sums

1. RISK RETURN CONCEPT
PROBLEMS

2. CALCULATION OF RISK USING AVERAGE RATE OF RETURN,
STANDARD DEVIATION , VARIANCES AND CALCULATION OF
EXPECTED RETURN:
Formulae:
• Average rate of return (𝑅) = 𝑅 /N
• Variance = (𝑅 − 𝑅)2 / N
• Standard deviation= 𝜎 =
• Expected return = ( P*R)

3. PROBLEM NO: 1
The rate of return of equity shares of Wipro ltd., for the past six years is given
below:
YEAR 1 2 3 4 5 6
RATE OF
RETURN
12 18 -6 20 22 24
Calculate the following:
1.average rate of return,
2.standard deviation
3. variance

4. Solution:
1. calculation of average rate of return :
𝑅 = 𝑅 /N = 12+18-6+20+22+24
6
= 15%
ANS: 15%

5. 2. Calculation of standard deviation and variance:
YEAR RATE OF RETURN 𝑅 − 𝑅 (𝑅 − 𝑅)2
2001 12 -3 9
2002 18 3 9
2003 -6 -21 441
2004 20 5 25
2005 22 7 43
2006 24 9 81
(𝑹 − 𝑹)𝟐
=614
= (𝑅 − 𝑅)2
/ N
=614/6
=102.33
VARIANCE: STANDARD DEVIATION:
𝜎 =
= √102.33
=10.12 %

6. PROBLEM NO:2

7. Return probability P* R 𝑅 − 𝑅 (𝑅 − 𝑅)2 (𝑅 − 𝑅)2*P
-15 0.05 -0.75 -5.5 30.25 1.15125
-10 0.10 -1.0 -0.5 0.25 0.0250
5 0.15 0.75 -4.5 20.25 3.0375
10 0.25 2.50 0.5 0.25 0.625
15 0.30 4.50 5.5 3.025 9.0750
20 0.10 2.00 10.5 110.25 11.0250
30 0.05 1.50 20.5 420.25 21.0125
1.00 𝑅=9.5% (𝑅 − 𝑅)2*P=45.75
Calculation of expected return and risk in terms of standard deviation
Expected return = ( P*R) = 9.55
Standard deviation = (𝑅 − 𝑅)2
*P = √45.75= 6.764

8. FORMULAE FOR ALPHA(α) AND BETA(β)
Beta (β) =N ( XY) - ( X)( Y)
N( 𝑋2) – ( 𝑋)2
Alpha (α) = 𝑌- β𝑋
COVERT PRICE INTO RETURN:
Return = Today’s price (TP) – yesterday’s price(YP) *100
yesterday’s price

9. Problem no :3
consider the daily sale price of Tata auto co., and NSE index for the period of 5th February to 16th February
calculate the alpha &beta for the following
date NSE index Tata auto co.,
5th Feb. 904.95 597.80
6th Feb. 845.75 570.80
7th Feb. 874.25 582.95
8th Feb. 847.95 559.85
9th Feb. 849.10 554.60
10th Feb. 835.80 545.10
13th Feb. 816.75 519.15
14th Feb. 843.55 560.70
15th Feb. 835.65 560.95
16th Feb. 839.50 567.40

10. Solution:
Calculation of alpha and beta:
date x y 𝑋2 XY
5th Feb. - - - -
6th Feb. -6.54 -4.52 42.77 29.56
7th Feb. 3.37 2.13 11.36 7.18
8th Feb. -3.01 -3.96 9.06 11.92
9th Feb. 0.14 -0.94 0.0196 -0.13
10th Feb. -1.57 -1.71 2.46 2.68
13th Feb. -2.28 -4.76 5.20 10.85
14th Feb. 3.28 8.00 10.76 26.24
15th Feb. 0.95 0.04 0.09025 -0.038
16th Feb. 0.47 1.15 0.2209 0.5405
X=-7.09 Y=-4.57 𝑿𝟐
=82.7 XY=88.81

11. • Calculation of beta:
Beta (β) =N ( XY) - ( X)( Y)
N( 𝑋2) – ( 𝑋)2
= 9(88.81) –(-7.09)(-4.57)
9(82.7)- (−7.09)2
= 799.29 – 32.401
744.3- 50.368
= 766.889
694.032
β = 1.10
Calculation of alpha:
Alpha (α) = 𝑌- β𝑋
= -0.507- (1.10)(-0.787)
= -0.507+ 0.8657
α = 0.36

12. Interpretation:
• If 1% increase in market index then 1.10 % increase in stock return
• If alpha is positive then it is profitable