Finmanrisk and Return

8/13/2019 Finmanrisk and Return

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Risk Risk is defined as the variability of return

(dividend, capital gain/loss-change in price etc.)from those that are expected.

Example :

Treasury bond is govt. bond whose price is mostlyfixed. Therefore it is the least risky of all bonds andshares.

Commercial shares/ bonds may be more risky

compared to Treasury bonds.


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Return The return from holding an investment over some

period- say , a year- is simply any cash paymentsreceived due to ownership, plus the change inmarket price, divided by the beginning year price.

For common stock, we define one period return as

R = Dt +(Pt Pt-1) / Pt-1 where R = actual/expectedreturn

T = time period

Dt= cash dividend / cash equivalent of bonus share

at end of time period, Pt an Pt-1 is the price of stock at time period t and t-1


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Using Probability distributions to

measure risks.

Return received from a security is different fromreturn expected.

For risky securities, the actual rate of return can beviewed as a random variable subject to a probability

distribution.


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Suppose that likely oneyear return from investing in a

particular security were as in the table below (%):

Possible

Return

Probability of

occurrence

Expected

Return

Calculation

Variance calculation

-0.10 0.05 -0.005 (-0.10-0.09)**2 x (0.05)

-0.02 0.10 -0.002(-0.02-0.09)**2 x(0.10)

0.04 0.20 0.008 (0.04-0.09)**2 x(0.20)

0.09 0.30 0.027 (0.09-0.09)**2 x(0.30)

0.14 0.20 0.028(0.14-0.09)**2 x(0.20)

0.20 0.10 0.020 (0.20-0.09)**2 x(0.10)

0.28 0.05 0.014 (0.28-0.09)**2 x(0.05)

Sum= 1.00Sum =0.090 =R Sum =0.00703 = variance

Std.dev =0.00703**0.5=0.0838


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The variability of the return is measured by standarddeviationgiven by the formula:

Std.dev= [Sum (Ri Avr.Ri)**2 (Pi)]**0.5

Where Ri = return from i-the event

Avr Ri = Average of Ri Pi = probability of the return

In the last table, standard deviation is found to be 8.38%


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Larger is the standard deviation,

grater is the risk. Distribution 1 with smaller standard deviation

Distribution 2 with larger stand.

Dev.

Expected value

Expected value


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As shown in the previous diagram,two distributions can have equalexpected values but differentstandard deviation and hence

different risks.


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Risk measured by Expected Return

and Standard deviation. Suppose that a company X has expected return equal

to 9% and standard deviation equal to 8.38%. What

does these mean?

It means that Share X is expected to give a 9% returnand that the risk is that likely average deviation from

the mean return (e.g.,9%) is 8.38%.


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Risk measured by Expected Return

and Standard deviation.

Suppose further that share Y gives 9% return but its

standard deviation is 24%. What does it mean?

It means share Y is more risky, even though theexpected return is same for both.


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Comparison of risk between two

investments

Investment X Investment Y

Expected Return 9% 24%

Standard deviation 8.38% 12%


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From the last table, we can see that Investment X willgive 9% return but the risk is that the variability ofthe return is 8.38%.

Whereas, Investment Y will give 24% return but therisk is that the variability of the return is higher at 12%


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Use of coefficient of variation to

measure riskWe see that relative to the amount of expected return

of X, investment X has greater variation or risk.

To adjust for the expected return, coefficient ofvariation is calculated to measure risk.


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From previous table, we find that Coefficient ofVariation (CV) provides a correct measure of risk.

This shows Risk per unit of the expected return. The larger is CV, he larger the relative risk from

investment.


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F I

N

A L


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Portfolio Risk So far we have considered investment is individual

share or bond.

However, in real life, investment is made on a number

of shares or bond e.g., a portfolio. The expected return from portfolio is calculated by

multiplying expected return from that security withproportion of total fund invested in that security.


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Example of portfolios Expected return and Covariance to measure risk

Share X Share Y Share Z For the PortfolioExpected return

is 0.09

Expected return is

0.24

Expected return

is 0.15

Expected Return of

portfolio is weighted exp.

Return e.g., 0.16

40% of fundinvested

35% of fundinvested

25% of fundinvested

Standard dev is

0.0838

Cov. Is 0.93

Standard dev is

0.12

Cov.is 0.50

Standard dev is

0.10

Cov.is 0.66

Weighted standard

deviation 0.1139

weighted

co variances = 0.712


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Portfolios Systematic and

Unsystematic risk Systematic risk is unavoidable risk or non-

diversifiable risk due to overall market conditionaffected by changes in a nations economy, tax

reforms, world-recession etc. It affects all securities uniformly

Unsystematic risk is specific to the company. Thisrisk is avoidable by portfolio balance/diversification.


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The Capital Asset Pricing Model

According to the Capital Asset Pricing Model ofWilliam Sharpe- noble prize winner, a security inmarket equilibrium, is supposed to provide anexpected return commensurate with its systematicrisk- the risk that cannot be avoided with

diversification and the unsystematic risk that can beavoided.

If the security fails to cover the systematic andunsystematic risk, investors will switch to other

securities.

CAPM d l i d i th i i f i k iti


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CAPM model is used in the pricing of risky securitiesexperiencing systematic and unsystematic risks.

CAPM is expressed as below:

Ra = Rf + B (Rm Rf)

Ra = Expected return from a security A

Rf = Risk free rate

B = Beta a measure of risk

Rm = Expected or Average Return from

share market

Ra = Rf + B (Rm Rf)

Th b f l h


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The above formula shows

1. Return from security should be such that it covers thetime value of money or risk free rate (Rf).

2. Return from share market measured as (Rm-Rf)should be +ve.

3. Moreover Return should be such so as to compensate

the risk factor (unsystematic) attached e.g., (beta) B(that depends on the risk-class of security)

This rate Ra = Rf + B (Rm-Rf)is necessary to keep-away a

investor from investing in other market securities than thesecurity in question to cover systematic and unsystematicrisk.


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If the security belongs to a more risky class, (beta=B)value will be higher, B value ranges from 0 to infinity.

Using the CAPM model , we can compute the expectedreturn of a security.

Suppose in a given situation, the risk-free rateis 3%, the beta (risk factor) of the security is 2

and the expected market return over the period is10%, the securitys expected return will be 17%

=(3%+2(10%-3%)).


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The characteristic line depicts the relationship

between a shares excess expected return(return in excess of the risk-free rate) and themarketsexcess expected return.

The slope (rise over run) of the characteristicline known as beta is an index of systematicrisk.

According to CAPM, the greater the beta,greater is the systematic/ unavoidable risk.

Therefore is the expected rate required to holdthat security.


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CAPMExcess Return

Required on a

Particular Share

Excess Return on Market

Portfolio

Characteristic line

Beta= slope,

rise over run

If dotted line is the

characteristic line of a share,

higher excess return is

required than when the

characteristic line is the solid

line.


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The Risk and Term Structure

Different bonds with same maturity are found to havedifferent rate of interest.

This is shown for three shares as shown below:

Tk 1000 per bond after1 year

X

Y

Z

Less RiskMore Risk

Most Risk

Tk 950Tk 900

Tk800

5.3%11.1%

25%

C i l / Sh M k Adj D


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Capital / Share Market Adjustment Due to

Unsystematic risk (+/-)

Price of Bond/ Share

D1D2

S1

S1

D1

D2

Return/Inte

rest Rate

Risk Premium

Risky Bonds

demand will shrink

Demand for Share Markets

other share will increase to

that extent.

Return/Interest

Rate


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Finmanrisk and Return