Math of Risk & Return

1. Risk n Return
1. There are two assets and three states o the economy:
States of the
Economy
Probability Rate of Return
Stock- A Stock- B
Recession 0.15 0.28 0.32
Normal 0.35 0.32 0.35
Boom 0.25 0.55 0.45
Required:
a. What are the expected return?
b. What will be the variance?
c. What will be the standard deviation or these two stocks?

2. 2. Microsoft Inc. is considering two mutually exclusive project X and project Y
costing Tk. 80,000 and Tk. 95,000 respectively:
Required:
Expected Value of Two Projects.
Standard Deviation of Two Projects.
Project X Project Y
Expected Cash inflows Probability Expected Cash inflows Probability
10,000 0.12 15,000 0.45
15,000 0.15 20,000 0.25
20,000 0.23 22,000 0.18
12,000 0.18 18,000 0.15
10,000 0.15 12,000 0.1

3. 3. LCD Company Ltd. Has to implement the 2 projects. Project X and Project Y.
Initial investment is Tk. 80,000
Calculate riskiness of the project and suggest which project should be accepted
and why?
Project X Project Y
Probability Expected Cash
Inflows
Probability Expected Cash
Inflows
0.12 20,000 0.13 15,000
0.15 22,000 0.16 23,000
0.18 25,000 0.22 24,000

4. 4. Following are the probabilities and rate of return of three stocks:
Required:
• Expected Rate of Return for each stock.
• Variance and standard deviation of each stock.
Probability Rate of Return of Stocks
A B C
0.22 0.25 0.18 0.04
0.28 0.15 0.10 0.08
0.32 0.12 0.09 0.12
0.18 -0.10 0.05 0.15
0.12 -0.14 0.03 0.25

5. 5. Standard deviation and expected rate of return of stock X is 0.05 and 0.15
respectively, whereas standard deviation and expected rate of return of stock Y is
0.08 and 0.18 respectively. Compute the co-efficient of variance and which project
do you recommend?

6. 6. A company is considering a proposal to buy one of the two machines to manufacture a new commodity. Each of
the machine requires investments of Tk. 50,000 and is expected to provide benefits over a period of 12 years. The
firm has made pessimistic, most likely and optimistic estimates of the return associated with each of these
alternatives. The estimates are as follows:
Which projects do you consider more risky and why?
Particulars Machine A Machine B
Cost Tk. 50,000 Tk. 50,000
Cash flow estimates:
Pessimistic 8,000 --------
Most Likely 12,000 10,000
Optimistic 16,000 20,000

7. 6. A company is considering a proposal to buy one of the two machines to manufacture a new commodity. Each of
the machine requires investments of Tk. 50,000 and is expected to provide benefits over a period of 12 years. The
firm has made pessimistic, most likely and optimistic estimates of the return associated with each of these
alternatives. The estimates are as follows:
Which projects do you consider more risky and why?
Particulars Machine A Machine B
Cost Tk. 50,000 Tk. 50,000
Cash flow estimates:
Pessimistic 8,000 --------
Most Likely 12,000 10,000
Optimistic 16,000 20,000