Risk and Return2

8/14/2019 Risk and Return2

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Risk and Return


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What are investment returns?

n Investment returns measure thefinancial results of an investment.

n Returns may be historical or prospective (anticipated).

n Returns can be expressed in:l Rupee terms .l Percentage terms .


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Return

Single period returnPo = Rs.300, P 1 = Rs.350

Return for the period is . %

P2 = 250

Return for the entire period .?Period-wise return ?


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Ex-post Returns

Return = current income + capitalgains

[(P2

P1

) + D2] / P

1


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Expected Return

Different scenario Chance / probability

Return in case of each chanceChance return10% 30%23% 40%

67% 25%Expected return ?


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Expected return from pf

E =E 1W1 + E 2 W2 + E 3 W 3E expected return

W proportion of money invested


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ReturnReturn : It is the primary motivating force that

drives investment. It represents the reward for undertaking the

investment. In security analysis we areprimarily and particularly concerned withreturns from investors perspective.

The return of an investment consists of twocomponents : (i) Current return (ii) Capitalreturn.

1 Current return : Periodic cash flow (income)such as dividend and interest. This can bezero or positive.

2 Capital return : The price appreciation orprice changes. This can be zero, positiveand negative also.

Thus Total Return = Current return + Capitalreturn


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What is investment risk?

n Typically, investment returns are notknown with certainty.

n Investment risk pertains to theprobability of earning a return lessthan that expected.

n The greater the chance of a return far below the expected return, thegreater the risk.


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Risk

Variability of security returns Standard deviation, variance

SD is extent of deviation from theaverage value of return = squareroot of variance and variance isthe average of squares deviationsof observed returns from expectedvalue of returns


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Assume the Following

Investment AlternativesEconomy Prob. T-Bill Alta Repo Am F. MP

Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0%

Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0

Average 0.40 8.0 20.0 0.0 7.0 15.0

Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0

Boom 0.10 8.0 50.0 -20.0 30.0 43.0

1.00


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What is unique about

the T-bill return?

n

The T-bill will return 8% regardlessof the state of the economy.n Is the T-bill riskless? Explain.


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In this context of security analysis, weinterpret risk essentially in the terms of thevariability of the security return. The mostcommon measures of risk ness of security isSD and Variance of return.

Given below returns of two stocks X and Y.

Period Return of stock X(%) Return of stockY(%)1 -6 42 3 63 10 114 13 155 16 19

Calculate which stock is more risky ?


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Mean of X = 36/5 = 7.2 =XMean of Y = 55/5 =11=YVariance of X = (X- X) 2 /(n -1)= 310.80/(5-1)= 77.7 and

the S.D =77.7=8.815

PeriodPeriod XX YY (X X)(X X) (Y Y)(Y Y) (X X)(X X) 22 (Y Y)(Y Y) 2211 -6-6 44 -13.2-13.2 -7 174.24 4949

22 33 66 -4.2-4.2 -5-5 17.6417.64 252533 1010 1111 2.82.8 00 7.847.84 0044 1313 1515 5.85.8 44 33.6433.64 161655 1616 1919 8.88.8 88 77.4477.44 6464

SumSum 3636 5555 310.84310.84 154154


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The expected return would be E(R) =(0.25*36)+(0.50*26)+(0.25*12) = 25%

The risk of the stock :2 =P

i*[R

i E(R)] 2

=(36-25) 2 *0.25 + (26-25) 2 * 0.50 + (12-25) 2 *0.25= 73%

SD = 8.54%

EconomicEconomicscenarioscenario

Probability of Probability of occurrenceoccurrence

Return fromReturn fromstock A(%)stock A(%)

BoomBoom 0.250.25 3636

StagnationStagnation 0.500.50 2626

RecessionRecession 0.250.25 1212


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Calculate the expected rateof return on each alternative.

.n

1=i

iiPr=r

r = expected rate of return.

r Alta = 0.10(-22%) + 0.20(-2%)+ 0.40(20%) + 0.20(35%)+ 0.10(50%) = 17.4% .

^

^


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n Alta has the highest rate of return.n Does that make it best?

r Alta 17.4%Market 15.0Am. Foam 13.8T-bill 8.0Repo Men 1.7

^


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What is the standarddeviation

of returns for eachalternative?

.

Variance

deviationStandard

1

2

2

=

=

==

=

n

i

ii P r r


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T-bills = 0.0%. Alta = 20.0%.

Repo = 13.4%. Am Foam = 18.8%. Market = 15.3%.

.1

2

=

=

n

iii

P r r

Alta Inds:

= ((-22 - 17.4)2

0.10 + (-2 - 17.4)2

0.20+ (20 - 17.4) 20.40 + (35 - 17.4) 20.20+ (50 - 17.4) 20.10) 1/2 = 20.0%.


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Prob.

Rate of Return (%)

T-bill

Am. F.

Alta

0 8 13.8 17.4


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Expected Return versus RiskExpected

Security return Risk, Alta Inds. 17.4% 20.0%Market 15.0 15.3Am. Foam 13.8 18.8T-bills 8.0 0.0Repo Men 1.7 13.4


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Coefficient of Variation:CV = Expected return/standard

deviation.CV T-BILLS = 0.0%/8.0% = 0.0.

CVAlta Inds = 20.0%/17.4% = 1.1.

CVRepo Men = 13.4%/1.7% = 7.9.

CVAm. Foam = 18.8%/13.8% = 1.4.

CVM = 15.3%/15.0% = 1.0.


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Expected Return versus

Coefficient of VariationExpected Risk: Risk:

Security return CVAlta Inds 17.4% 20.0% 1.1Market 15.0 15.3 1.0Am. Foam 13.8 18.8 1.4T-bills 8.0 0.0 0.0Repo Men 1.7 13.4 7.9


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AltaMkt USR

T-bills

Coll.0.0%2.0%4.0%6.0%8.0%10.0%

12.0%14.0%16.0%18.0%20.0%

0.0% 10.0% 20.0% 30.0%

R e t u r n

Risk (Std. Dev.)

Return vs. Risk (Std. Dev.):Which investment is best?


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# Stocks in Portfolio

10 20 30 40 2,000+

Company Specific(Diversifiable) Risk

Market Risk20

0

Stand-Alone Risk, p

p(%)

35


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Stand-alone Market

DiversifiableMarket risk is that part of a securitys

stand-alone risk that cannot beeliminated by diversification.

Firm-specific , or diversifiable , risk isthat part of a securitys stand-alone riskthat can be eliminated bydiversification.

risk risk risk= + .

R d i f i k h h


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Reduction of risk throughDiversification

Security Analysis: Measuring risk &return.

Portfolio Mgt: minimize risk or maximizereturn.

Example:Concept of Covariance: the degree to

which the return of two securities varyor change together.

Concept of Correlation: the degree of relationship between two variables.


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No. Rational investors will minimizerisk by holding portfolios.

They bear only market risk, soprices and returns reflect thislower risk.

The one-stock investor bears higher(stand-alone) risk, so the return isless than that required by the risk.

Can an investor holding one stock earn

a return commensurate with its risk?


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How are betas calculated?

In addition to measuring a stockscontribution of risk to a portfolio,beta also which measures the

stocks volatility relative to themarket .


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Thanks

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Risk and Return2