Illustration 1
Calculate the expected rate of return from the following information relating to B Ltd.
State of the Economy  Probability of Occurrence  Rate of Return 
Boom
Normal Recession 
0.30
0.50 0.20 
40%
30% 20% 
Illustration 2
An investor would like to find the expected return on the share of Golden Ltd. The following data have been available:
State of the Economy 
Probability of Occurrence 
Rate of Return (%) 
Boom
Normal Recession 
0.30 0.50 0.20 
30 18 10 
Calculate the expected return from the share.
Illustration 3
Given below are the likely returns in case of shares of VCC Ltd. and LCC Ltd. in the various economic conditions. Both the shares are presently quoted at 100 per share.
Economic Conditions 
Probability 
Returns of VCC Ltd. 
Returns of LCC Ltd. 
High Growth
Low Growth Stagnation Recession 
0.3 0.4 0.2 0.1 
100 110 120 140 
150 130 90 60 
Which of the two companies are risky investments?
Illustration 4
The rate of return of stocks of A and B under different states of economy are presented below along with the probability of the occurrence of each state of the economy.

Boom 
Normal 
Recession 
Probability of Occurrence
Rate of Return on stock A (%) Rate of Return on stock B (%) 
0.3 20.0 50.0 
0.4 30.0 30.0 
0.3 50.0 20.0 
(a) Calculate the expected rate of return and standard deviation of return for stocks A and for stocks B.
(b) If you could invest in either stocks A or stocks B, but not in both, which stock would you prefer and why?
(c) If the rate of return on stocks A was revised as shown below, would your preference in question (b) above change? Why?
Boom 
Normal 
Recession 

Rate of Return on stock A (%) 
50.0 
40.0 
30.0 
Illustration 5
Shankar has been considering investment in stock X or Y. He has estimated the following distribution of returns of stock X and Stock Y.
Return on stock X 
Return on stock Y 
Probability 
– 10 0 10 20 30 
05 10 15 20 25 
10 25 40 20 05 
Illustration 6
The rate of return on Stocks X and Y under different states of the economy are given below:
Boom 
Normal 
Recession 

Probability of occurrence
Rate of Return on stock X (%) Rate of Return on stock Y (%) 
0.35 20 40 
0.50 30 30 
0.15 40 20 
(i) Calculate the expected return and standard deviation of return on both the stocks.
(ii) If you could invest in either stocks X or stock Y, but not in both, which stock would you prefer?
(iii) What would be your decision if the probability changes to 0.30: 0.40: 0.30?
Illustration 7
Calculate the holding period return in the following example:

A Ltd. () 
B Ltd. () 
Price as on 3132010
Price as on 3132011 Dividend for the year 
20 15 1 
10 15 1 
Illustration 8
In January 2011, Mr. Dhimant Kapadia purchased the following 5 scrips:
Co.’s Name 
No. of Shares 
Purchase Price 
H Ltd.
C Ltd. S Ltd. F Ltd. M Ltd. 
100 100 100 100 100 
250 180 80 240 260 
He paid brokerage of 1,500
During the year 2011, Mr. Dhimant Kapadia received the following:
Co’s Name 
Dividend 
Bonus Shares 
H Ltd.
C Ltd. S Ltd. F Ltd. M Ltd. 
300 290 450 500 600 
1:2 







In January 2012, Mr. Dhimant Kapadia sold all his holdings at the following prices:
Co’s Name 
Market Price 
H Ltd. 
275 
C Ltd. 
240 
S Ltd. 
108 
F Ltd. 
200 
M Ltd. 
400 
He paid brokerage of 1,865.
Calculate the holding period return.
Illustration 9
Dr. Shah purchased 400 shares of Sundar Ltd. @ 61 each on 15^{th} Oct 2008. He paid a brokerage of 600. The company paid the following dividends:
June 2009  800 
June 2010  1000 
June 2011  1,200 
He sold his holdings for 34,500 (net) on 15th October, 2011.
(1) What is the holding period return? (2) What is the annualized return? (3) Is Mr. Shah a good investor?
Illustration 10
Mr. Ashok purchased 10 shares of ACC Ltd. four years ago at 50 each. The company paid the following dividends.

Year l 
Year 2 
Year 3 
Year 4 
Dividend per Share () Dividend Amount () 
2 20 
2 20 
2.5 25 
3 30 
The current price of the share is 60. What rate of return has he earned on his investment if he sells the shares now?
Illustration 11
You own a portfolio that is 60% invested in Stock X, 25% in stock Y and balance in Stock Z. The excepted returns on these stocks are 12%, 16% and 19% respectively. What is the expected return on the portfolio?
Illustration 12
You have 10000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 18% and Stock Y with an expected return of 11%. If your goal is to create a portfolio with an excepted return of 16.5%, how much money will you invest in Stock X and in Stock Y?
Illustration 13
Rahul invest the following sums of money in common stocks having expected return as follows:
Security  Amount Invested () 
Expected Return 
Moser Baer 
6000 
14% 
Kirloskar Cummins 
11000 
16% 
FDC Ltd. 
9000 
17% 
Novartis India 
7000 
13% 
GTL 
5000 
20% 
Pfizer 
13000 
15% 
Excel Industry 
9000 
18% 
 What is the expected % return on his portfolio?
 What would be his expected return if Rahul quadruples his investment in GTL while leaving everything else the same?
Illustration 14
The common stocks of Bajaj and TVS have expected returns of 15% and 20% respectively, while the standard deviations are 20% and 40%. The excepted correlation coefficient between the two stocks is 0.36. What is the excepted value of return and the standard deviation of a portfolio consisting of: (a) 40% Bajaj and 60% TVS? (b) 40% TVS and 60% Bajaj?
Illustration 15
Mr. X is interested to build a portfolio of investment comprising of riskfree securities (R_{f} = 8%) and the market portfolio (R_{m} = 18% and Standard deviation = 6%). The minimum expected rate of return of the investor is 15%. In what proportion should he hold the riskfree securities and the market portfolio? Also calculate the expected risk if correlation between the two stock is 0.24.
Illustration 16
(a) Stock A has an expected return of 18% and a standard deviation of 30%. Stock B has expected return of 12% and a standard deviation of 36%. The correlation between the two stocks is 0.25 if you form a portfolio where you put 40% of your money in A and 60% in B, what is the expected return and standard deviation for the portfolio?
(b) How will the excepted return and standard deviation change if the correlation between the two stocks is zero?
Illustration 17
You have decided to invest 40% of your wealth in McDonalds which has an excepted return of 15% and a standard deviation of 15%, and 60% of your wealth in GE which has an excepted return of 9% and a standard deviation of 14%.
a) What is the excepted return of your portfolio?
b) If the correlation between McDonalds and GM is 0.5, what is the standard deviation of your portfolio?
c) If you wanted an excepted return of 13%, what percentage should you invest in McDonalds?
Based on your percentage in part C, what would the standard deviation of this portfolio be?
Illustration 18
Following are the price and other details of three stocks for the year 20X1. Calculate the total return as well as the return relative for each of three stocks.
Stock 
Beginning Price 
Dividend Paid 
Ending Price 
A B C 
30 72 140 
3.40 4.70 4.80 
34 69 146 
Illustration 19
During the past five years, the returns of a stock were as follows:
Year 
Return 
1 2 3 4 5 
0.07 0.03 – 0.09 0.06 0.10 
Compute the following: (a) cumulative wealth index, (b) arithmetic mean, (c) geometric mean, (d) variance, and (e) standard deviation.
Illustration 20
You are thinking of acquiring some shares of ABC Ltd. The rates of return expectations are as follows:
Possible rate of return 
Probability 
0.05 0.10 0.08 0.11 
0.20 0.40 0.10 0.30 
Compute the expected return E(R) on the investment.
Illustration 21
The returns of two assets under four possible states of nature are given below:
State of nature 
Probability 
Return on asset 1 
Return on asset 2 
1 2 3 4 
0.10 0.30 0.50 0.10 
5% 10% 15% 20% 
0% 8% 18% 26% 
a. What is the standard deviation of the return on asset 1 and asset 2?
b.What is the covariance between the returns on assets 1 and 2?
c. What is the coefficient of correlation between the returns on assets 1 and 2?
Illustration 22
A portfolio consists of 3 securities, 1, 2, and 3. The proportions of these securities are w_{1} = 0.3, w_{2} = 0.5, and w_{3} = 0.2. The standard deviations of returns on these securities (in percentage terms) are: = 6, = 9, and = 10. The correlation coefficients among security returns are p_{12} = 0.4, p_{13} = 0.6, p_{23} = 0.7. What is the standard deviation of portfolio returns?
Illustration 23
The following information is available.

Stock A 

Stock B 
Expected return
Standard deviation Coefficient of correlation 
16% 15% 
0.60 
12% 8% 
(a) What is the covariance between stocks A and B?
(b) What is the expected return and risk of a portfolio in which A and B have weights of 0.6 and 0.4?
Illustration 24
The rate of return on stocks of Ben and Ten under different states of the economy are presented below along with the probability of the occurrence of each state of the economy.
Particulars 
Boom 
Normal 
Recession 
Probability of occurrence 
0.3 
0.5 
0.2 
Rate of Return on Stock Ben (%) 
25 
35 
45 
Rate of Return on Stock Ben (%) 
45 
35 
25 
(i) Calculate the expected rate of return and standard deviation of return on stock Ben and Ten.
(ii) If you could invest in either stock Ben or stock Ten, but not in both, which stock would you prefer?
Illustration 25
Ms. Manasi has invited in Mumbai and Goa Limited in the proportion of 40% and 60%. The returns from these companies are given below:
Year 
Mumbai Limited 
Goa Limited 
1 
20% 
24% 
2 
30% 
36% 
Standard Deviation of both the companies is 3.
Calculate:
(i) Expected return of Manasi’s portfolio
(ii) Covariance between Mumbai Limited and Goa Limited.
(iii) Portfolio Risk for Manasi.
Illustration 26
(A) Explain Capital Market Line with suitable diagram and example.
(B) Solve following:
Particulars 
Initial Price 
Market Price (at the end of the year) 
Beta Risk factor 
A 
13 
19 
1.25 
B 
20 
25 
1.00 
C 
24 
30 
1.33 
Riskfree Return may be taken at 10% you are required to calculate.
(i) Expected Rate of Return of Portfolio in each by using CAPM
(ii) Average Returns of Portfolio
Illustration 27
The stock of Box Limited performs relatively well to other stocks during recessionary periods. The stock of Cox Limited, on the other hand, does well during growth periods. Both the stocks are currently selling for 100 per share. You assess the rupee return (dividend plus price) of these stocks for the next year as follows:

Economic Condition 

High growth 
Low growth 
Stagnation 
Recession 

Probability
Return on Box’s stock Return on Cox’s stock 
0.3 100 150 
0.4 110 130 
0.2 120 90 
0.1 140 60 
Calculate the expected return and standard deviation of investing:
(a) 1,000 in the equity stock of Box Limited
(b) 1,000 in the equity stock of Cox Limited
(c) 500 each in the equity stock of Box Limited and Cox Limited.
Illustration 28
The Returns of 2 Assets, under four possible states of nature, are given below:
State of Nature 
Probability 
Returns on Asset 01 
Returns on Asset 02 
1 
0.10 
5% 
0% 
2 
0.30 
10% 
8% 
3 
0.50 
15% 
18% 
4 
0.10 
20% 
26% 
Find out: (i) Standard Deviation for Asset 01 and Asset 02.
(ii) Covariance between Returns of Asset 01 and 02.
(MU,BFM, Apr. 2011)
Illustration 29
Solve following:
Particulars  Initial Priel  Market Priel
(at the end of the year) 
Beta Risk facton 
A 
13 
19 
1.25 
B 
20 
25 
1.00 
C 
24 
30 
1.33 
Riskfree Return may be taken at 10% you are required to calculate.
(i) Expected Rate of Return of Portfolio in each by using CAPM.
(ii) Average Returns of Portfolio.
(MU,BFM, Apr. 2011)
Illustration 30
Mr. Anil purchased 2500 shares, of JKL Ltd. @ 20/ each (Face Value 5 per share) and paid brokerage @ 2% on 01012009. The company paid dividend @ 50% each year he sold all the shares at 25/ each on 31122010 and paid brokerage of 1,200/.
The other investment alternative available to him was SBI Fixed Deposit carrying interest @ 12% p.a., for year on compounded basis.
Was his decision to go for share investment right? Offer your comments with reasoning. 10
(MU, BMS, Apr. 2011)
Illustration 31
Mr. Anil purchased 200 Shares of JKL Ltd. @ 200/ each (Face Value 5 per share) and paid brokerage @ 1.50% on 01012009. On 17072010 the company declared Bonus Shares in the ratio of 1:1. He received no dividend on these shares in 2009. But on 24122010 the company paid dividend @ 40% dividend. He sold all the shares at 150/ each on 31122010 and paid brokerage of 1,200/. What is the yearly rate of return on his investment?
Rate the quality of the investment as a Investment Consultant. (MU, BMS, Oct. 2011)
For Solution/ Answer Please refer IAPM Textbook By Author Pawan Jhabak, Himalaya Publication.
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