Accounts

Sanjay's Investment Dilemma

(Decision under Uncertainty)

Sanjay is looking to invest the savings from his first salary. He consults Farzee Investments pvt. ltd. The broker @ Farzee

advises Sanjay to build a diversified portfolio consisting of four asset class – gold, bonds, stocks and t-bills; and offers his

own assessment about the future of stock market.

The following table gives the broker's subjective estimates and the probable payoffs:

Market condition

Large rise

Small rise

Stagnant

Small fall

Large fall

20%

30%

30%

10%

10%

Gold

– Rs. 100

Rs. 100

Rs. 200

Rs. 300

Rs. 0

Bonds

Rs. 250

Rs. 200

Rs. 150

– Rs. 100

– Rs. 150

Stocks

Rs. 500

Rs. 250

Rs. 100

– Rs. 200

– Rs. 600

T-Bills

Rs. 60

Rs. 60

Rs. 60

Rs. 60

Rs. 60

Chance of occurrence

1.

What are the prospective payoffs for the portfolio, when the market has

(a) large rise (b) small rise (c) stagnant (d) small fall (e) large fall

2.

Under uncertainty which asset class is most favorable?

3.

With perfect information which asset class(es) becomes favorable with each changing market conditions?

4.

What is the expected payoff with perfect information?

5.

What is the expected value of perfect information?

RBI gives regular forecast indicating either positive or negative economic growth in the coming quarter. Using a relative

frequency approach based on past information it has been observed that:

P (positive | large rise) = 0.8

P (positive | small rise) = 0.7

P (positive | small fall) = 0.4

P (positive | large fall) = 0

P (positive | stagnation) = 0.5

Given the above information, calculate the following revised probabilities:

P (large rise | positive) = ?

P (large rise | negative) = ?

P (small rise | positive) = ?

P (small rise | negative) = ?

P (stagnation | positive) = ?

P (stagnation | negative) = ?

P (small fall | positive) = ?

P (small...