risk & return

Risk & Return

Introduction

• Return is the motivating force for making an investment

• Risk is inherent to all investment decisions• For a financial manager, risk means:

“uncertainty in future cash flows”• Risk should be measured, and• Discount rate should be adjusted to measure returns• Understanding the risk-return relationship is very

important– helps in decision making

Return

• Enables comparison of alternative options of investment

• Measures past performance

• Helps in estimating future

• Two Types:– Historical or Realized return or Holding period

return– Expected return

Income receivedIncome received on an investment plus any change in market price change in market price (if being (if being

traded)traded), usually expressed as a percent of the beginning market pricebeginning market price (initial (initial

value) value) of the investment.

Income receivedIncome received on an investment plus any change in market price change in market price (if being (if being

traded)traded), usually expressed as a percent of the beginning market pricebeginning market price (initial (initial

value) value) of the investment.

DDtt + (PPtt - P - Pt-1t-1 )

PPt-1t-1

R =

Defining Return

Rate of Return of a Stock

• Returns from holding a stock – Dividend(s)– Capital Gain/ Loss

The stock price for Stock A was Rs. 1010 per share 1 year ago. The stock is currently trading

at Rs. 9.509.50 per share, and shareholders just received a Rs. 1 dividendRs. 1 dividend. What return was

earned over the past year?

The stock price for Stock A was Rs. 1010 per share 1 year ago. The stock is currently trading

at Rs. 9.509.50 per share, and shareholders just received a Rs. 1 dividendRs. 1 dividend. What return was

earned over the past year?

1.00 1.00 + (9.509.50 - 10.00 10.00 )10.0010.00RR = = 5%5%

Example

Return of a Bond/ Debenture

• Returns of holding a Bond/ Debenture– Interest (annually, semi-annually, quarterly,

etc.)– Change in the price (if being traded in a

market)

14% Rs. 1,000 IDBI debenture was purchased for Rs. 1050 and was sold when the price of the

security raised to Rs. 1080 at the end of one year. What return was earned over the past

year?

14% Rs. 1,000 IDBI debenture was purchased for Rs. 1050 and was sold when the price of the

security raised to Rs. 1080 at the end of one year. What return was earned over the past

year?

140 140 + (1,0801,080 – 1,0501,050)1,0501,050RR = = 16.2%16.2%

Example

Return: Single Asset

• Rate of return =Current yield + Capital gain/loss yield

• Current yield or Dividend yieldAnnual Income/ Beginning price

• Capital gain (loss) yield(End price – Beginning price) / Beginning

price

Illustration

Assume that IPCL was trading at Rs. 142 per share one year back. It declared a dividend of

60% and the price now is Rs. 176.

Compute the returns: current yield and capital gain yield on IPCL stocks.

Current yield: 4.23%

Capital gain yield: 23.94%

Expected Return

• Return in a future period

• Future is uncertain

• If possibilities of returns and their chance of occurrence can be defined i.e. probability of outcomes…

Expected Rate of Return

• It is the weighted average of all possible returns multiplied by their respective probabilities

R = expected returnRi = return for the i th possible outcomepi = probability associated with Rin = no. of possible outcome

R = pi Ri

n

i = 1

Illustration

Probability distribution of rate of return on stocks of Bharat Foods and Oriental shipping

State of Probability of Rate of Return (%)Economy Occurrence ABC XYZBoom 0.20 25 30Normal 0.50 15 8Recession 0.30 10 -5

ABC Ltd R = 15.5%XYZ Ltd R = 8.5%

What rate of return do you expect on your What rate of return do you expect on your investment (savings) this year?investment (savings) this year?

What rate will you actually earn?What rate will you actually earn?

Does it matter if it is a bank FD or equity share?Does it matter if it is a bank FD or equity share?

What rate of return do you expect on your What rate of return do you expect on your investment (savings) this year?investment (savings) this year?

What rate will you actually earn?What rate will you actually earn?

Does it matter if it is a bank FD or equity share?Does it matter if it is a bank FD or equity share?

The variability of returns from those The variability of returns from those that are expected.that are expected.

The possibility that actual outcome will differ The possibility that actual outcome will differ from expected outcomefrom expected outcome

The variability of returns from those The variability of returns from those that are expected.that are expected.

The possibility that actual outcome will differ The possibility that actual outcome will differ from expected outcomefrom expected outcome

Defining Risk

Sources of Risk

• Interest rate risk– Change in level of interest rates– Security prices move inversely to interest rates

• Market risk– Fluctuations in the securities market

• Inflation risk– Purchase power risk

Sources of Risk…

• Business Risk– Industry, Environment

• Financial Risk– Use of debt financing

• Liquidity Risk– Transaction of a asset/ conversion

Measures of Risk (Variability of Return)

• Range– Maximum & Minimum value

• Variance / Standard deviation (historical)

var = 2 = 1/n (Ri – R)2

= 2

• Variance (expected return)

2 = Pi (Ri – R)2

Illustration (historical)

Johnson & Nicholson has the following dividend per share (DIV) and market price per share (MP) for the period 2003-2008s

Year DIV MP2003 1.53 31.252004 1.53 20.75 2005 1.53 30.882006 2.00 67.002007 2.00 100.002008 3.00 154.00

What are the annual rate of returns for the last five years? How risky is the share?

Solution

• R04 = - 28.07%• R05 = 56.2%• R06 = 123.4%• R07 = 52.2%• R08 = 57%• Mean Return = 52.0% 2 = 2,330.63 = 48.28• The standard deviation of J&N’s share of returns is

quite high. • The share is very risky.

Stock Returns of CompaniesYear Bajaj Auto Ltd. Hero Honda Motors Ltd.Jul-08 18.86 17.95

Aug-08 13.13 5.94Sep-08 1.88 7.24Oct-08 -8.69 -14.5Nov-08 -39.71 5.5Dec-08 27.45 6.61Jan-09 21.14 8.92Feb-09 15.39 6.4Mar-09 15.96 15.5Apr-09 4.58 13.07May-09 60.74 13.23Jun-09 -3.36 4.25Jul-09 24.2 14.84

Aug-09 -0.75 -4.61Sep-09 22.94 10.47

Average 11.58 7.39Std. Deviation 21.87 8.24

Chart Showing Monthly Returns

Spot Prices of Castor Oil (10 Kgs)

Nov 2008 Oct 2009

Average Monthly Spot Prices of Castor Oil (10 Kgs)

Months Rs. November-08 632.16December-08 612.80January-09 492.43February-09 473.90March-09 472.12April-09 491.77May-09 503.00June-09 493.07July-09 504.68August-09 541.14September-09 566.11October-09 556.40

Average Monthly Spot Prices of Castor Oil (10 Kgs)Months Rs. Monthly ReturnsNovember-08 632.16December-08 612.80 -3.06%January-09 492.43 -19.64%February-09 473.90 -3.76%March-09 472.12 -0.38%April-09 491.77 4.16%May-09 503.00 2.28%June-09 493.07 -1.97%July-09 504.68 2.35%August-09 541.14 7.22%September-09 566.11 4.61%October-09 556.40 -1.72%

Avg. Returns -0.90%

Risk & Expected Rate of Return

Expected return: is the weighted average of all possible returns multiplied by their respective probabilities

R = expected returnRi = return for the i th possible outcomepi = probability associated with Rin = no. of possible outcome

R = pi Ri

n

i = 1

Variance

• Variance of an asset’s return is the sum of the squared deviations of each possible rate of return from the expected rate of return multiplied by their probabilities

• Variance (expected return)

2 = Pi (Ri – R)2

Illustration

• Probability distribution of rate of return on stocks of Bharat Foods and Oriental shipping

State of Probability of Rate of Return %Economy Occurrence Bharat Foods Oriental shipping

Boom 0.30 25 40Normal 0.50 20 10Recession0.20 15 -20

Bharat Foods R = 20.5%

Oriental Shipping R = 13.0%

Risk of Expected Returns

State of Economy

pi Ri pi Ri Ri – R (Ri – R)2 pi(Ri–R)2

Boom 0.30 25 7.5 4.5 20.24 6.075

Normal 0.50 20 10.0 -0.5 0.25 0.125

Recession 0.20 15 3.0 -5.5 30.25 6.050

R = pi Ri = 20.5 pi (Ri – R)2 = 12.25 = [ pi (Ri – R)2]1/2 = (12.25)1/2 = 3.5%

Expected returns of Bharat Foods’ Stock

Risk of Expected Returns

State of Economy

pi Ri pi Ri Ri – R (Ri – R)2 pi(Ri–R)2

Boom 0.30 40 12 27.0 729.0 218.7

Normal 0.50 10 5 -3.0 0.25 4.5

Recession 0.20 -20 -4 -33.0 1089.0 217.8

R = pi Ri = 31.0 pi (Ri – R)2 = 441.0 = [ pi (Ri – R)2]1/2 = (441.0)1/2 = 21.0%

Expected returns of Oriental Shipping’s Stock

Why Standard Deviation (σ)?

• Standard deviation is a measure of dispersion around the average (expected) value

• Standard deviation considers every possible event and assigns equal weight to its probabilities

• Easy to calculate, widely accepted

Certainty EquivalentCertainty Equivalent (CECE) is the amount of cash someone would require with

certainty at a point in time to make the individual indifferent between that

certain amount and an amount expected to be received with risk at the

same point in time.

Certainty EquivalentCertainty Equivalent (CECE) is the amount of cash someone would require with

certainty at a point in time to make the individual indifferent between that

certain amount and an amount expected to be received with risk at the

same point in time.

Risk Attitudes

Certainty equivalent > Expected valueRisk PreferenceRisk Preference

Certainty equivalent = Expected valueRisk IndifferenceRisk Indifference

Certainty equivalent < Expected valueRisk AversionRisk Aversion

Most individuals are Risk AverseRisk Averse.

Certainty equivalent > Expected valueRisk PreferenceRisk Preference

Certainty equivalent = Expected valueRisk IndifferenceRisk Indifference

Certainty equivalent < Expected valueRisk AversionRisk Aversion

Most individuals are Risk AverseRisk Averse.

Risk Attitudes

Portfolio

• A portfolio refers to a group of assets owned by an investor

• Assets in which an investor has made investments

• Why Portfolio?– 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 individual assets

– To reduce risk, investors hold a diversified portfolio (equity capital, bonds, real estate, FDs, Bulion, etc.)

RP = ( Wj )( Rj )

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,

m is the total number of assets in the portfolio.

RP = ( Wj )( Rj )

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,

m is the total number of assets in the portfolio.

m

j=1

Portfolio (Expected) Return

Portfolio Risk: Standard Deviation

• Standard deviation = variance

• Variance of the portfolio (2-security case)

P P

xxx x

yyy y xxyyxxyyCorCorxyxy

m

j=1

m

k=1PP = Wj Wk jk

Wj is the weight for the jth asset in the portfolio,

Wk is the weight for the kth asset in the portfolio,

jk is the covariance between returns for the jth and kth assets in the portfolio.

PP = Wj Wk jk

Wj is the weight for the jth asset in the portfolio,

Wk is the weight for the kth asset in the portfolio,

jk is the covariance between returns for the jth and kth assets in the portfolio.

Portfolio Risk: Standard Deviation

jk = j k rrjk

j is the standard deviation of the jth asset in the

portfolio,

k is the standard deviation of the kth asset in the

portfolio,

rjk is the correlation coefficient between the jth and kth assets in the portfolio.

jk = j k rrjk

j is the standard deviation of the jth asset in the

portfolio,

k is the standard deviation of the kth asset in the

portfolio,

rjk is the correlation coefficient between the jth and kth assets in the portfolio.

What is Covariance?

Portfolio Risk: Classification

Systematic (non-diversifiable)

• Market Risk• Inflation risk• Interest rate risk

Non-Systematic (diversifiable)

• Business Risk• Financial Risk

TotalTotalRiskRisk

Unsystematic riskUnsystematic risk

Systematic riskSystematic risk

ST

D D

EV

OF

PO

RT

FO

LIO

RE

TU

RN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors such as changes in nation’s economy, tax reform, Inflationor a change in the world situation.

Total Risk = Systematic Risk + Unsystematic Risk

TotalTotalRiskRisk

Unsystematic risk or DiversifiableUnsystematic risk or Diversifiable

Systematic risk or Non-Diversifiable Systematic risk or Non-Diversifiable

ST

D D

EV

OF

PO

RT

FO

LIO

RE

TU

RN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors unique to a particular companyor industry. For example, the death of akey executive or loss of a govt. contract.

Total Risk = Systematic Risk + Unsystematic Risk

CAPM is a model that describes the relationship between risk and expected

(required) return; in this model, a security’s expected (required) return is the risk-free rate risk-free rate plus a premium a premium based on the systematic risksystematic risk

of the security.

CAPM is a model that describes the relationship between risk and expected

(required) return; in this model, a security’s expected (required) return is the risk-free rate risk-free rate plus a premium a premium based on the systematic risksystematic risk

of the security.

Capital Asset Pricing Model (CAPM)

CAPM: Expected Return

• The expected rate of return of a security: Expected return = Risk-free rate + Risk premium

Risk premium =(Mkt return – Risk-free rate) x Beta

Ri = Rf + (Rm – Rf) βi

βi = COVim / 2m

Ri = i + βiRm + I (Characteristic Regression

Line)

1. Capital markets are efficient.

2. Homogeneous investor expectations over a given period.

3. Risk-freeRisk-free asset return is certain (use short- to intermediate-term

Treasuries as a proxy).

4. Market portfolio contains only systematic risksystematic risk (use SENSEX or similar as

a proxy).

1. Capital markets are efficient.

2. Homogeneous investor expectations over a given period.

3. Risk-freeRisk-free asset return is certain (use short- to intermediate-term

Treasuries as a proxy).

4. Market portfolio contains only systematic risksystematic risk (use SENSEX or similar as

a proxy).

CAPM Assumptions

An index of systematic risksystematic risk.

It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio.

The betabeta for a portfolio is simply a weighted average of the individual stock betas in the portfolio.

An index of systematic risksystematic risk.

It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio.

The betabeta for a portfolio is simply a weighted average of the individual stock betas in the portfolio.

What is Beta?

Beta Calculation

Beta =N XY – ( X) (Y)

N X2 – (X)2

WhereX = return of marketY = return of stock