risk & return measurements for investment decisions

2009

INTERNATIONAL INSTITUTE OF PLANNING AND MANAGEMENTAHMEDABAD

RISK AND RETURNMEASUREMENT

FORINVESTMENT DECISIONS

Submitted To : Prof. Paresh Shah(Applied Finance)

Submitted By : Siddharth Sinha(PGP/FW/07-09/Fin)

Risk And Return Measurement For Investment Decisions

Submitted To: Prof. (Dr.) Paresh Shah (Applied Finance) Submitted By: Siddharth Sinha (PGP/FW/07-09/Fin)

ACKNOWLEDGEMENT

While presenting this report, I heartily thank and express my deep

gratitude to those who have helped me and given me valuable knowledge

in knowing all the concepts and making my project to immense heights. I

thank those people who have provided there assistance & shown their

enthusiasm & interest. Without them this project would not have been a

success.

First of all I am extremely grateful and thankful to THE

INTERNATIONAL INSTITUTE OF PLANNING AND

MANAGEMENT, AHMEDABAD for instilling in me new and lively

subjects along with a new experience which are practically observed in

the industry.



Special thanks and sincere regards to:

Prof. (Dr.) Paresh Shah, for guiding me during times of need and giving

me opportunity to work on this valued project in which, I got a chance

to use all my classroom theories and practices that he had taught me, for

understanding and analyzing the working & operations of the real world

market scenario of “RISK AND RETURN MEASUREMENT FOR

INVESTMENT DECISIONS”.



PREFACE

Risk analysis and prediction now goes

far beyond that of the 1950s when

Harry Markowitz formalized the

concept of portfolio risk and the

1960s, when William F. Sharpe did

his initial work. Since then there has

been huge progress in risk

measurement and forecasting.

However, it remains an imperfect art.

Prior to the 1950s and 1960s most

people hardly talked about risk, and

few even tried to estimate it. The

focus on risk as well as return came in

large part from the work that was

done in the 1950s and the 1960s. It

continued with options pricing theory

in the 1970s and has been a fruitful

line of research and practice ever

since. The key steps were the

recognition that there is risk and that

one should try to estimate it as best

one can. But as we have learned, it is

not an easy task.

At a fundamental level, when

one is concerned with a return over a

specific future period, say a year, one

needs to think about a probably

distribution. When the year is over he

seeks one point from that distribution

— the return that actually resulted.

Unhappily, it is very difficult to say

ex-post whether the probability

distribution that he estimated a year

earlier was a good estimate or not.

There are of course extreme cases. If

the realized return was not even in the

forecasted distribution, the forecast

was clearly inadequate. In effect, one

assigned a probability of zero that the

return in question could happen and it

happened so the true probability must

have been greater than zero. That

would be a clear case in which his

estimate was wanting. But as long as

an outcome is somewhere in the range

that he thought might happen, even

though he may have assigned a tiny

probability to it, no one can prove that

the estimate of the probability

distribution was wrong.



INDEX

Sr. No Topic Page No1 Acknowledgment 22 Preface 43 Executive Summary 64 Introduction 95 Larry’s Riskless Stock Strategy 136 Core of the Story 147 Story Continued 168 Measurement of Earning Stability 269 Risk Diversification 2810 Stable Businesses with No Competition 3011 Discounted Cash Flow Valuation 3212 Risk Hedging 3513 Combining a Hedge Fund with Equities 3914 The Payoff To Risk Management 4315 Risk and Return Portfolio Analysis 4416 Conclusion 5117 Key Terms: Definitions 5318 References 5919 Annexure: Synopsis 60



EXECUTIVE SUMMARY

Risk, in some of the conversations, is

defined quite simply as the standard

deviation of returns. In other words,

risk captures the variability of returns.

There are a lot of little quibbles that

one can have with this definition, but

it does in fact do a very good job of

reflecting the essential characteristics

of what market risk is.

In "big picture" terms, the

market risk of which I speak here is

risk due to movements in market

prices. Other classes of risk, such as

operational risks or sovereign risk are

not captured by this framework.

To provide a small illustration

of what it means to say, that a

portfolio has a risk of ‘X%’, this

means that the standard deviation of

returns for the portfolio is ‘X%.’

Standard deviations on the normal

curve follow the old principle 65-95-

99. In other words, 65% of outcomes

will be within one standard deviation

of the mean, 95% will be within two

standard deviations, and 99% will be

within three standard deviations.

So, for a portfolio whose mean

expected return is 10%, with risk of

8% (these numbers are all annualized

by convention); there is a 65% chance

that the return over the next year will

be between 2% and 18%.

All sorts of subtle elaborations

are possible, but the basic idea of

market risk is very simple, and

(usefully) very amenable to

calculations using standard statistical

methods.

Now, when we have

understood what risk means; let’s

move on to risk diversification:

Diversification is the one tool,

freely available to everybody, that

enables investors to reduce the risk of

their portfolio. A wise portfolio

manager will consider portfolio-wide

needs when deciding how to construct

a portfolio. Portfolio construction

should not just be the accidental



coming-together of securities that

seem attractive to hold; rather, one

should give careful consideration to

the impact of each security on the

overall portfolio characteristics.

The next section, for example,

shows why it can still be worthwhile

to add a security to a portfolio when

the security has higher risk (and equal

expected return).

After having the above

knowledge we are in a position to

make the following comment.

Risk is an axiom of financial

economics that a rational investor will

seek to minimize the risk of their

portfolio, and to maximize their

return. Indeed, to explain this axiom

more explicitly, there are two

principles that financial economics

assumes about rational investors:

If two possible portfolios have

the same expected risk but different

returns, the rational investor will

prefer the portfolio with a higher

return.

If two possible portfolios have

the same expected return but different

expected risk levels, the rational

investor will prefer the portfolio with

the lower expected risk level.

These two statements say a lot

about the risk/return preferences of

rational investors. However, they

certainly don't mean that all rational

investors have the same risk/return

preferences! Different investors have

different risk/return preferences.

Nevertheless, the principles of return

maximization and risk minimization

make it possible to make a lot of

generalizations about how to

construct investment portfolios.

An interesting practical aspect

of this, which the traditional financial

economics textbooks tend not to

mention very much, is the question of

how many actual investors conform to

these assumptions about what it takes

to make someone a rational investor.

Psychological evidence, such as

Kahneman and Tversky's prospect

theory, and Richard Thaler's concept



of mental accounting shows not just

that there are limits to human

rationality, but that there are

systematic ways in which people are

irrational in their decision making.

Having said, that, it is undoubtedly

useful to explore issues of risk and

return from the standpoint that of the

hypothetical "rational investor".



INTRODUCTION

Risk is a topic that is much abused in

financial modeling and a proper

exploration is required. However, we

do encounter the basic ideas of the

risk analysis in any sort of modeling,

and we should be able to understand

why risk modeling is not as

straightforward as it seem. When

carrying out sensitivity analysis, the

presumption is that each of the values

in the data table is equally likely.

Using professional judgment and

experience one would of course

recognize that this is not the case, and

that within the population of values

used in the table some are indeed

more likely than others. When we

start assigning probabilities to these

values we are starting to think about

risk. The exact definitions vary, but a

risk implies that all outcomes can be

predicted and that we can predict the

likelihood of one outcome over

another. If a risk factor has a value of

zero then it will never happen, and a

factor with a value of 1 is guaranteed

to happen. When assigning risk to a

set of values, for example in a data

table, the total of the probabilities

must equal 1. If it is less than 1, than

there is an outcome which has not

been predicted, and this leads to the

concept of uncertainty.

Where do we obtain the

information from which to derive

our probabilities? With operational

factors we may be able to draw on

significance previous experience, for

example, that we incur a 3% wastage

rate in the manufacture in the type of

biscuit, but with financial factors this

becomes much less precise – what

exactly is the interest rate? The risk

modeler refers to objective and

subjective probability – the former is

based on past experience, the latter on

expert opinion. We can improve the

wastage rate at the biscuit factory if

the food scientists apply their

knowledge of the interaction of flour,



water, fat, sugar, and heat to the

manufacturing process – the results

will be measurable and reproducible.

But what about the interest rates? In

the UK advertising for personal

financial products always carries a

strap line to the effect that

‘investments may go down in value,

as well as up’. What will the interest

rate be next month? Next year? In 10

years?

Another point is that certain

sets of figures do not show the

features of random variation and

therefore are not subject to any

chance or probability. Staying with

the biscuit factory for a moment, the

production capacity does not fluctuate

in itself. Capacity is a variable in that

we can increase or decrease

production levels, but we would not

claim that there is 10% chance of

production exceeding 1000

boxes/day. It is the management who

make this decision. Although the

production capacity is deterministic,

the appetite or demand for my biscuit

is highly variable and in consultation

with marketing colleagues we may be

able to assign probabilities to the level

of demand for the product over a

particular forecast period.

When looking at carrying out

any form of risk analysis careful

thoughts needs to be given to

relationships: if we are going to run a

sensitivity or other analysis on a

factor, are there any related factors

which would be affected? The class is

example is the relationship of interest

rates and inflation, and we have seen

models in which one has been tested

independently of the other. Similarly,

does inflation have an equal effect on

revenues and on costs? Before

carrying out any such analysis we

must make sure that the correlations

and the dependencies of the elements

of the model are fully understood if

the results are to have any value.

Monte Carlo Simulation

For some analysts, Monte Carlo

simulation is the acme of the



modeling process. We use third-party

software to perform this analysis, the

two leading products being @RISK

from palisade, and Crystal Ball from

Decisioneering. The analysis requires

the modeler to define each input in

terms of a statistical population and

there are many populations to choose

from. When the simulation is run, the

software generates a random number

from within the population, enters

into the input cell, recalculates the

model, and stores the fled. In this way

the model can simulates the millions

of permutations that can result from

the interaction of the selected inputs.

In my opinion this is fine for scientific

and engineering purposes, but of little

use for financial modeling. In simple

terms, the financial variables we use

in our modeling do not fit into the

population distributions used by the

software. Although they may have a

stochastic appearance, with

randomness of sorts, the only

meaningful constraints that can be

applied relate to the triangular

distribution of lowest value-most

likely value-highest value.

Unfortunately, the very ease with the

software allows the modelers to set up

the Monte Carlo simulation, leads us

into problems.

Most people have had little

exposure to statistics other than at

college or at university, and most such

courses are based around the statistics

of the normal distribution.

From this we learn expression such

as:

Arithmetic mean: The sum of all

observations in a sample, divided by

the number of observations in the

sample.

Mode: The most frequent, or

common, value in sample.

Median: The middle value of the

sample.

Standard Deviation is used to

describe the spread of the numbers in

the sample about the mean. One

standard deviation of each side of the

mean will include 68% of the sample,



two standard deviations covers 95%,

and three standard deviations cover

98% of the sample.

The moment we consider a

different population we realize that

these terms no longer have the same

meaning and must be used with much

more care.

But when looking at models

using the Monte Carlo technique we

often find a casual disregard for what

is very specific terminology and

indeed we often find that the analyst

has chosen the wrong population

distribution, failed to identify the

correlating factors, or has assigned a

distribution to what should be a

deterministic element. Quite often we

note that Monte Carlo analysis has

been before simply because the

software was available, and the

analyst thought that it would add

value to the model. There are indeed

certain kinds of model in which

specialist risk techniques are required,

and risk modeling is a specialism in

itself, but our general

recommendation is for the general

modeler to be aware of the techniques

but to use them with caution.



LARRY’S RISKLESS STOCK STRATEGY

Larry had always wanted to invest in

stocks to invest in stocks but has

considered them too risky. Having

thought long and hard about why

stocks were risk, he concluded that

the culprit was volatility in earnings.

He was convinced that he could

construct a portfolio without risk.

Without much effort, Larry was able

to identify the companies that had

reported the most stable earnings over

the previous five years in each sector,

and he put his money in the stocks.

Even as he bought the stocks,

he found that many of them were

pricey; trading at high multiples of

earnings, suggesting that other

investors had come to the same

conclusion as Larry about the low risk

and high quality of these stocks.

Having bought the stocks, he also

noticed that stock prices were volatile

at some of these companies, even

though their earnings were stable.

One of the stocks in Larry’s portfolio

was a gold mining stock, and when

gold prices jumped because of a crisis

in the Middle East; Larry noticed that

the company did not report higher

earnings, even though other gold

mining companies did. When he

confronted management about this,

they admitted they used gold future

contracts to hedge the risk. While

these contracts reduced their exposure

to downside risk, it also reduced their

upside profits. When Larry assessed

the end results of his portfolio, he

found that he had still been exposed to

risk and had relatively little to show

for it. Larry’s search for a free lunch

had come to an end.

Moral: “No Downside – No Upside”



CORE OF THE STORY

Equities are riskier than bonds

because equity earning represents

what is left over after everyone else

has been paid and thus are volatile.

The stock in a firm should become

more safe and potentially a better

investment. As the argument goes, if

you can make returns on stocks in

these companies that are comparable

to what you would make on stocks in

these companies that are comparable

to what you would make on stocks in

more firms with more volatile

earnings, you could argue that you are

getting the best of both worlds – high

returns and low risk. There are three

elements to this story.

Stocks with stable earnings are

less risky than socks with volatile

earnings.

For this story to work, one has to

accept the idea that volatility in

equity earnings is a good measure

of equity risk. Luckily for those

who use this story, that is not a

difficult sell. The alternative

measures of risk used in finance,

such as stock price volatility or

betas, are all market – based

measures. To those investors who

do not trust markets – they feel

that markets are subject to mood

swings and speculation, for

instance – earnings stability or lack

thereof seems to provide a more

dependable measure of equity risk.

Stocks with more stable earnings

generate less volatile returns for

stockholders. According to this

argument, firms with stable

earnings are less likely to roil

markets with earnings

announcements that surprise

investors. The resulting price

stability should make returns on

these stocks more predictable than

returns on the rest of the market,

especially if the firm takes



advantage of its more stable

earnings to pay larger dividends

every period.

Stocks with more stable earnings

to be underpriced by market.

This is perhaps the toughest portion

of the argument to sustain. One

reason given is that companies with

stable earnings are often boring

companies that do not make the

news and investors in search of fads

and stars are not interested in them.

As, a result stable earnings

companies will be underpriced

relative to companies with more

volatile histories.



STORY CONTINUED

Investing is full of stories that sound

good when they are told but don’t

hold up under close serenity. Consider

a few: Buy stock in good companies

and the returns will surely follow.

Buy after bad news. Buy after good

news. Stocks always win in the long

term. Follow the insiders. Buy stocks

with big dividends. Buy stocks that

have gone down the most. Go with

stocks that have gone up the most.

What makes these stories alluring is

that there is a kernel of truth to each

one of these stories but none of them

is foolproof. You will examine these

and other investment sales pitches in

this book, consider the potential

downside with each, and study how

you might be able to modify each one

to reduce downside risk.

The Power of the Story

Human beings are much more likely

to be swayed by good stories than

they are by graphs and numbers. The

most effective sales pitches to

investors tell a compelling story,

backed up by anecdotal evidence. But

what makes a story compelling in the

first place? Investment stories are

convincing not only because they are

told well but also because they draw

on several common factors:

Most good investment stories

appeal to a fundamental

component of human nature,

whether it is greed, hope, fear or

envy. In fact, what often sets apart

successful investment salespeople

from unsuccessful ones is their

uncanny ability to gauge an

investor’s weak spots and create a

story to take advantage of them.

Good investment stories are also

backed up by the evidence, at least

as presented by the storyteller. As

you will see in this book, though,

the evidence may only tell part of

the story and much of what is

presented as incontrovertible proof



of the efficacy of an investment

strategy falls apart on closer

examination.

In each chapter that follows, you will

see the rationale that allows the

stories presented in this book to

resonate with investors. As you read

these sections, you will undoubtedly

remember variants of these stories

told by your broker, investment

advisor or neighbor.

Categorizing Investment Stories

Investment stories come in all forms.

Some are designed to appeal to

investors who do not like to take

risks, and they generally talk about

low-risk ways to play the stock

market, others are oriented toward

risk seekers who want to get rick

quickly; these stories emphasize the

potential upside and hardly ever talk

about risk. Still others are structured

for those who believe that you can get

something for nothing if you are

smarter or better prepared than others

in the market. Finally, there are

stories for the optimists who believe

that you always win in the long term.

Stories for the Risk Averse

Some investors are born risk averse,

whereas, others become risk averse

because of circumstances-an insecure

job or impending retirement can make

you far more concerned about losing

money. Still others are scared into risk

aversion by an extended bear market.

Whatever is the reason for the risk

aversion, the investment stories that

sell the bet to these investors

emphasize low-risk strategies while

promising much higher returns than

they are making currently on their

safe investments?

High Dividend Stocks:

Risk adverse investors generally

prefer the safety of government or

high-grade corporate bonds to the

riskiness of stocks. They feel more

secure with bonds, knowing that

they can count on these bonds



delivering income in the form of

coupons while they hold them and

that the principal invested in these

bonds is intact. To attract these

investors to stocks, you have to try

to offer them comparable income

and safety, while also providing

them a premium for taking the

additional risk. Stocks that pay

high dividends are attractive to

risk-averse investors because they

resemble bonds in terms of

generating income, with the added

bonus of price appreciation. The

dividends on some stocks are

higher than the coupons earned on

safe bonds, and while the principal

invested in stocks is not protected

in the same way that the principal

invested in bonds is, the risk can

be alleviated if the company

paying the dividend is large and

has substantial assets.

Stocks with Low Price-Earning

Ratios:

Stocks that trade at low multiples

of earnings have historically been

viewed as both cheap and as safe

equity investments. While you can

see why a stock that trades at 5

times earnings is considered cheap,

why would it be classified as safe?

The presumption is that the firm

will continue to make these

earnings in the long term and that

this earnings power should provide

a floor on the price. In fact, value

investors like Ben Graham have

long argued that buying stocks

with low PE ratio is a low-risk,

high-return strategy. For investors

who are concerned about the risk

in equities, this seems to offer a

low-risks way of entering the stock

market.

Stock That Trade at Less Than

Book Value:

A close relative of the low PE

stock in the cheap stock family is

the stock that trades at below book

value. To some investors, the book

value of a stock is not only the

accountant’s measure of how

much the equity in a firm is worth



but is also a more reliable measure

of a stock’s worth than the market

price, which is set by investors

swayed by fads and fancies. Thus,

a stock that trades at less than book

value is viewed as an undervalued

stock. To some risk-averse

investors, who believe that book

value is equivalent to liquidation

value, stocks that trade a below

book value also come with what

they see as backup insurance. If

the stock price does not go up, the

firm should be ableto liquidate its

assets and deliver the (higher)

book value.

Stable Earnings Companies:

For many investors, the risk of

investing in the equity of company

is tied to uncertainty about the

company’s capacity to earn money

in the future. Even the best-run

companies can have earnings that

are volatile and unpredictable.

Consequently, if you could invest

in a company that has stable and

predictable earnings, you could

invest in a company that has stable

and predictable earnings, you

could essentially combine the

benefits of stock ownership with

the reliability of bonds. How

would a company achieve this

earnings stability? It could do so

by diversifying into multiple

businesses or countries and

becoming a conglomerate or

multinational; bad times in one

business or country would then be

offset by good times in another,

leading to more stable earnings

over time. It could draw on a

variety of products now available

in financial markets-futures,

options and other derivatives- to

protect itself against interest rate,

currency or commodity price risk

and thus make its earnings more

predictable. In its least benign

form, the earnings stability can be

purely cosmetic, created by

accounting ploys and sleight of

hand.



Stories for the Risk Seekers

In buoyant markets, investors often

seek out risk, hoping to make high

returns to compensate. Not

surprisingly, they are not interested in

stocks that look like bonds. Instead,

they want to find companies that

provide the best upside potential even

though they might be risky. The

investment stories that work best for

them are the ones that emphasize risk,

but present them as a chance to make

a killing (upside risk) rather than as a

danger (downside risk).

Great Companies:

Buy good companies, you are told,

and the returns will follow. While

the definition of good can vary

from investors and from

investment publication to

publication, most definitions of

good companies revolve around

financial yardsticks. Companies

that earn high accounting rates of

return and have done well for their

stockholder in the past usually

qualify. In recent years, a new

category has been created with

good defined more broadly to

ignition would be one that does

well for its stockholders,

employees, customers and society

at the same time. The rationale for

investing in these companies is

that the superior management of

these companies will find ways to

turn threats into opportunities,

leading to dual benefits-higher

returns and lower risks.

Growth Stocks.

If you put your money into the

companies with the highest

earnings growth in the market, you

are playing the segment of the

market that is most likely to have

an exponential payoff (or

meltdown). While growth stocks

do not offer much in terms of

dividends, usually trade at high

multiples of earnings, and usually

risk, risk-seeking investors are not

fazed by any of these concerns.

They buy stocks for that the high



earnings multiples will only

translate into even higher prices as

the earnings grow over time. To

the skeptic’s question of what

happens if the growth does not

manifest itself, these investors will

respond that they have the skill to

pick the right companies-

companies that have found the key

to sustainable, long term growth.

Loser Stocks:

Stocks that have fallen

dramatically in the recent past

offer interesting opportunities for

investors who are willing to take

risk. While these companies

generally have serious problem-

some have incompetents

management, others have too

much debt and still others have

made strategic missteps-the

argument used to justify investing

in them is that they have fallen so

much that they cannot fall much

more. Risk-seeking investors, who

believe that markets have

overreacted to bad news and

pushed prices down too far, buy

these stocks hoping that stock

prices bounce back.

Hidden Bargains:

To the bargain hunters, the best

stocks to buy are the ones that few

other investors are aware of. In a

market like the United States, in

which thousands of professional

money managers and analysts

track stocks, this may seem like a

tall order, but there are thousands

of stocks in smaller companies that

are neither tracked by analysts nor

held by institutions. The ranks of

these ignored stocks are swelled

each year by initial public

offerings that buying new firms

into the marketplace. The hope of

finding the next great growth

company like Microsoft or Cisco -

before anyone else does drive

many risk-seeking investors to

forage through these smaller, less

followed segments of the market,

looking for young and promising

companies. In fact, some investors



with more funds at their disposal

try to get in even earlier in the

process by being venture

capitalists and private equity

investors in small, private

businesses.

Stories for the Greedy

In any listing of human vices, greed

usually finds itself somewhere near

the top. Philosophers and priests have

inveighed against greed through the

ages, but it is also the fuel that drives

financial markets. The demand for

stocks would be limited in a world

where investors were not greedy for

higher returns. Not surprisingly, those

selling investment stories have also

recognized that even a subtle appeal

to the greed of investors is sufficient

to get them interested. The investment

stories that play to greed share a

common theme: they allow you to

believe that you can get something for

nothing.

Get on the Fast Track:

Growth companies can be good

investments in the long term, but it

usually takes a long times for a

small firm to grow into a big one.

For impatient investors who want

their payoff now, the wait can

seem endless. Some firms

accelerate the growth process by

acquiring other companies in their

own and in other businesses. By

paying for these acquisitions with

new stock issues, these firms can

speed the process even further.

Investors are attracted to these

companies for two reasons: the

first is that they are usually the

newsmakers in any market;

acquisitions accounting often make

these firms look much better then

their peer group; in fact, with the

right accounting treatment the

growth can be made to look close

to costless. Investors play both

sides of the acquisition game, with

some buying acquisitive

companies, hoping to ride their



growth to high payoffs, and others

trying to invest in potential target

companies, hoping to gain a share

of the premium paid on the

acquisition

No Money Down, No Risk, Big

Profits:

Every investor dreams of finding

the investment equivalent of a free

lunch: an investment with no risk

and high returns (at least relative

to what you could have earned on

a bona fide riskless investment like

a government bond). For these

“arbitrage” opportunities to exist,

you have to find two identical

investments that are priced

differently at the same time by

markets and a guarantee that the

prices will converge over time.

Not surprisingly these pure

arbitrage opportunities are rare and

are most likely to exist in futures

and options markets. Even in those

markets, they are accessible only

to a few investors with low

transactions costs and superior

execution capabilities. Since there

is no guarantee of price

convergence these investments

will remain risky even to the most

sophisticated investors and become

even riskier when a significant

portion of the investment comes

from borrowing.

Go with the Flow: Momentum

Strategies:

To some investors, a low-risk and

high-return strategy is to buy

stocks that are going up and to go

along the ride. Implicit in this

strategy is the assumption that

there is significant momentum in

stock prices: stocks that go up will

continue to go up and stocks that

go down will continue to go down.

Chartists and technical analysts

have used chart patterns-trend

lines, support lines and resistance

lines, to name but three-for

decades to both decipher the trend

and, just as importantly, to get

advance notice of shift in the

trend. After all, the momentum



that brought you profits can very

quickly turn against you. In recent

years, momentum investors have

also expand their analysis to

include trading volume. A stock

that surges on high trading volume

has both price and volume

momentum and is considered a

better investment than one that

goes up on low trading volume.

Stories for the Hopeful

No matter how poor their past

investment choices have been, some

investors seem all too willing to

forget the past and to try yet again to

find a way of beating the average

investors. For some, the hope for

success rests on finding and following

the right investment experts, investing

in the stocks they pick. For others, the

hope comes from an almost religious

belief that stocks always win in the

long term and that all you need to

succeed is patience.

Just Follow the Experts:

There is no shortage of experts,

self-anointed or otherwise, in

financial markets. There are equity

research analysts, touting their

superior access to information and

management, making

recommendations on which stocks

to buy and sell. You have insiders

at firms, from chief executive

officers to board members, acting

as cheerleaders in public but

telling us far more about what they

really think about their companies

when they buy and sell stock in

them. There are investment

newsletters and advisory services,

too many to keep track of, each

claiming to have found the secret

formula for great stock picking.

For some investors, who are

confused by the cacophony of

contradictory views on markets

and the volume of news about

stocks, these experts offer

welcome solace by taking on the



responsibility of picking the right

stocks?

Stocks Always Win in the Long

Term:

It has almost become conventional

wisdom in the United States that

the stock market may have a bad

year or even a string of bad years

but that stocks always win in the

long term. Take any 10-year

period in market history, you will

be told, and stocks have done

better than government bonds or

bills. If you buy into this reasoning

and you have a long time horizon,

you would put all of your money

in stocks since they will earn more

for you than less risky alternatives

over long periods. Of course, you

can augment your returns if you

can invest in stocks only in the

good years and avoid them in the

bad years. There are dozen of

indicators, from the winner of the

Super Bowl to the level of interest

rates, that claim to tell you when to

get into stocks and when to get

out. The payoff to timing markets

correctly is so large that everyone

who invests in the stock markets,

individual or institution, tries to do

it at one time or another.



MEASUREMENT OF EARNINGS STABILITY

When it is about measurement of the

stability or volatility of earnings, there

are three broader choices in front of a

person; they are as per the mentioned

below:

The first and perhaps the most

direct measure is to look at the

variability in earnings over time.

At one extreme, one would have

stocks that deliver the same dollar

earnings year after year and thus

exhibit no volatility in earnings. At

the other, one would have

companies, whose earnings

fluctuate wildly from huge profits

to large losses, creating high

variance in earnings. The problem

with this measure is that the

variability in dollar earnings will

be greater for companies with

higher dollar earnings and lower

for companies with smaller dollar

earnings.

To alleviate the bias created when

one work with dollar earnings, he

could look at the percentage

changes in earnings from period to

period and look for companies that

exhibit low variance of these

changes. By doing this, one is

shifting away from stable earnings

to stable growth rates in earnings.

While this measure has statistical

appeal, it has a significant problem

that it shares with the first

measure. It treats increases in

earnings and decreases in earnings

equivalently when it comes to

measuring risk. Generally,

investors do not consider increase

in earnings as risky; it is declines

in earnings that worry them.

The third measure of earnings

stability focuses only on earnings

decreases. A firm that reports

higher earnings each year, relative

to earnings in the prior year, year

after year, would be viewed as safe



firm. On the other hand, firms that

report increases in others would be

viewed as risky. In fact, one could

construct a measure of variance in

earnings that looks at only earning

decreases.

Once one has chosen ones measure of

earnings stability, one has to decide

on the earnings number that one will

focus on. Here, one has several

choices. One can estimate the

variance in operating income, which

is before interest expenses and non-

operating items. While there are

obvious benefits to this, it can be a

misleading measure of earnings

variability if one is considering the

risk associated with buying stock and

the firm has substantial debt. When it

comes to income to equity investors,

you can look at net income, which is

the aggregate income left over for

equity investors, or you can examine

earnings per share, which adjusts for

changes in the number of shares

outstanding. The advantage of the

latter is that it allows you to separate

firms that grow their net income by

issuing new shares and investing

those funds from those that grow

earnings by earnings by reinvesting

internal funds. Other things remaining

equal, the latter should be more

valuable than the former.



RISK DIVERSIFICATION

Investors have always been told that

putting your eggs in one basket (or all

the money in one stock) is a

dangerous thing to do. In fact, the

argument for diversification is at the

core of the modern portfolio theory.

As Novel prize winner, Harry

Markowtiz, noted in his path-breaking

paper portfolio risk, if stocks do not

move in tandem (and they do not), a

portfolio’s risk can be lower than the

risk of the individual stocks that go

into it.

If a person is a diversified investor, he

is concerned primarily about the value

of his portfolio and the variance in its

value. Consequently, he measures the

risk of an investment by looking at

how it will change the overall risk of

his portfolio. In fact, most risk and

return models in finance are built on

the premise that the investors who set

prices by trading in large quantities

are diversified and that only the risk

added on by a stock to a diversified

portfolio (called non-diversifiable or

market risk) is rewarded by the

market. What does this have to do

with earnings stability and its payoff

(or lack thereof)? One could construct

a portfolio of 50 firms, each of whose

earnings are volatile. If the earnings

volatility in these firms comes from

factors that are specific to their

operations or management, it is

entirely possible that the composite

earnings to the portfolio will be

stable. If this is the case, one as an

investor would not discount the value

of an individual firm just because the

firm’s earnings are volatile. Nor

would one pay a premium for a firm

just because its earnings are stable.

So, when will more stable

earnings generate higher value for a

firm? This first scenario is one in

which the earnings stability translate

into lower market risk; in other words,

the earnings of the firm serve to

stabilize the composite earnings of the



portfolio. The second scenario is one

in which investors are not well

diversified and assess the risk of firms

as standalone investment s rather than

as a part of a portfolio.

Global Diversification

An alternative to business

diversification (which creates

conglomerates) is geographical

diversification. By having operations

in multiple countries, a firm may be

able to offset a decline in business in

one country with an increase in

another. The net effect should be a

reduction in the variability of

operating earnings. There is, though,

at least one confounding factor at

work here that does not apply to

business diversification. As your

operations spread out over different

countries, your earnings will be

exposed to foreign currency risk; a

US company will find its earnings

affected by the strengthening or

weakening of USD. One can,

however, partially protect your

earnings from this risk by using

futures and options contracts.

Again, there are two basic questions

that one needs to address in the

context of global diversification…

The first is ‘whether such

diversification results in more stable

earnings’ and the second is ‘whether

investing in globally diversified

companies generates higher or lower

returns’. An examination on Swedish

firms that diversify globally

concluded that geographical

diversification does increase value,

unlike industrial diversification. This

is consistent with the findings of

another study in the US. The effect is

small, though, and investing in a firm

that is already globally diversified

yields little in terms of excess returns.

One would need to invest in

companies just before they embark on

global diversification to gain any

potential benefits.



STABLE BUSINESSES WITH NO COMPETITION

For several decades, utility stocks

(phone, water and power companies)

were prized by risk-adverse investors

for their steady earnings and high

dividends. In fact, these firms could

pay the high dividends that they did

because their earnings were so

predictable. The reasons for the stable

earnings were not difficult to uncover.

These stocks were regulated

monopolies that provided basic and

necessary services. The fact that their

products and services were

nondiscretionary insulated them from

overall economic conditions, and the

absence of competition gave them

secure revenues. In return for the

absence of competition, these firms

gave up pricing power to the

regulatory authorities.

The key question for investors,

though, is not whether utility stocks

have more stable earnings than other

companies, but whether such stable

earnings translate into higher stock

returns. A simple way of examining

this question is to compare the returns

earned by utility stocks to returns

earned on overall market. The figure

below makes this comparison.

The average annual returns on

utility stocks are lower than the

average annual returns on the overall

market, but this comparison may not

be fair to utility stocks. After all, they

are less risky than the rest of the

market, and the returns they earn

should be adjusted to the risk. The

figure above also compare s risk

adjusted returns on utility stocks to

the returns on the market. In this

comparison, utility stocks perform

much better, earning an excess return

of about 1.4% a year over the last 50



years. It is worth noting that this

result mirrors the findings on high

dividend yield stocks (which include a

disproportionate number of utility

stocks) and many of the caveats about

that strategy apply to this one as well.

In particular, this strategy would have

generated higher tax liabilities and

would have required a long time

horizon to pay off.



DISCOUNTED CASH FLOW VALUATION

This approach has its foundation in

the present value rule, where the value

of any asset is the present value of

expected future cash flows that the

asset generates.

The cash flows will vary from

asset to asset -- dividends for stocks,

coupons (interest) and the face value

for bonds and after-tax cash flows for

a real project. The discount rate will

be a function of the riskiness of the

estimated cash flows, with higher

rates for riskier assets and lower rates

for safer projects. You can in fact

think of discounted cash flow

valuation on a continuum. At one end

of the spectrum, you have the default-

free zero coupon bond, with a

guaranteed cash flow in the future.

Discounting this cash flow at the

riskless rate should yield the value of

the bond. A little further up the

spectrum are corporate bonds where

the cash flows take the form of

coupons and there is default risk.

These bonds can be valued by

discounting the expected cash flows at

an interest rate that reflects the default

risk. Moving up the risk ladder, we

get to equities, where there are

expected cash flows with substantial

uncertainty around the expectation.

The value here should be the present

value of the expected cash flows at a

discount rate that reflects the

uncertainty.

Example: (Effects of mismatching

cash flows and discount rates).

Assume that you are analyzing a

company with the following cash

flows for the next five years. Assume

also that the cost of equity is 13.625%

and the firm can borrow long term at

10%. (The tax rate for the firm is

50%). The current market value of

equity is $1,073 and the value of debt

outstanding is $800.



The cost of equity is given as an input

and is 13.625%, and the after-tax cost

of debt is 5%.

Given the market values of equity and

debt, we can estimate the cost of

capital.

Method 1: Discount CF to Equity at

Cost of Equity to get value of equity

We discount cash flows to equity at

the cost of equity:

PV of Equity:

(50/1.13625) + (60/1.136252) +

(68/1.136253) + (76.2/1.136254) +

{(83.49+1603)/1.136255}

= $1073

Method 2: Discount CF to Firm at

Cost of Capital to get value of firm

PV of Firm:

(90/1.0994) + (100/1.09942) +

(108/1.09943) + (116.2/1.09944) +

(123.49+2363)/1.09945

=$1873

PV of Equity:

{PV of Firm – Market Value of Debt}

= $ 1873 – $ 800

= $1073

YearCashFlow(in $)

Int.(l-t)

(in $)

CashFlow to

the Firm(in $)

1 50 40 902 60 40 1003 68 40 1084 76.2 40 116.25 83.49 40 123.49

TerminalValue 1603.008 2363.008

WACC = Cost of Equity {Equity / (Debt

+ Equity)} + Cost of Debt

{Debt / (Debt + Equity)}

= 13.625% (1073/1873) + 5%

(800/1873) = 9.94%

Cost of Debt = Pre-tax rate (1 – tax rate)

= 10% (1-.5) = 5%



{Note: the value of equity is $1073

under both approaches. It is easy to

make the mistake of discounting cash

flows to equity at the cost of capital or

the cash flows to the firm at the cost

of equity.}

Error 1: Discount CF to Equity at

Cost of Capital to get too high a value

for equity

PV of Equity:

50/1.0994+60/1.09942+68/1.09943

+76.2/1.09944+83.49+1603)/1.09945

= $1248

Error 2: Discount CF to Firm at Cost

of Equity to get too low a value for

the firm

PV of Firm:

90/1.13625+100/1.136252+

108/1.136253+116.2/1.136254+

(123.49+2363)/1.136255

= $1613

PV of Equity:

{PV of Firm – Market Value of Debt}

= $1613 – $800

= $813

The effects of using the wrong

discount rate are clearly visible in the

last two calculations. When, the cost

of capital is mistakenly used to

discount the cash flows to equity the

value of equity increases by $175

over its true value of $1073. When the

cash flows to the firm are erroneously

discounted at the cost of equity, the

value of the firm is understated by

$260. We have to point out that

getting the values of equity to agree

with the firm and equity valuation

approaches can be much more

difficult in practice than in this

example. We will return and consider

the assumptions that we need to make

to arrive at this result.



RISK HEDGING

A number of external factors,

including interest rates commodity

prices and exchange rates, can affect

the revenues, earnings and value of a

firm. Thus, even the best-managed

airline may see its profits decline if oil

prices go up. In recent years, firms

have been able to hedge a significant

portion of this risk, using financial

instruments and products. In this

section, you will consider two

questions. The first relates to whether

firms should try to manage this risk.

The second looks at the payoff of risk

management to investors.

Before going further let’s

understand the need of managing

Project Risk… Firms are exposed to a

multitude of macroeconomics risks in

their investments. Sometimes shifts in

interest rates and exchange rates can

augment income and sometimes they

can reduce it. Thus, a portion of the

variation in earnings over time for any

firm can be attributed to these risks.

The manager can leave the firm

exposed to these risks and assume that

its stockholders in the firm will be

able to diversify away the risk, or the

manager can hedge the risk, using a

variety of financial instruments.

To evaluate whether a firm

should try to manage or hedge its

exposure to this risk, one need to

consider three factors. The first is the

magnitude of the risk and the impact

that it can have on the overall firm’s

earnings and value. 30% of the

volatility of earnings for an airline but

only 5% of the variation in earnings

for a steel company. Since large shifts

in earnings can cause serious

problems for firms (including

defaulting on debt and going

bankrupt); firms should be more

likely to hedge large risks than small

ones. The second factor is the extent

to which different investments the

firm mat have in different parts of the

world may result in diversification of



some or a great portion of the risk.

For instance, Coca-Cola and Citicorp,

with operations in dozens of countries

that reduce value may be offset by

favorable movements in other

countries. If firms such as these

hedges risk in each country, they will

be doing so unnecessarily. The third

factor is the degree to which investors

in the firm can diversify away the risk

on their own by holding portfolios

that include stocks that are affected

both positively and negatively by

exchange rate movements. Firms such

as the Home Depot and Boeing,

which have a base of well-diversified

investors, may find it cheaper not to

hedge risk and allow it to pass

through to their investors, who will

diversify it away at far less expense.

In addition, one needs to

consider the cost of managing risk.

Hedging risk exposure is cheaper for

some types of risk (exchange rate,

interest rate) than for others (political

risk) and for shorter periods than for

longer ones. Other things remaining

equal, the greater the cost of hedging

risk, the less likely firms will be to

hedge.

Now another question arises i.e.,

‘how to manage Project Risk?’

Assume now that there is a form that

should be managing project risk and

that it is considering the different

alternatives available to it to do so.

When firms decide to manage risk,

they have a variety of choices. They

can use futures contracts, forward

contracts, and options to manage

interest rate, exchange rate and

commodity price risk; and they can

use insurance products to manage

event risk (such as the eventuality of a

revolution). They can also manage

risk by choosing the financing for the

project wisely.

The simplest way of hedging some

of the risk on a project is to choose

financing instruments with cash

flows that mirror the cash flows on

the project. Thus, Wal-Mart can



use a loan denominated in

Mexican pesos to finance its retail

expansion in Mexico. If the peso

depreciates, its assets (the store in

Mexico) will be worth less, but so

will its liabilities (the loan),

leaving it less affected by the

exchange rate movement.

Matching financing to the assets

can only partially reduce risk, but

it is generally a low-cost option for

risk management. All firms should

therefore try to do this as much as

they feasibility can.

The most widely used products in

risk management are futures,

forwards, options, and swaps.

These are generally categorized as

derivative products since they

drive their value from an

underlying asset that is traded.

Today, you can buy futures and

options contracts to hedge away

commodity price risk, currency

risk and interest rate risk, to name

a few.

The alternative route to risk

management is to buy insurance to

cover specific event risk. Just as

homeowners buy insurance on

their home to protect against the

eventuality of fire or other

damage, companies can buy

insurance to protect their assets

against possible loss. In fact, it can

be argued that, in spite of the

attention given to the use of

derivatives in risk management,

traditional insurance remains the

primary vehicle for managing risk.

Insurance does not eliminate risk.

Rather, it shifts the risk from the

firm buying the insurance to the

insurance company may be able to

create a portfolio of risks, thereby

gaining diversification benefits

that the self-insured firms itself

cannot obtain. Second, the

insurance company might acquire

the expertise to evaluate risk and

thus process claims more

effectively as a consequence of its

repeated exposure to that risk.



Third, insurance companies might

provide other services, such as

inspection and safety services, that

benefit both sides. While a third

party could arguably provide the

same services, the insurance

company has an incentive to

ensure the quality of the service.



COMBINING A HEDGE FUND WITH EQUITIES

The most valuable aspect of a hedge

fund may not be that it offers higher

returns, or that it offers lower risk.

The unique value-adding potential of

a hedge fund is the way it can reduce

the investor's overall portfolio risk by

offering "extreme diversification".

Consider the example of an

investor who can construct their

portfolio out of two possible assets: a

hedge fund, or equities.

Assume that the hedge fund and

the equity market both have

expected returns of 13%.

Assume also that the hedge fund

has an expected risk of 14%, while

the equity market has an expected

risk of 12%.

Since the risk of the hedge fund is

higher than the risk of the equity

market, one might think that it

would be best for the investor to

avoid investing in the hedge fund.

However, this is not the case.

The missing ingredient that one

needs to consider is the correlation

between the hedge fund and the

equities market.

The chart above contains three

different lines plotting the total risk of

the portfolio against the proportion of

equities in the portfolio. The left side

of the chart shows the risk for 0%

equities, 100% hedge fund. This is

14%. The right side of the chart

shows the risk for 100% equities, 0%

hedge fund. This is 12%. The lines

in between these point show how the

risk changes with different

concentrations of assets:



If one assumes that the correlation

between the hedge fund and

equities is 1.0, the risk of a

combined portfolio will fall on the

green line. This line is straight,

and accordingly never falls below

12%.





red line. Because of the

diversification effect from having

uncorrelated assets in the portfolio,

this line bows downward. The

minimum risk is 11.7%, at a

combination of 70% equities, 30%

hedge fund.





blue line. This line bows down

quite noticeably. The minimum

risk is 9.1%, at a combination of

60% equities, 40% hedge fund.

This is just one particular

numerical example, but it illustrates

the general principle that introducing

low-correlation assets into a portfolio

can reduce risk quite appreciably. At

a correlation of 1.0, there would be no

advantage at all in allocating assets

into the hedge fund. At a correlation

of 0.7, one has the potential to reduce

the risk to 11.7% by allocating assets

into the hedge fund. This is a fairly

marginal benefit: only 30 basis points

of risk reduction. A practical person

might be inclined to say that a

theoretical risk reduction of 30 basis

points means little in practice,

because of the danger that reality can

turn out differently from a

mathematical model.

However, at a correlation of

0.0, the potential risk reduction

becomes hard to ignore. The potential

is to get the risk down to 9.1%, which

eliminates (through diversification),

almost one quarter of the existing risk

in an equities portfolio. This is very

considerable risk reduction. We



could simply accept this risk

reduction "as is", or we could convert

it into higher return by leveraging the

portfolio.

For example, the expected

return of all our portfolios including

equities and hedge fund is 13%

(remember this is the expected return

that we assumed both for hedge funds

and for equities). Our diversified

portfolio with a risk of 9.1% has this

13% expected return. To take the

level of risk back up to 12% (the level

of equities on their own), we could

increase the portfolio weight of risky

assets to 131.56%, and hold -31.56%

cash in this leveraged portfolio. We

assume that the cash interest rate is

5%. The final result is a portfolio

with risk = 12% (just as for a plain

equities portfolio), but expected return

boosted up to 15.52%. This is a nice

return enhancement of 252 basis

points, for zero incremental risk.

Surely every rational investor would

seek-out a solution of this kind, if

they were able to access it? Well,

perhaps maybe not, because some

investors use Thaler's mental-

accounting principle of ignoring the

fungibility of money, and instead

concerning themselves primarily with

the labels attached to different sub-

parts of their portfolio (specifically,

they might shun having any leverage

or hedge funds, without regard to the

consequences for the overall

risk/return profile of their portfolio).

So, to pose another question of

great practical importance is it

possible to find hedge funds that offer

the sort of risk/return characteristics

shown in this example? Sometimes

yes, but you do need to watch out for

the great pretenders. Some hedge

funds are constructed in an explicitly

market-neutral way. Typically, this

would mean that every long asset was

offset by a similar short asset. For

example, the hedge fund manager

might bet on copper vs. steel, oil vs.

natural gas, Euro vs. Japanese Yen,

Swedish bonds vs. British bonds, etc.

Each bet is essentially a relative bet,



that one asset will outperform another

asset. When this sort of portfolio

construction is done rigorously

(especially with the assistance of

sophisticated factor models), the

resulting portfolio tends to have zero

correlation with equities markets.

Yet, if the hedge fund manager has

skill in picking disvalued assets, the

expected return from this sort of

portfolio can be quite reasonable. A

rigorously constructed market neutral

hedge fund will have zero correlation

with equity markets, and it will offer

attractive long-term returns.

However, as somebody once

said, "hedge fund" means a

remuneration structure, not a portfolio

management style. There are many

"wannabe" investment managers who

love the idea of charging 2+20 fee

structures. So, they often cobble

together a fairly standard long-only

investment style, and then add a bit of

short selling in order to get a product

that they can market to a gullible

public as a hedge fund.

Suggestion is that all so-called

market neutral hedge funds should be

required to report in detail on their

correlations with major asset classes.

That way, investors would have a

reliable piece of information to help

them decide whether they are truly

likely to gain significant benefits from

something claiming to be a hedge

fund.



THE PAYOFF TO RISK MANAGEMENT

Firms can use a variety of products to

manage risk, and doing so, they can

reduce the variability in their

earnings. But do investors in these

firms that use foreign currency

derivatives to hedge exchange rate

risk concluded that they have both

smoother earnings and trade at higher

values. A subsequent examination

suggests that most of the benefit

comes from hedging short-term

transaction risk and there seems to be

little gained from hedging translation

exposure (which also affects

earnings). Another strand of the

researcher looks at why some firms

hedge risk more than others and

uncovers interesting factors. Many

firms that use derivatives to manage

risk often do so to reduce tax

liabilities, maintain required

investments, and alleviate the fear of

financial distress. At the same time,

managerial risk aversion also plays a

role in whether derivatives get used.

Studies indicate that managers are

most likely to use derivatives when

they hold a larger percent of the

outstanding stock in a company.

In summary, the evidence

indicates that there is a payoff to

managing risk and that firms that

manage risk are more highly valued

than firms that do not. Two notes of

caution are in order, though. The first

is that the payoff is a small one and it

is unlikely that investors will even

notice unless they look closely. The

second is that payoff occurs when

these firms switch to using the risk

management products and not

subsequently.



RISK AND RETURN: PORTFOLIO ANALYSIS

Of all possible questions which the

investor may ask, the most important

one is concerned with the probability

of actual yield being less than zero,

that is, with the probability of loss.

This is the essence of risk. A useful

measure of risk should somehow take

into account both the probability of

various possible “bad” outcomes and

their associated magnitudes. Instead

of measuring the probability of a

number of different possible

outcomes, the measure of risk should

somehow estimate the extent to which

the actual outcome is likely to diverge

from the expected.

Two measures are used for this

purpose: the average (or mean)

absolute deviation and the standard

deviation. Table 1.1 shows how the

average absolute deviation can be

calculated. First the expected return is

determined. In this case it is 10.00%.

Next, each possible outcome is

analyzed to determine the amount by

which the value deviates from the

expected amount. The figures shown

in Column 5 of table 1.1 include both

positive and negative values. As

shown in column 6 also, a weighted

average, using probabilities as

weights, will equal zero. This is

mathematical necessity, given the way

expected value is calculated. To

Table: 1.1 Calculating the Mean Absolute Deviation

Event Probability Return%

ExpectedReturn Deviation Probability

* Deviation

AverageAbsoluteDeviation

(1) (2) (3) (4)=(2)*(3) (5) (6)=(2)*(5) (7)=a .20 -10 -2.0 -25.0 -5.0 5.0b .40 25 10.0 10.0 4.0 4.0c .30 20 6.0 5.0 1.5 1.5d .10 10 -1.0 -5.0 -0.5 0.5

Total 15.0 0 10.0



assess the risk the signs of deviations

can simply be ignored. As shown in

column 7 the weighted average of the

absolute values of the deviations,

using the probabilities as weights, is

10.00%. This constitutes the first

measure of “likely” deviation.

Table 1.2 presents slightly

more complex but preferably

analytical measure. In this, the

deviations are squared (making the

value all positive); then a weighted

average of these amounts is taken,

using the probabilities as weights. The

result is termed the variance. It is

converted to the original units by

taking the square root. The result is

termed the standard deviation.

Although the two measures are

often interchangeable in this manner,

the standard deviation is generally

preferred for investment analysis. The

reason is simple. The standard

deviation of a portfolio’s return can

be determined from (among other

things) the standard deviations of the

returns of its component securities, no

matter what the distributions. No

relationship of comparable simplicity

exists for the average absolute

deviations.

When an analyst predicts that a

security will return 15% next year, he

or she is presumably stating

something comparable to an expected

value. If asked to express the

uncertainty about the outcomes, he or

she might reply that the odds are 2 out

of 3 that the actual return will be

within 10% of the estimate (i.e. 5%

Table: 1.2 Calculating the Standard Deviation

Event Probability Deviation Deviation Squared Weighted AverageSquared Deviation

(1) (2) (3) (4)=(3)2 (5)= (2)*(4)a .20 -25.0 625.0 125.0b .40 10.0 100.0 40.0c .30 5.0 25.0 7.5d .10 -5.0 25.0 2.4

Variation = Weighted Average Square Deviation = 175.0Standard Deviation = Square Root of Variance = 13.2287



and 25%). The standard deviation is a

formal measure of uncertainty, or risk,

expressed in this manner, just as the

expected value is a formal measure of

“best guess” estimate. Most analysts

make such predictions directly,

without explicitly assessing

probabilities and making the requisite

computations.

Portfolio Risk

In order to estimate the total risk of a

portfolio of assets, several estimates

are needed: the variance of each

individual asset under consideration

for inclusion in the portfolio and the

covariance, or correlation co-efficient,

of each of the other assets.

Table 2.1 shows the returns on

two securities and on a portfolio that

includes both of them. Security X

constitutes 60 per cent of the market

value of the portfolio and security Y

the other 40 per cent. The predicted

return on the portfolio is simply a

weighted average of the predicted

returns on the securities, using the

proportionate values as weights.

Summary measures show

values computed from the estimates in

Table 2.2. The expected return for the

portfolio is simply the weighted

average of expected returns on its

security, using the proportionate value

as weights (17.0%=.6*15%+.4*20%).

however, this is not true for either the

variance or the standard deviation o

turn for the portfolio are smaller than

the corresponding values for either of

the component securities.

Table 2.1 Returns in Portfolio and Security Risks

Event Probability Return onSecurity X

Return onSecurity Y Return on Portfolio

(1) (2) (3) (4) (5)=(3)*0.6 + (4)*0.4a 0.20 -10% 5.0% -4.0%b 0.40 25 30.0 27.0c 0.30 20 20.0 20.0d 0.10 10 10.0 10.0



This rather surprise result as a simple

explanation. The risk for a portfolio

depends not only on the risk of its

securities considering its isolation, but

also on the extent to which they are

affected similarly by underlying

events. To illustrate this, two extreme

cases are shown in Table 3. In the first

case both the variances and the

standard deviation of the portfolio are

the same as the corresponding values

of the securities.

Then diversification has no

effect at all on risk.

In the second case the situation is very

different. Here the security’s returns

offset one another in such a manner

that the particular combination that

makes up this portfolio has no risk at

all. Diversification has completely

eliminated risk. The difference

between these two cases concerns the

extent to which the security’s returns

are correlated i.e., tend to “go-

together”. Either of two measures can

be used to state the degree of such a

Table: 2.2 Summary MeasuresSecurity X Security Y Portfolio

Expected Return 15.0 20.0 17.0Variance of Return 175.0 95.0 135.8Standard Deviation of Return 13.72287 9.7468 11.65

Table: 2.3 Covariance and Correlation

Event PDeviation ofReturn forSecurity X

Deviation ofReturn forSecurity Y

Product ofDeviation

ProbabilityTimes Product

of Deviation(1) (2) (3) (4) (5) = (3) * (4) (6) = (2) * (5)a 0.20 -25.0% -15.0% 375 75.0b 0.40 25 10.0 100 40.0c 0.30 20 0 0 0d 0.10 10 100 50 50.0

Covariance 120.0



relationship: the covariance or the

correlation co-efficient.

The computations required to

obtain the covariance for the two

securities are presented in Table 2.3.

The deviation of each securities return

from its expected value is determined

and the product of the two obtained.

The variance is simply a weighted

average of such products, using the

probabilities of the events as weights.

A positive value for the

covariance indicates that the securities

returns tend to go together – for

example, a better than expected return

for one is likely to occur along with

the better than expected return for the

other. A small or zero value for the

covariance indicates that there is little

Table:3.1 Two Securities with equal returns

Event P Return onSecurity X%

Return onSecurity Y% Return on Portfolio

(1) (2) (3) (4) (5) = (3)X0.6*(4)X0.4A 0.20 -10.0 -10.0 -10.0B 0.40 25.0 25.0 25.0C 0.30 20.0 20.0 20.0D 0.10 10.0 10.0 10.0

Expected Return 15.0 15.0 15.0Variance of Return 175.0 175.0 175.0Standard Deviation of Return 13.2287 13.2287 13.2287

Table: 3.2 Two Securities with Offsetting returns

Event P Return onSecurity X%

Return onSecurity Y% Return on Portfolio

(1) (2) (3) (4) (5)a (2) (3) 40.0 10.0b 0.20 -10.0 -20.0 10.0c 0.40 25.0 -5.0 10.0d 0.30 20.0 10.0 10.0

Expected Return (%) 15.0 -0.5 10.0Variance of Return 175.0 37.47 0Standard Deviation 13.2287 6.1217 0



or no relationship between the two

returns. The correlation coefficient is

obtained by dividing the covariance

by the product of the two securities

standard deviation. As shown in Table

2.3, in this case value is 0.9307.

Correlation coefficients always

lie between +1.0 and -1.0, inclusive.

The former value represents perfect

positive correlation, of the type shown

in the example in Table 3.1. The latter

value represents perfect negative

correlation in Table 3.2. The

relationship between the covariance

and the correlation coefficient can be

represented as follows:

Where:

CXY = covariance between return on Xand return on Y.

rXY = coefficient of correlation betweenreturn on X and return on Y.

SX= standard deviation of return for X.SY = standard deviation of return for Y.For two securities, X and Y, the

relationship between the risk of a

portfolio of two securities and the

relevant variables, the formula is:

Where:

Vp = the variance of return for theportfolio.

Vx = the variance of return for securityX.

Vy = the variance of return for securityY.

CXY = the covariance between the returnon security X and Y.

WX = the proportion of the portfoliovalue invested in security X.

WY = the proportion of the portfoliovalue invested in security Y.

For the case shown in Table 2

WX = 0.6

WY = .4

VX = 175

VY= 95

CXY= 120



Inserting these values in the formula,

we get the variance of the portfolio as

a whole:

Vp = {(0.6)2 * 175.0} + {2*0.6*0.4*120}

+ {(0.4)2 * 95.0}

= 63.00 + 57.60 + 15.20

= 135.80

Where:

Vp= the variance of return for the

portfolio

Wx= the proportion of the portfolio

value invested in security X.

Wy= the proportion of the portfolio

value invested in security Y.

Cxy= the covariance between the return

on security X and Y.

N= the number of securities

The two summation signs mean that

every possible combination must be

included in the total, with a value

between 1 and N substituted where x

appears and a value between 1 and N

substituted where y appears. In those

cases in which the values are the

same, the relevant covariance is that

between a security’s return and itself.



CONCLUSION

Not all firms that report stable

earnings are good investments. At the

minimum, you need to consider

whether these firms offer any growth

potential, whether earnings stability

translates into price stability and

finally, whether the market is pricing

these stocks correctly. It is no bargain

to buy a stock with stable earnings,

low or no growth, substantial price

volatility and a high price-earnings

ratio. Reverting to the sample of all

firms in the US, the following screens

were used:

The coefficient if variation in

earnings per share has to be in the

bottom 10% of the overall sample.

One can use alternative measures

of earnings stability to make this

judgment, still the argument for

using earnings per share rather

than net income or operating

income were presented earlier in

the project. One can also add on

additional screens such as the

requirement that earnings have

increased every year for the last

few years.

The beta of the stock has to be less

than 1.25, and the standard

deviation in the stock prices over

the last three years has to be less

than 60%. While it is unlikely that

many stable earnings companies

will be high risk, there will be

some companies for which prices

remain volatile even as earnings

are stable. The risk screens will

eliminate these firms.

The price-earnings ratio has to be

less than 15. Buying a great

company at too high a price is no

bargain. Consequently, you need

to make sure that you are not

paying a premium for earnings

stability that is not justified.

The expected growth rate in

earnings per share over the next

five years has to be 10% or higher.

Earnings growth is always a



bonus. A company with stable and

growing earnings is clearly a

better investment than one with

stable and stagnant earnings.

Firms that report a steady and stable

stream of positive earnings per share

are considered by some investors to

be good investments because they are

safe. Both the theoretical backing and

the empirical evidence for this

proposition are weak. Firms that pay a

large price (on risk management

products or acquisitions) to reduce or

eliminate risk that investors could

have diversified away at no cost are

doing a disservice to their

stockholders. Stable earnings

notwithstanding, one should not

expect these firms to be a great

investments. In this project report, we

considered this issue by first looking

at how best to measure earnings

volatility. When you construct a

portfolio of stocks that have the most

stable earnings, other problems show

up.

The first is that some of these

firms, despite their earnings stability,

have high stock prices volatility and

seem risky. The second is that a

substantial number of these firms

have a low or negative growth rates.

Finally, many of the remaining

firms trade at high PE ratios and do

not seem to be bargain at prevailing

prices.

KEY TERMS DEFINED



Risk

Risk is a concept that denotes the precise probability of specific eventualities.

Technically, the notion of risk is independent from the notion of value and, as

such, eventualities may have both beneficial and adverse consequences. However,

in general usage the convention is to focus only on potential negative impact to

some characteristic of value that may arise from a future event.

Systematic risk

In finance, systematic risk is that risk which is common to an entire market and not

to any individual entity or component thereof. It should not be confused with

systemic risk, which is the risk that the entire financial system will collapse as a

result of some catastrophic event.

Unsystematic risk

This is the risk other than systematic risk and which is due to the factors which are

controllable by the people working in market and market risk premium is used to

compensate this type of risk.

Operating risk

An operational risk is a risk arising from execution of a company's business

functions. As such, it is a very broad concept including e.g. fraud risks, legal risks,

physical or environmental risks, etc. The term operational risk is most commonly

found in risk management programs of financial institutions that must organize

their risk management program according to Basel II. In Basel II, risk management

is divided into credit, market and operational risk management. In many cases,

credit and market risks are handled through a company's financial department,

whereas operational risk management is perhaps coordinated centrally but most



commonly implemented in different operational units (e.g. the IT department takes

care of information risks, the HR department takes care of personnel risks, etc)

Currency risk

Currency risk is a form of risk that arises from the change in price of one currency

against another. Whenever investors or companies have assets or business

operations across national borders, they face currency risk if their positions are not

hedged.

Transaction risk is the risk that exchange rates will change unfavorably over

time. It can be hedged against using forward currency contracts;

Translation risk is an accounting risk, proportional to the amount of assets

held in foreign currencies. Changes in the exchange rate over time will

render a report inaccurate, and so assets are usually balanced by

borrowings in that currency.

Political risk

political risk refers to the complications businesses and governments may face as a

result of what are commonly referred to as political decisions—or “any political

change that alters the expected outcome and value of a given economic action by

changing the probability of achieving business objectives.”[1] . Political risk faced

by firms can be defined as “the risk of a strategic, financial, or personnel loss for a

firm because of such nonmarket factors as macroeconomic and social policies

(fiscal, monetary, trade, investment, industrial, income, labour, and

developmental), or events related to political instability (terrorism, riots, coups,

civil war, and insurrection).”[2] Portfolio investors may face similar financial

losses. Moreover, governments may face complications in their ability to execute

diplomatic, military or other initiatives as a result of political risk.



Market risk

Market risk is the risk that the value of an investment will decrease due to moves

in market factors.

Return

In finance, rate of return (ROR), also known as return on investment (ROI), rate of

profit or sometimes just return, is the ratio of money gained or lost (realized or

unrealized) on an investment relative to the amount of money invested. The

amount of money gained or lost may be referred to as interest, profit/loss,

gain/loss, or net income/loss. The money invested may be referred to as the asset,

capital, principal, or the cost basis of the investment. ROI is usually expressed as a

percentage rather than a fraction.

Co-relation

In probability theory and statistics, correlation (often measured as a correlation

coefficient) indicates the strength and direction of a linear relationship between

two random variables. That is in contrast with the usage of the term in colloquial

speech, denoting any relationship, not necessarily linear. In general statistical

usage, correlation or co-relation refers to the departure of two random variables

from independence. In this broad sense there are several coefficients, measuring

the degree of correlation, adapted to the nature of the data.

Hedging

In finance, a hedge is a position established in one market in an attempt to offset

exposure to the price risk of an equal but opposite obligation or position in another

market — usually, but not always, in the context of one's commercial activity.



Hedging is a strategy designed to minimize exposure to such business risks as a

sharp contraction in demand for one's inventory, while still allowing the business

to profit from producing and maintaining that inventory.

Portfolio

In finance, a portfolio is an appropriate mix of or collection of investments held by

an institution or a private individual.

Beta

Beta coefficient is a parameter in Capital Asset Pricing Model (CAPM) that

describes how sensitive the expected return of a stock (or portfolio) is to the

market.

Leverage

In finance, leverage (or gearing) is borrowing money to supplement existing funds

for investment in such a way that the potential positive or negative outcome is

magnified and/or enhanced.[1] It generally refers to using borrowed funds, or debt,

so as to attempt to increase the returns to equity. Deleveraging is the action of

reducing borrowings.

Diversification

Diversification in finance is a risk management technique, related to hedging, that

mixes a wide variety of investments within a portfolio. Because the fluctuations of

a single security have less impact on a diverse portfolio, diversification minimizes

the risk from any one investment. There are three primary strategies used in

improving diversification:



Spread the portfolio among multiple investment vehicles, such as stocks,

mutual funds, bonds, and cash.

Vary the risk in the securities. A portfolio can also be diversified into

different mutual fund investment strategies, including growth funds,

balanced funds, index funds, small cap, and large cap funds. When a

portfolio includes investments with varied risk levels, large losses in one

area are offset by other areas.

Vary your securities by industry, or by geography. This will minimize the

impact of industry- or location-specific risks. The example portfolio above

was diversified by investing in both umbrellas and sunscreen. Another

practical application of this kind of diversification is mixing investments

between domestic and international funds. By choosing funds in many

countries, events within any one country's economy have less effect on the

overall portfolio.

Diversification reduces the risk of a portfolio, and consequently it can reduce the

returns. However, since diversification reduces the risk of an entire portfolio being

diminished by a single investment's loss, it is referred to as "the only free lunch in

finance."[1] Statistical analysis shows that there may be some validity to this

claim.

CAPM



The Capital Asset Pricing Model (CAPM) is used to determine a theoretically

appropriate required rate of return of an asset, if that asset is to be added to an

already well-diversified portfolio, given that assets’ non-diversifiable risk. The

model takes into account the asset's sensitivity to non-diversifiable risk (also

known as systemic risk or market risk), often represented by the quantity beta (β)

in the financial industry, as well as the expected return of the market and the

expected return of a theoretical risk-free asset.



REFERENCES

Books:Financial Management; by: Paresh ShahInvestment Management; by: V.K. BhallaInvestment Fables; by: Aswath DamodaranPractical Financial Modeling; by: Jonathan SwanIn the Wonderland of Investment; by: AN ShanbagValuation; by: McKinesy & Co., Inc;Tom Copland; TimKoller;Jack MurrinThe Intelligent Investor; by: Graham

Web – Links:http://www.wikipedia.comhttp://www.google.comhttp://www.investopedia.comhttp://www.wikianswers.comhttp://www.investword.com



ANNEXURE: PROJECT SYNOPSIS

Topic : RISK AND RETURN MEASUREMENT FOR INVESTMENT

DECISION

Group Members : 1. Bharat Agnani2. Mahesh Nakhwani3. Siddharth Sinha

Key Terms : 1) Risk2) Systematic risk3) Unsystematic risk4) Operating risk5) Currency risk6) Political risk7) Market risk8) Return9) Co-relation10) Hedging11) Portfolio12) Beta13) Leverage14) Diversification15) CAPM



Objective of Study: The Object of the Research will be the realization ofinvestment process under conditions of risk andthe theoretical and practical issues related to it.

1) The Risk/Return Trade-off in Financial Analysis2) Measurement of Risk and Return3) Categories of Risk and Leverage Faced by the Firm

and by Stockholders4) Risk and Diversification5) Risk in a Portfolio Setting6) Measuring the Expected Return and Standard

Deviation of a Portfolio7) Hedging by using various tools

Research Methodology :

In the research we will be conducting we will be using

Generally accepted scientific qualitative and quantitative methods, includingmonographic method, analysis and synthesisLogical constructive, mathematical and statistical methods.



Current Knowledge of the Topic:

The, so-called, ‘market neutral hedge funds’ are required to report in detail on theircorrelations with major asset classes. That way, investors would have a reliablepiece of information to help them decide whether they are truly likely to gainsignificant benefits from something claiming to be a hedge fund.

The risk/return relationship is a fundamental concept in not only financial analysis,but in every aspect of life. If decisions are to lead to benefit maximization, it isnecessary that individuals (investors) consider the combined influence on expected(future) return or benefit as well as on risk (cost). The requirement that expectedreturn/benefit be commensurate with risk is known as the "risk/return trade-off", infinancial terms.

References :Books:

Financial Management; by: Paresh ShahInvestment Management; by: V.K. BhallaInvestment Fables; by: Aswath Damodaran

Web – Links:http://www.wikipedia.comhttp://www.google.com

{Note: The reference can change during the proceedings with the project; and anychange will be intimated to the Prof. Paresh Shah via., e-mail, sms, and eventhrough personal interactions. Anyhow the references written above will beconsidered as the base of the project and any change will result in the addition ofthe sources of concept understanding…}

risk & return measurements for investment decisions

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