sapm future returns and risk

8/6/2019 SAPM Future Returns and Risk

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Returns


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Simple methods fordetermining future

returns.

Measuring Returns:

Historical returns

Single Period

Multiple Periods


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Return is the aggregate during a period

of the dividend and interest payoffsalong with the capital gain or loss.


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Investors are interested in futurereturns or to be more precise they

are interested in expected returnsrather than past returns.

Historical returns are

good indicators andcan be useful in providing a base for

future estimates


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But it is the correct or nearly correctestimates of future returns is what this

subject is all about and which is whatwe would be interested in knowing.


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Determining FutureReturns

To anticipate future returns a number offorecasts come in to play namely for the:

1. The economy

2. Stock and bond markets

3. Sectors of the market

4. Industries5. Individual companies


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Based on these calculations andconsidering all the factors:

we come to a reasonable conclusionthat the chances of an expected rate ofreturn are say 1 in 100 or 80% or 90%

this is the probability of an expectedrate of returns materializing accordingto a set of circumstances that mayprevail at a particular time in the future.


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2) Scenario 2 with a probability of0.50%

A coalition government lasting itsfull term.

A rate of return is forecasted to bearound 26%


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3) Scenario 3 with a probability of0.25%

Re-elections in the immediatefuture.

A rate of return is forecasted to bearound 12%


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This three scenarios will cover llpossible situations and hence the

total of all the probabilities willbe 1meaning there cannot be anotherpossible situation.

We put the information in the form of atable


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Scenario Probability

ExpectedReturn

1 0.25 36%

2 0.50 26%

3 0.25 12%


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Now an investor will ask a very simplequestion considering all the possiblesituations and values involved whatwould be my average expectedreturn?


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The expected average return is nothingbut the weighted average return of allthe returns and where the weights arethe respective probabilities.


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Scenario Probability ExpectedReturn

Average

1 0.25 36% (.25*36) =9

2 0.50 26% (.50*26)=13

3 0.25 12% (.25*12)=3

9+13+3=25%


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Expected Return on A

Portfolio of securities:

A portfolio is nothing but an investment ina number of individual securities in

different proportions.


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Stock Price 91 Price92 div Return

X 20 30 2 60

Y 30 40 3 43.33

Z 50 60 5 30

XYZ 100 130 10 40


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Now the return on a portfolio is theweighted average of the returns on

individual securities in the portfoliowhere the weights are the

proportion of investments in eachsecurity

and can be calculated as follows


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Stock

X

Y

Z

Price 91

20

30

50

Return Wt * Ret Weighted

avg

60 .20*60 12

43.33 .30*43.33 13

30 .50*30 15

40


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Which is the same as per ourcalculations above

XYZ 100 130 10 40


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Returns alone do not form the solecriteria for investment we have to

also consider risk


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Risk

Suppose we have to evaluate two sharesfor which we have collected data for thepast five years as follows


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Year 1 2 3 4 5

Share A 30 28 34

32 31

Share B 26 13 48

11 57

The returns as a percentage

are


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Which share would you like to investin?

You would say the share that gives abetter average return would be the

better share correct


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Fine but there is one hitch

Both the shares have the sameaverage return of 31%


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Now What

We have to search for some other

criterion for investmentWe now see which of the two

shares are a more riskier proposal.

By simple observance it is seen thatreturns on B fluctuate more widelythan A


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an hence a prudent investor would preferA .

Why?


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Because he perceives A to be lessriskier than B .

Thus an investor would evaluate bothreturn and risk to arrive at aninvestment decision.


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How Risky Is Risk

How do we evaluate the riskiness of aparticular return or how do we measure

risk.

A common measure is Standard Deviation

and Variance of returns,


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The mean of the squared deviations of

each member of a population from the

population mean. The square of thepopulation standard deviation.


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We tend to associate investmentrisk with the variability of the rate

of returns .

The standard deviation is onemethod by which the variability of

returns may be calculated


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Time Period Return

1 10

2 8

3 -4

4 22 5 8

6 -11

7 14

8 12 9 -9

10 12


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The simple average of the returnsare

10+8-4+22+8-11+14+12-9+12

--------------------------------------

10

= 6.20


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Now standard deviation is the rootof the squares of the deviations

from the mean and is given by thefollowing formula

1------(x-)2n -1


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The square of the standard deviationis called the variance

From the information given abovethe variance will be


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1/9{(10-6.2)^2 +(8-6.2)^2+(-4-6.2)^2+(22-6.2)^2+(8-6.2)^2+(-

11-6.2)^2+(14-6.2)^2+(12-6.2)^2+(-9-6.2)^2+(12-6.2)^2

=1/9 (1029.6)

=114.4


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Now the square root of the varianceis the standard deviation

Hence

S= (114.4)

= 10.7


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The standard deviation gives us a measure oftotalrisk

Butas we shallsee later risk hastwocomponentssystematic risk andunsystematicrisk

Or

Totalrisk= systematic risk+ unsystematic risk

oralsoTotalRisk= nondiversifiable + diversifiablerisks


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Risk in a Traditional Sense

Risk in holding securities is generally associated

with the possibilitythat realized returns will be less than

the returns that were expected.

The source of such disappointment is the

failure of dividends (interest) and/orthe security's price to materialize asexpected.


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Forces that contribute to variationsin return-price or dividend

(interest)-constitute elements ofrisk.

These forces are categorised into

two parts for the purpose ofascertaining risk


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Some influences are external to thefirm, cannot be controlled, and

affect large numbers of securities.

Other influences are internal to thefirm and are controllable to a large

degree.


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systematic &

unsystematic risk.In investments, those forces that are

uncontrollable, external, and broad in

their effect are called sources ofsystematic risk.

Conversely, controllable, internal factorssomewhat peculiar to industries and/or

firms are referred to as sources ofunsystematic risk.


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Systematic risk refers to that portion of totalvariability in return caused by factors affectingthe prices of all securities.

Economic,

political,

and sociological changes

are sources of systematic risk.

Their effect is to cause prices of nearly all-individual common stocks and/or all individualbonds to move together in the same manner.


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Unsystematic risk is the portion of totalrisk that is unique to a firm or industry.

Factors such as management capability,consumer preferences, and labor strikescause systematic variability of returnsin a firm.

Unsystematic factors are largelyindependent of factors affectingsecurities markets in general.


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A BriefReview ofdifferenttypesofRisks


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Sources of Risk

The principle sources of risk which concern

Investors and regulators.y Credit Risk

y Settlement Risk

y Market Risk

y Other Risks


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Credit RiskThe risk of a trading partner not fulfilling his obligations in

full on due date or at any time thereafter is a risk that affectsall aspects of business. Among the risks that face financial

institutions, credit risk is the one with which we are mostfamiliar. It is also the risk to which supervisors of financial

institutions pay the closest attention because it has been therisk most likely to cause a bank to fail.

credit risk is not equal to the principal amount of the trade,but rather to the cost of replacing the contract if the

counterparty defaults. This replacement value fluctuates overtime and is made up of current replacement and potential

replacement costs.


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Market Risk

This is the risk to an institution's financial condition resulting from adversemovements in the level or volatility of market prices of interest rateinstruments, equities, commodities and currencies. Market risk is usually

measured as the potential gain/loss in a position/portfolio that isassociated with a price movement of a given probability over a specifiedtime horizon. This is typically known as value-at-risk (VAR). An institution

with a 10-day VAR of $100 million at 99% confidence will suffer a loss inexcess of $100 million in one fortnightly period out of 20, and then only if it

is unable to take any action to mitigate its loss

Finding stock prices falling from time to time while a company'searnings are rising, and vice versa, is not uncommon.

Variability in return on most common stocks that is due to basicsweeping changes in investor expectations is referred to as market

risk.


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Settlement Risk

Settlement risk is the risk that a settlement in a transfersystem does not take place as expected. Generally, this

happens because one party defaults on its clearing obligationsto one or more counterparties. As such, settlement risk

comprises both credit and liquidity risks. The former ariseswhen a counterparty cannot meet an obligation for full valueon due date and thereafter because it is insolvent. Liquidity

risk refers to the risk that a counterparty will not settle for fullvalue at due date but could do so at some unspecified time

thereafter; causing the party which did not receive its expectedpayment to finance the shortfall at short notice. Sometimes acounterparty may withhold payment even if it is not insolvent(causing the original party to scramble around for funds), soliquidity risk can be present without being accompanied by

credit risk.


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Other RisksInterest - Rate Risk

Interest-rate risk refers to the uncertainty of future market values and

of the size of future income, caused by fluctuations in the general levelof interest rates.

The root cause of interest-rate risk lies in the fact that,

as the rate of interest paid on government securities rises or falls, therates of return demanded on alternative investment vehicles, such as

stocks and bonds issues in the private sector, rise or fall


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Purchasing-Power Risk (Inflation)

. Purchasing-power risk is the uncertainty of the purchasing power of the amounts to be

received.In more everyday terms, purchasing-power risk refers to the impact of inflation or

deflation on an investment.

Investment is the postponement of consumption,

If during the holding period, prices on desired goods and services rise, theinvestor actually loses purchasing power.

Rising prices on goods and services are normally associated with what is referredto a inflation.

Falling prices on goods and services are termed deflation.

Both inflation and deflation are covered in the all-encompassing termpurchasing-power risk


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Business Risk

Business risk is a function ofthe operating conditions faced by a firm

and the variability these conditions inject into operating income and expected

dividends.

To Illustrate

y y

if operating earnings could grow as much as 14 percent or aslittle as 6 percent than a range of risk say from a high of 11 percent

to a low of 9 percent.

y The degree of variation from the expected trend would measure

business risk.

Business risk can be divided into two broad categories: external and internal. Each

firm has its own set of internal risks, and the degree to which it is successful in

coping with them is reflected in operating efficiency.


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Financial Risk

. A firm with no debt financing has no financial risk.

y Financial risk is associated with the way in which a company

finances its activities.

y We usually gauge financial risk by looking at the capital

structure of a firm. The presence of borrowed money or debt in thecapital structure creates fixed payments in the form of interest that

must be sustained by the firm.


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Some More TypesOf Risk

1. liquidity risk, which comes in two forms. Marketliquidity risk arises when a firm is unable to concludea large transaction in a particular instrument atanything near the current market price. Funding

liquidity risk is defined as the inability to obtain fundsto meet cashflow obligations.2. legal risk, which is the risk that a transactionproves unenforceable in law or because it has been

inadequately documented; and3. operational risk, i.e. the risk of unexpected lossesarising from deficiencies in a firm's managementinformation, support and control systems and

procedures.


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Unsystematic Risk

An element of price risk that can be largely

eliminated by diversification within an asset class.

In factor models estimated by regression

analysis, it is equal to the standard error. Alsocalled Security Specific Risk, Idiosyncratic Risk,

Unsystematic Risk.

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