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Question 1: Assume that return of portfolio A is described by the following regressed model: r = 10% + 0.6GDP 0.2INT 0.4INF + e. Risk premiums of macroeconomic factors in the above model has the following values: Risk premium of GDP: 8% Risk premium of INT: 6% Risk premium of INF: 4% Risk free rate is 6%. What is expected return of portfolio A based on APT theory. Is there any Arbitrage opportunity? Please describe Arbitrage strategy of the investor to exploit the Arbitrage opportunity if it exists. Question 2: Mr. Kay has a plan of buying an apartment. He has to borrow from a bank with 12%year interest rate, the borrowing time is 4 year and the amount of money (including principal and interest) to be paid each year is 400 million VND. To immunize the interest rate risk of his loan, Mr. John invests in bond A and bond B: Bond A ‘s maturity time is 3 years, coupon rate is 12%. Bond B ‘s maturity time is 4 years, coupon rate is 10%. Both bond A and bond B pay coupon annually, the face value of bond A and bond B is 600 millions VND. Yield to maturity or the market rate is 10% a. Calculate Macaulay duration and Modified duration of bond A and bond B. When yield to maturity decreases 1%, how price of bond A and bond B change? b. What is the invested weight of bond A and bond B that Mr. John needs to invest to immunize interest rate risk of his loan?
Question 1: Assume that return of portfolio A is described by the following regressed model: r = 10% + 0.6*GDP - 0.2*INT - 0.4*INF + e Risk premiums of macro-economic factors in the above model has the following values: - Risk premium of GDP: 8% Risk premium of INT: 6% Risk premium of INF: 4% Risk free rate is 6% What is expected return of portfolio A based on APT theory Is there any Arbitrage opportunity? Please describe Arbitrage strategy of the investor to exploit the Arbitrage opportunity if it exists Question 2: Mr Kay has a plan of buying an apartment He has to borrow from a bank with 12%/year interest rate, the borrowing time is year and the amount of money (including principal and interest) to be paid each year is 400 million VND To immunize the interest rate risk of his loan, Mr John invests in bond A and bond B: - Bond A ‘s maturity time is years, coupon rate is 12% - Bond B ‘s maturity time is years, coupon rate is 10% Both bond A and bond B pay coupon annually, the face value of bond A and bond B is 600 millions VND Yield to maturity or the market rate is 10% a Calculate Macaulay duration and Modified duration of bond A and bond B When yield to maturity decreases 1%, how price of bond A and bond B change? b What is the invested weight of bond A and bond B that Mr John needs to invest to immunize interest rate risk of his loan? Question 3: Show the Payoff Table and draw Payoff Diagram of the following portfolio: - Buy call option with strike price (X1) $120 Sell call option with strike price (X2) $150 Buy put option with strike price (X3) $120 Know that all above options are European Option, have the same maturity and right on the same stock Question 4: Expected return and risk of stock A and stock B as follow: Stock Expected return Beta Unique standard deviation (Ϭei) A 15% 0,8 32% B 20% 1,2 45% Standard deviation of market index is 24% and risk free rate is 9% a Calculate the standard deviation of stock A and stock B b A Portfolio is created with the folloing invested weight: Stock A: 35% Stock B: 45% Risk free asset: 20% Please calculate expected return, beta coefficient, total standard deviation and unique deviation of the portfolio Question 5: If CAPM theory is efficient, which of the following situation can or cannot be exist? Give explanation Situation Situation Portfolio A B Risk free Market A Risk free Market A Expected return 30% 40% 8% 16% 15% 8% 16% 18% Standard deviation 35% 30% 22% 14% 22% 30% Portfolio Risk free Market A Expected return 8% 16% 18% Beta Coefficient 1,5