Risk%20and%20Return

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Risk and Return

• Two sides of the Investment Coin

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Overview

• Investment decisions are influenced by various
  motives.
• Some invest in a business to acquire control and
  enjoy the prestige.
• Some invest in expensive yatchs and famous villas
  to display their wealth.
• Most investors however, are largely guided by the
  pecuniary movite of earning a return on their
  investment.
• For earning returns, investors have to almost
  invariably bear some risk.
• In general, risk and return go hand in hand.
• While investors like returns, they abhor risk.
• Investment decisions, therefore, involve a
  tradeoff between risk and return.

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Return

• Return is primary motivating force that drives
  investment.
• It represents the reward for undertaking
  investment.
• Sine the game of investing is about returns
  (after allowing for risk), measurement of
  realized (historical) returns (ex post facto) is
  necessary to access how ell the investment
  manager has done.
• In addition, historical returns are often used as
  a important input in estimating future
  (prospective) returns.

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The components of Return

• The return of an investment consists of two
  components
• Current return
• Capital return

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Current Return

• Periodic cash flow (income) such as dividend or
  interest, generated by the investment in various
  instruments.
• Current return is measured as the periodic income
  in relation to the beginning price of the
  investment.

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Capital Return

• Reflected in the price change - Capital
  gain/loss
• It is simply the price appreciation/depreciation
  divided by the beginning price of the
  asset/security.

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Total Return

• The current return can be zero or positve
• The capital return can be negative, or zero or
  positive.

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Risk

• Risk refers to the possibility that the actual
  outcome of an investment will differ from its
  expected outcome.
• More specifically, most investors are concerned
  about the actual outcome being less than the
  expected outcome.
• The wider the range of possible outcomes, the
  greater the risk.
• Risk is the variability in possible returns.
• In investment analysis, its measured by
• Variance / Standard Deviation
• Beta

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Sources of Risk

• Risk emanates from several sources.
• The three major ones are
• Business Risk
• Interest Rate Risk
• Market Risk

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Business Risk

• Risk of poor business peformance. (Operating
  Risk)
• May be caused by variety of factors
• Heightened competition
• Emergence of new technologies
• Development of subtitute products,
• Shifts in consumer preference
• Inadequate supply of essential inputs
• Changes in governmental policies, and so on.
• Principle factor may be inept and incompetent
  management.
• It can affect the interest of shareholders and
  even bond/debenture holders (default risk)

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Interest Rate Risk

• The changes in interest rate have a bearing on
  welfare of investors.
• As interest rate goes up, the market price of
  existing fixed income securities falls and vice
  versa.
• It also affects equity prices, albeit some what
  indirectly.
• The changes in the relative yields of debentures
  and equity shares influence equity prices.

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Market Risk

• Changing psychology of the investors.
• There are periods when investors become bullish
  and their investment horizons lengthen.
• Investors optimism, which may broder on
  euphoria, during such periods drives share prices
  to great heights.
• The buoyancy created in the wake of this
  development is pervasive, affecting almost
  allshares.
• On the other hand, when a wave of pessimism
  (which often is an exaggerated response to some
  unfavourable political or economic development)
  sweeps the market, investors turn bearish and
  myopic.
• Prices of almost all equity shares register
  decline as fear and uncertainty prevade the
  market.

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The ebb and flow of mass emotion is quite
regular Panic is followed by relief, and relief
by optimism then comes enthusiasm, then euphoria
and rapture, then the bubble brusts, and public
feeling slides off again to concern, desperation,
and finally a new panic
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You need to get deeply into your bones, the
sense that any market, and certainly the stock
market, moves in cycles, so that you will
infallibly get wonderful bargains every few
years, and have a chance to sell again at
ridiculously high prices a few years later
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Types of Risk
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Unique Risk Diversifiable Risk Unsystematic
Risk

• Portion of total risk which stems from firm
  specific factors.
• Examples of sources
• Development of new products
• Labour strike
• Emergence of new competitor. Etc...
• Events of this nature primarily affect the
  specific firm and not all firms in general.
• Hence unique risks of a stock can be washed away
  by combining it with other stocks
• In a diversified portfolio, unique risks of
  different stocks tend to cancel each other.

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Market Risk Undiversifiable Risk Systematic
Risk

• Portion of total risk which is attributable to
  economy-wide macro factors like
• Growth rate of GDP
• Level of government spending,
• Money supply,
• Interest rate structure
• Inflation rate etc..
• These factors affect all firms to a greater or
  lesser degree, investors cannot avoid the risk
  arising from them.

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Measuring Historical Return
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Return Relative

• When a Cumulative Wealth Index or a Geometric
  Mean has to be calculated, we need to calculate
  Return Relative (coz, negative return cannot be
  used)

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Cumulative Wealth Index

• Total Return reflects changes in the level of
  wealth.
• Sometimes its useful to measure the level of
  wealth (or price), rather than the change.
• To do this, we must measure the cumulative effect
  of returns over time, given some stated intitial
  amount, which is typically rupee one.
• The cumulative wealth index, captures cumulative
  effect of total returns.

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Cumulative Wealth Index
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• Holding Period Return

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Holding Period Yield HPY HPR - 1 1.10 - 1
0.10 10
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Measures of Historical Rates of Return

• Annual Holding Period Return
• Annual HPR HPR 1/n
• where n number of years investment is held
• Annual Holding Period Yield
• Annual HPY Annual HPR - 1

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Measures of Historical Rates of Return

• Arithmetic Mean

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Summary Statistics

• While Total Return, Return Relative, and Wealth
  Index are useful measures of return for a given
  period of time, in investment analysis, we also
  need statistics that summarize a series of total
  returns.
• Two most popular summary statistics are
• Airthmetic Mean
• Geometric Mean

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Airthmetic Mean
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Contd....

• When you want to know the central tendency of
  series of returns, the airthmetic mean is the
  appropriate measure.
• It represents the typical performance for a
  single period.
• However, when you want to know the average
  compound rate of growth that has actually occured
  over multiple periods, the airthmetic mean is not
  appropriate.

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Example

• Consider a stock whose price is 100 at the end of
  year 0.
• The price declines to 80 at the end of year 1 and
  recovers to 100 at the end of year 2.
• Assuming that there is no dividend payment during
  the two year period, the annual returns and their
  airthmetic mean are as follows
• Return for year 1 (80-100)/100 - 20
• Return for year 2 (100 80)/ 80 25
• Airthmetic Mean Return (-2025)/2 2.5
• Thus we find that though the return over the two
  year period is nil, the airthmetic mean works out
  to be 2.5.
• So this measure of average return can be
  misleading.
• In multiperiod context, the geometric mean
  describes accurately the true average return.

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Geometric Mean
The geometric mean reflects the compound rate of
growth over time. GM 8.9 means, an
investment of Rs 1 produces a cumulative ending
wealth of 1x (1 0.089)5 Rs 1.532
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Contd...

• Geometric Mean is always lower than Airthmetic
  mean, except in the case where all the return
  values being considered are equal.
• The difference between GM and AM depends upon the
  variability of the distribution.
• The greater the variability, the greater the
  difference between the two means.
• The relationship between the three is given by

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Real Returns

• The returns so far discussed, without elimination
  of inflation content is called nominal returns,
  or money returns.
• Real Return after adjusting for the inflation
  factor.

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Measuring Historical Risk

• Risk refers to the possibility that the actual
  outcome of an investment will differ from the
  expected outcome.
• Refers to variability or dispersion.
• If an assets return has no variability, its
  riskless.
• Measure
• Variance and Standard Deviation

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Variance and Standard Deviation
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Criticism of Variance and Std. Deviation

• It consideres all deviations, negative as well as
  positive. Investors however, do not view positive
  deviations unfavourably in fact, they welcome
  it. Hence, some researchers have argued that only
  negative deviations should be considered while
  measuring risk.
• Hence some suggest the use of semi-variance.
  Semivariance is calculated the way variance is
  calculated, except that it considers only
  negative deviations.

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Contd...

• However, as long as returns are distributed
  symmetrically, variance is simply 2 x
  Semi-variance and it doesnot make any difference
  whether variance is used or semi-variance.
• When the probability distribution is not
  symmetrical around its expected value, variance
  alone does not suffice. In addition to variance,
  the skewness of the distribution should also be
  used.
• Variance can be used by assuming that the
  historical returns of the stock are approximately
  symmetrical.

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Risk Aversion and Required Returns

• Take an example
• You are in a game show, where you are given the
  option to open one among two boxes and take away
  whatever you find in the box.
• One box contains Rs 10,000
• Another box is empty
• (Of course the expected return with equal
  probability of two outcomes is Rs 5,000)
• You are not sure which box should you open.
• Sensing your vacillation, host offers you a
  certain Rs 3,000 if you forfeit the option to
  open the box.
• You dont accept his offer. He raises his offer to
  Rs 3,500

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Contd...

• Now you feel indifferent between a cerain return
  of Rs 3,500 and a risky (uncertain) expected
  return of Rs 5,000.
• This means that a cerain amount of Rs 3,500
  provides you with the same satisfaction as a
  risky expected value of Rs 5,000
• Thus your certainty equivalent (Rs 3,500) is less
  than the risky expected value (Rs 5,000)
• Emperical evidence suggests that most
  individuals, if placed in a similar situation,
  would have a certainty equivalent which is less
  than the risky expected value.

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Contd..

• The relationship of a persons certainty
  equivalent to the expected monetary value of a
  risky investment defines his attitute toward
  risk.
• If the certainty equivalent is less than the
  expected value, the person is risk-averse
• If the certainty equivalent is equal to expected
  value, the person is risk-neutral.
• If the certainty equivalent is more than the
  expected value, the person is risk-loving.

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Contd...

• In general, investors are risk-averse.
• This means that risky investments must offer
  higher expected returns than less risky
  investments to induce people to invest in them.
• However, we are talking about expected returns
  the actual return on a risky investment may well
  turn out to be less than the actual return on a
  less risky investment.
• Put differently, risk and return go hand in hand.
  

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Risk Premiums

• Investors assume risk so that they are rewarded
  in the form of higher return.
• Risk premium may be defined as the additional
  return investors expect to get, or investors
  earned in the past, for assuming additional risk.
• There are three well known risk premiums
• Equity Risk Premium
• Bond Horizon Premium
• Bond Default Premium

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Contd...

• Equity Risk Premium
• This is the difference between the return on
  equity stocks as a class and the risk free rate
  represented commonly by the return on Treasury
  Bills.
• Bond Horizon Premium
• This is the difference between the return on
  long-term government bonds and the return on
  Treasury Bills.
• Bond Default Premium
• This is the difference between the return on
  long-term corporate bonds (which have some
  probability of default) and the return on
  long-term government bonds (which are free from
  default risk)

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Measuring Expected (ex ante) return and risk

• When you invest in a stock, the return from it
  can take various possbile values with various
  probabilities.
• Hence, you can think returns in terms of
  probability distribution.
• The probability of an event represents the
  likelihood of its occurance.
• When you define the probability distribution of
  rate of return remember that
• The possible outcomes must be mutually exclusive
  and collectively exhaustive.
• The probability assigned to an outcome may vary
  between 0 and 1.
• The sum of the probabilities assigned to various
  possible outcomes is 1.

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Expected Rate of Return

• The expected rate of return is the weighted
  average of all possible returns multiplied by
  their respective probabilities.

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Variance and Standard Deviation of Return

• The variance of a probability distribution is the
  sum of the squares of the deviations of actual
  returns from the expected return, weighted by
  associated probabilities.

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Continuous Probability Distributions

• In finance, probability distributions are
  commonly regarded as continuous, even though they
  may actually be discrete.
• In a continuous probability distribution,
  probabilities are not assigned to individual
  points as in the case of discrete distribution.
• Instead, probabilities are assigned to intervals
  between two points on a continuous curve.
• Hence, when a continuous probability distribution
  is used, the following kinds are questions are
  answered
• What is the probability that the rate of return
  will fall between say, 10 and 20?
• What is the probability that the rate of return
  will be less than 0 or more than 25?

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The Normal Distribution

• The normal distribution, a continuous probability
  distribution, is the most commonly used
  probability distribution in investment finance.
• Normal distribution resembles a bell shaped
  curve.
• It appears that stock returns, at least over
  short time intervals, are approximately normally
  distributed.
• The following features of the normal distribution
  may be noted
• It is completely characterized by just two
  parameters, viz. Expected return and standard
  deviation of return.
• A bell-shaped distribution which is perfectly
  symmetric around the expected return.

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• Band Probability
• One standard deviation 68.3
• Two standard deviation 95.4
• Three standard deviation 99.7