A stock mark advisory service offers three investments portfolios for one of its

Question

A stock mark advisory service offers three investments portfolios for one of its customers. All portfolios have the same investment cost. Portfolio A contains speculative stocks, which aim for capital gain through price appreciation. Portfolio B is made up of stocks of stable companies that pay good dividends overt the long run. Portfolio C comprises stocks with a moderate potential for growth and a moderate yield of dividends. The customer has enough money to invest in only one of these three portfolios for a period of one year. The net return on investments will depend on whether the economy during the period will be in a stage of inflation, recession, or depression. The net potential gains or losses are calculated as follows: 1. What would be the decision according to (1) Maximax (optimism): (2) Maximin (pessimism): (3) Equal Likelihood: (4) Minimizing Regret: and, (5) Realism where alpha = .6? Be sure to show work and indicate the recommended alternative each time. Consider the objective probabilities for inflation, recession and depression are 70%, 20%, and 10%, respectively. Which portfolio should now the customer choose by applying the method of coefficient of variation? (N.B. Remember to find x bar and sigma) 3. What is the probability of making a profit of at least $40 for each alternative? (N.B. Use the Z-Table.) Which alternative is preferred under this requirement?

Explanation / Answer

For equal likely :

Ans3:

will choose B. sINCE IT has max prob.

Formula:

Payoff table Alternatives Scenarios for alternatives Inflation Recession Depression Probability of this scenario 70% 20% 10% Portfolio-A 100 50 -60 Portfolio-B 50 45 40 Portfolio-C 70 40 -10 Approach-1 Expected value (probability approach) Alternatives Scenarios for alternatives Inflation Recession Depression Probability of this scenario 70% 20% 10% Expected value for the alternative Portfolio-A 100 50 -60 74 (highest gain) Portfolio-B 50 45 40 48 Portfolio-C 70 40 -10 56 Go for-> Portfolio-A Expected value with Perfect Information 84 Expected value without Perfect Information 74 Expected value for Perfect Information (EVIP) 10 Approach-2 MaxiMax (without probability; optimistic; maximise the maximum gain) Alternatives Scenarios for alternatives Inflation Recession Depression Maximum gain Portfolio-A 100 50 -60 100 (highest gain) Portfolio-B 50 45 40 50 Portfolio-C 70 40 -10 70 Go for-> Portfolio-A Approach-3 MaxiMin (without probability; pessimistic; maximise the minimum gain) Alternatives Scenarios for alternatives Inflation Recession Depression Minimum gain Portfolio-A 100 50 -60 -60 Portfolio-B 50 45 40 40 (highest gain) Portfolio-C 70 40 -10 -10 Go for-> Portfolio-B Approach-4 MiniMax (without probability; opportunistic; minimise the maximum loss) Alternatives Scenarios for alternatives Inflation Recession Depression Portfolio-A 100 50 -60 Portfolio-B 50 45 40 Portfolio-C 70 40 -10 Regret table (if we invest on the alternative other than the best one, how much loss/regret we have to bear?) Alternatives Scenarios for alternatives Inflation Recession Depression Maximum regret Portfolio-A 0 0 100 100 Portfolio-B 50 5 0 50 (minimum regret) Portfolio-C 30 10 50 50 (minimum regret) Go for-> Portfolio-C or B Approach-5 Hurwicz Alpha Criteria (without probability; middel of optimistic and pessimistic) Since Optimistic and Pessimistic approaches are 2 extreme approach so Hurwicz introduced a mid way based on coefficient of optimizm i.e. More the more the 'optimizm' 0<= <=1 Let's say = 0.6 Alternatives Scenarios for alternatives Inflation Recession Depression Maximum Minimum Expected value Portfolio-A 100 50 -60 100 -60 36 Portfolio-B 50 45 40 50 40 46 (Maximum) Portfolio-C 70 40 -10 70 -10 38 Go for-> Portfolio-B

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