This document contains 15 problems related to risk and return concepts in capital market theory. Problem 1 calculates the total return and percentage return for an investment in shares of L&T. Problem 2 calculates the dividend yield, capital gain percentage, and total share return for an investment based on closing price and dividend information from two years. Problem 3 similarly calculates dividend yield, capital gain percentage, and total percentage return for an investment in shares of Telco. The remaining problems involve calculations related to compound returns, standard deviation, variance, beta, risk premiums, probability distributions, and other capital market concepts.

1. Chapter 4: Risk and Return: An Overview of Capital Market Theory
Problem 1
Purchase price of L&T’s share 212
Number of shares purchased – 1 Jan. 2004 100
Share price on sale after one year – 31 Dec. 2004 215
Total dividend received 700
Capital gain per share: 215 - 212 3
Total capital gain: 3 × 100 300
Total return: 700 + 300 1000
Percentage return: 1,000/(212 × 100) 4.72%
Problem 2
Closing price last year, Rs 50
Dividend per share, Rs 5
Closing price current year, Rs 57
Dividend yield: 5/50 10%
Capital gain percentage: (57 – 50)/50 14%
Percentage total share return: 5/50 + (57 – 50)/50 24%
Problem 3
Purchase price, Rs 87
Number of shares purchased 200
Total price paid for shares, Rs 17,400
Par value of Telco’s share, Rs 10
Dividend rate 15%
Dividend per share (Rs): 10 × 15% 1.5
Total dividend (Rs): 1.50 × 200 300
Realised amount from sale of shares after one year, Rs 18,500
Capital gain: 18,500 – 17,400 1,100
Dividend yield: 1.50/87 or 300/17,400 1.72%
Capital gain percentage: 1,100/17,400 6.32%
Total rupee return: 300 + 1,100 1,400
Total percentage return: 1,400/17,400 or 1.72% + 6.32% 8.05%
Problem 4
90 125 + 4,535
4, 250 = +
(1 + r )1 (1 + r ) 2
By trial and error = 5.8%
Problem 5
Nominal rate of return 17%
Inflation rate 5.50%
Real rate of return:1.17 = (1 + real rate) × (1.055)
Real rate = 1.17/1.055 - 1 10.90%
Problem 6
Share price – Hind & Nirmala - two years ago, Rs 100
Fall in Hind price – after one year -12%
Increase in Hind price after two years 12%
Hind’s share price after two years, Rs: 100 × 0.88 × 1.12 98.56
Fall in Nirmala’s price – after one year 12%

2. Increase in Nirmala’s price after two years -12%
Nirmala’s share price after two years, Rs: 100 × 1.12 × 0.88 98.56
Problem 7
7-year holding period return:
(1.153 × 0.945 × 1.173 ×1.25 × 1.168 ×1.095 × 1.288) -1 = 1.63 or 163% 1.63
Compound rate of return:
= 7
1.153 × 0.945 × 1.173 × 1.25 × 1.168 × 1.095 × 1.288 − 1 = 1 . 15 or 115 % 1.15
Problem 8
Year Return, r (ri - 9.7%)2
1 5.30% 0.19%
2 15.60% 0.35%
3 -7.30% 2.88%
4 15.00% 0.28%
5 19.80% 1.02%
Sum 48.40% 4.73%
Average 9.68%
Variance 0.0118317
Stdev 0.10877362 10.88%
Problem 9
(r i - 12.73%) 2
Year Return, r Prob. r × prob. × Prob
Rapid growth 19.50% 0.15 2.93% 0.07%
Moderate growth 14.00% 0.55 7.70% 0.01%
Recession 7.00% 0.3 2.10% 0.10%
Expected return 12.73%
Variance 0.18%
Stdev 4.20%
Problem 10
Expected Square of
Return, ER Deviation Deviation
Return, Ri Probability, Rip (Ri - ER) (Ri - ER)2
p
20 0.10 2.0 8.1 65.61
18 0.45 8.1 6.1 37.21
8 0.30 2.4 -3.9 15.21
0 0.05 0.0 -11.9 141.61
-6 0.1 -0.6 -17.9 320.41
ER 11.9 å(Ri - ER)2p
STDEV, s 66.99 = 8.18
Problem 11
Security X
Return Probability p Exp. Return Deviation Sq. Deviation
Rx ER = Rxp (Rx - ER) 2
(Rx - ER)
30 0.1 3 19 361
20 0.2 4 9 81
10 0.4 4 -1 1
5 0.2 1 -6 36

3. -10 0.1 -1 -21 441
ER 11 å(Rx - ER)2
920
STDEV, s 1 0 4 = 1 0 .2
Security Y
Return Probability p Exp. Return Deviation Sq. Deviation
Ry ER = Ryp (Ry - ER) (Ry - ER)2
-20 0.05 -1.0 -40.5 1640.25
10 0.25 2.5 -10.5 110.25
20 0.30 6.0 -0.5 0.25
30 0.30 9.0 9.5 90.25
40 0.1 4.0 19.5 380.25
ERy 20.5 2
å(Ry - ER)
2221.25
STDEV, s 1 7 4 .4 5 = 1 3 .2 2
Portfolio of Security XY
Probability, Deviation, X Dev. x Prob. Probability, Y
X
px (Rx - ERx) (Rx - ERx)p py
0.10 19 1.9 0.05
0.20 9 1.8 0.25
0.40 -1 -0.4 0.30
0.20 -6 -1.2 0.30
0.10 -21 -2.1 0.10
Var. X Var. Y Weight X Sq. weight X
varx vary wx 2
w x
104 174.75 0.5 0.25
The formula for calculating the standard deviation of portfolio of X and Y securities is as follows:
2 2 2 2
σ p = σ x × w x + σ y × w y + 2 w xw y c o v ar xy
= 1 0 4 × 0 .2 5 + 1 7 4 .7 5 × 0 .2 5 + 2 × 0 .5 × 0 .5 × -1 6 .0 3
= 6 1.6 7 = 7 .8 5
Problem 12
Security P
Exp. ret Deviation
Probability, Return, RP RP x pP (RP - ERP)
p
0.3 30 9 13
0.4 20 8 3
0.3 0 0 -17
ER 17
STDEV, σP

4. Market portfolio M
Return , RM Exp. ret. Deviation Deviation sq.
RM x pM (RM - ERM) (RM - ERM)2
-10 -3 -24 576
20 8 6 36
30 9 16 256
ERM 14 varM
σM
P M
Standard 11.87 16.25
deviation
Covariance
Correlation corrPM = covarPM/sM sP
Beta 2
bata = corrPMsPsM / s M
Problem 13
Return
Share
Year portfolio Treasury Bills Risk premium
1 22.50% 11.40% 11.10%
2 -6.80% 9.80% -16.60%
3 26.80% 10.50% 16.30%
4 24.60% 9.90% 14.70%
5 3.20% 9.20% -6.00%
6 15.70% 8.90% 6.80%
7 12.30% 11.20% 1.10%
Average 14.04% 10.13% 3.91%
Realised premium is based on historical data, and as we can see from the above table, in some years it can be negative. The
average risk premium is expected to be positive when a very long period of time, covering various phases of economic cycles,
is considered.
Problem 14
Return Expected return
Economic state Prob. Market Treasury Bills Market
Growth 0.2 28.50% 9.70% 5.70%
Decline 0.3 -5.00% 9.50% -1.50%
Stagnation 0.5 17.90% 9.20% 8.95%
Average 13.80% 9.47% 4.38%
Problem 15
0 − 20 . 0
S= = − 2 .0
10 . 0
S equal to -2 implies that zero return is positioned 2 standard deviations to the left of the expected value of the probability distributions of possible returns.
The probability of being less than 2 standard deviations from the expected value is 0.0228 (see Annexure Table F). This means that there is 2.28%
probability that the return will be zero or less. There is about 67% probability that the return would range between 10% and 30%. There is 95% chance that
the return will be between zero [20% - 2 × 10%] and 40% [20% + 2 × 10%].
Problem 16
30 . 0 − 22 . 0
S= = 0 . 32
25 . 0
S equal to 0.32 lies to the right of the expected value. From Annexure Table F, we find that there is about 12.6 % probability that the return will be 30% or more.

6. Product
(Ri - ER)2p
6.56
16.74
4.56
7.08
32.04
66.99
8.18 8.18
Product
2
(Rx - ER) p
36.1
16.2
0.4
7.2

7. 44.1
å(Rx - ERx)2p
104
10.20
Product
2
(Ry- ER) p
82.0125
27.5625
0.075
27.075
38.025
2
å(Ry - ER) p
174.75
22 13.22
Covariance
Deviation, Y Dev. x Prob. (Rx - ERx)p
(Ry - Ery) 2 2
(Ry - Ery) p x (Ry - Ery) p
-40.5 -2.03 -3.85
-10.5 -2.63 -4.73
-0.5 -0.15 0.06
9.5 2.85 -3.42
19.5 1.95 -4.10
Covxy -16.03
Weight Y Sq weight Y Cov. XY Var XY SD XY
wy 2 covxy varxy sxy
wy
0.5 0.25 -16.03 61.67 7.85
Deviation sq.
2 2
(RP - ERP) (RP - ERP) p
169 50.7
9 3.6
289 86.7
varP 141
11.87

8. [(RP - ERP) [(RP - ERP)
2 (RM - ERM)] (RM - ERM)]p
(RM - ERM) pM
172.8 -312 -93.6
14.4 18 7.2
76.8 -272 -81.6
264 covarPM -168
16.25
-168
-0.871
-0.636
Expected return
Risk
Treasury Bills premium
1.94% 3.76%
2.85% -4.35%
4.60% 4.35%
3.13% 1.25%
ue of the probability distributions of possible returns.
xure Table F). This means that there is 2.28%
nge between 10% and 30%. There is 95% chance that
bout 12.6 % probability that the return will be 30% or more.