1. Which stock – A or B – is more risky compared to the other? Do note that both the stocks have same average rate of return of 15%. The return distribution of Stock B is more flat than that of Stock A, i.e. the range of possibilities of returns is more compared to Stock A. From this figure one can conclude that Stock B is more risky than Stock A.

Consider the following Assets for which the returns under various conditions of economy are given.

Economy Prob. G-sec Stock 1 Stock 2 Stock 3 Stock 4

Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0%

Below average 0.20 8.0 -2.0 14.7 -10.0 1.0

Rate of  Return (%) 

Stock A

Stock B 

0 15 50‐20

Probability Distribution 

Figure 1 

Average 0.40 8.0 20.0 0.0 7.0 15.0

Above average 0.20 8.0 35.0 -10.0 45.0 29.0

Boom 0.10 8.0 50.0 -20.0 30.0 43.0

1.00

Expected Return 8.0% 17.4% 1.7% 13.8% 15.0%

The G-sec has same return irrespective of the economic outcome. This appears to be risk free.

Stock 1 moves along with the economy (positively correlated) whereas Stock 2 moves in opposite direction of the economy (negatively correlated).

Measuring Risk: the simplest measure of risk is range which is defined as the difference between the highest possible return and lowest possible return. In the above table, the range for Stock 1 is 72.0% whereas for Stock 2 it is 48%. However standard deviation is considered as one of the very well accepted measure of risk. Standard deviation is the square root of variance.

For Stock 1:

σ = ((-22 - 17.4)20.10 + (-2 - 17.4)20.20 + (20 - 17.4)20.40 + (35 - 17.4)20.20 + (50 - 17.4)20.10))1/2 = 20.0%.

Similarly for other investments, the standard deviation is given in the following table.

Investment G-Sec Stock 1 Stock 2 Stock 3 Stock 4

0% 20.0% 13.4% 18.8% 15.3%

Additional Readings:

Alexander, Gordon, J., Sharpe, William, F. and Bailey, Jeffery, V., “Fundamentals of Investment, 3rd Edition, Pearson Education.

Bodie, Z., Kane, A, Marcus,A.J., and Mohanty, P. “ Investments”, 6th Edition, Tata McGraw-Hill. Fisher D.E. and Jordan R.J., “Security Analysis and Portfolio Management”, 4th Edition., Prentice-

Hall. Jones, Charles, P., “Investment Analysis and Management”, 9th Edition, John Wiley and Sons. Prasanna, C., “Investment Analysis and Portfolio Management”, 3rd Edition, Tata McGraw-Hill. Reilly, Frank. and Brown, Keith, “Investment Analysis & Portfolio Management”, 7th Edition,

Thomson South-Western.

Additional Questions:

.

Variance

1

2

2

n

iii Prr

Q. 1: Suppose one has bought a share of PQR Limited at Rs.224 one year back. Over the last year PQR has distributed dividend of Rs.8 per share. If the share of PQR sells at Rs.250 today, what is the return? If the share is trading at Rs.220 today, what is the return earned?

Ans.: The total return is Rs.34 that comprises of Rs.8 of dividend and Rs.26 (Rs.250 – Rs.224) in terms of appreciation in the market price of the share. Hence the % return is Rs.34/Rs.224 i.e. 15.18%. if the share is trading at Rs.220, return earned is: 1.79%.

Q.2: Suppose an investment provides the following periodic return over last four years as below:

Year 1 2 3 4

Return (%) 10 12 -6 12

What is the holding period return?

Ans. Holding period return = (1.10 x 1.12 x 0.94 x 1.12)1/4 – 1 = 0.672 = 6.72%

Q.3: Consider the two assets A and B for which returns (%) under different conditions of economy are given as below. Find the expected return and risk (as measured by standard deviation of return) of each asset.

Returns

Condition of Economy

Prob. Stock A Stock B

Recession 0.10 -18.0 -10.0

Below avg. 0.20 -4.0 2.0

Average 0.40 12.0 8.0

Above avg. 0.20 24.0 12.0

Boom 0.10 30.0 18.0

1.00

Ans.:

Condition of Economy

Prob. Return Prob.*Return Prob.*(Return - Exp. Return)2

Stock A Stock B Stock A Stock B Stock A Stock B

Recession 0.1 18.00 14.00 1.80 1.40 13.92 6.08

Below avg. 0.2 (4.00) 2.00 (0.80) 0.40 41.47 15.49

Average 0.4 12.00 8.00 4.80 3.20 30.98 14.40

Above avg. 0.2 24.00 12.00 4.80 2.40 15.49 9.25

Boom 0.1 30.00 18.00 3.00 1.80 11.24 5.48

Exp. Return

(%):

13.6 9.2 Variance (%Square):

113.10 50.70

Standard Deviation

(%):

10.63 7.12

Q.4: What are the different sources of risk?

Ans.: The different types of risks are as below (not an exclusive list):

Business Risk

Financial Risk

Interest rate risk

Liquidity risk

Market risk

Event Risk

Exchange Rate Risk

Purchasing-power risk

Tax risk