Risk & Return

Dr. Vinita KalraAssociate Professor

RSMT

Variance

Where, VAR (k) = Variance of returns

Pi = Probability of ith possible outcome

ki = Rate of return of ith possible outcome

k = Expected rate of Return

n = Number of possible values of returns

Computation of Standard Deviation

Possible Outcomes

ki (%) ki - ќ (ki - ќ)2 Pi Pi(ki - ќ)2

1 50 40 1600 0.1 160

2 30 20 400 0.2 80

3 10 0 0 0.4 0

4 -10 -20 400 0.2 80

5 -30 -40 1600 0.1 160

∑ Pi( ki - ќ)2 = 480

Risk & Return of Shares

Risk & Return of Portfolio

ShareEconomy

Proportion Good Avg Poor1 0.5 10 7.5 52 0.5 6 7.5 9 1 16 15 14

Probability 30% 50% 20%

Expected Return 4.8 7.5 2.8 15.1

State of Economy Good Average Poor Exp Rate (%)Probability (p) 0.3 0.5 0.2

15.10%Return (R in %) 16 15 14

Deviations 0.9 -0.1 -1.1(Deviation)2 0.81 0.01 1.21

p x (Deviation)2 0.243 0.005 0.242Variance 0.49

Standard Deviation (%) 0.7

Coefficient of Correlation

Conditions

Economic Scenario

Good Average Poor

Returns % Expected Return

X Ltd 20.00 15.00 10.00 15.50

Y Ltd 12.00 15.00 18.00 14.70

Covariance

Probability (p) 30% 50% 20%

Deviation (X Ltd) 4.5 -0.5 -5.5

Deviation (Y Ltd) -2.7 0.3 3.3

p x Product of Deviations -3.65 -0.08 -3.63

Covariance -7.35

Coefficient of correlation -1

Beta Computation ( β )

Month Returns on Security(%)=Y

Return on Market(%)=X X*Y X2

Jan 6.06000 7.89000 47.81340 62.25210Feb -2.86000 1.51000 -4.31860 2.28010Mar -8.18000 0.23000 -1.88140 0.05290Apr -7.36000 -0.29000 2.13440 0.08410May 7.76000 5.58000 43.30080 31.13640Jun 0.52000 1.73000 0.89960 2.99290Jul -1.74000 -0.21000 0.36540 0.04410

Aug -3.00000 -0.36000 1.08000 0.12960Sep -0.56000 -3.58000 2.00480 12.81640Oct -0.37000 4.62000 -1.70940 21.34440Nov 6.93000 6.85000 47.47050 46.92250Dec 3.08000 4.55000 14.01400 20.70250

Total 0.2800000 28.52000 151.17350 200.75800

No of Observations 12Average 0.023333333 2.376666667

β= ((12*151.1735)-(.2800*28.52))/( (12*200.7580)-(28.52)2 )β 1.13184813

α= .023333-(1.13184813*2.376666667)α -2.66669272

Beta Computation (β)

Month kj ki-kj km km-km P P(ki-kj)(km-km) P(km-km)2

Jan 6.06 6.03667 7.89 5.51333 1/12 2.77351 2.53307

Feb -2.86 -2.88333 1.51 -0.86667 1/12 0.20824 0.06259

Mar -8.18 -8.20333 0.23 -2.14667 1/12 1.46749 0.38401

Apr -7.36 -7.38333 -0.29 -2.66667 1/12 1.64074 0.59259

May 7.76 7.73667 5.58 3.20333 1/12 2.06526 0.85511

Jun 0.52 0.49667 1.73 -0.64667 1/12 -0.02676 0.03485

Jul -1.74 -1.76333 -0.21 -2.58667 1/12 0.38010 0.55757

Aug -3.00 -3.02333 -0.36 -2.73667 1/12 0.68949 0.62411

Sep -0.56 -0.58333 -3.58 -5.95667 1/12 0.28956 2.95682

Oct -0.37 -0.39333 4.62 2.24333 1/12 -0.07353 0.41938

Nov 6.93 6.90667 6.85 4.47333 1/12 2.57465 1.66756

Dec 3.08 3.05667 4.55 2.17333 1/12 0.55360 0.39361

Average 0.023333 2.376667

Total 1 12.54233611 11.08129β 1.13184813

Capital Asset Pricing Model

The CAPM is represented mathematically by

Kj = Rf + Bj(km-Rf)

Where,

Kj = expected or required rate of return on security jRf =risk free rate of return

Bj = beta coefficient of security jkm = return on market portfolio