This presentation deals in basic concepts of risk and return in Security Analysis

1. Risk & Return
Dr. Vinita Kalra
Associate Professor
RSMT

2. 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

3. 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

4. Risk & Return of Shares

5. Risk & Return of Portfolio
Share
Economy
Proportion Good Avg Poor
1 0.5 10 7.5 5
2 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 0.242
Variance 0.49
Standard Deviation
(%) 0.7

6. 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

7. Beta Computation ( β )
Month
Returns on
Security(%)=Y
Return on
Market(%)=X
X*Y X2
Jan 6.06000 7.89000 47.81340 62.25210
Feb -2.86000 1.51000 -4.31860 2.28010
Mar -8.18000 0.23000 -1.88140 0.05290
Apr -7.36000 -0.29000 2.13440 0.08410
May 7.76000 5.58000 43.30080 31.13640
Jun 0.52000 1.73000 0.89960 2.99290
Jul -1.74000 -0.21000 0.36540 0.04410
Aug -3.00000 -0.36000 1.08000 0.12960
Sep -0.56000 -3.58000 2.00480 12.81640
Oct -0.37000 4.62000 -1.70940 21.34440
Nov 6.93000 6.85000 47.47050 46.92250
Dec 3.08000 4.55000 14.01400 20.70250
Total 0.2800000 28.52000 151.17350 200.75800
No of Observations 12
Average 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

8. 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 11.08129
β 1.13184813

9. 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 j
Rf =risk free rate of return
Bj = beta coefficient of security j
km = return on market portfolio

10. 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 j
Rf =risk free rate of return
Bj = beta coefficient of security j
km = return on market portfolio