Question

You are managing an investor's account with $200,000. Investor's goal is to minimize the total risk. Possible investment options, expected rate of return, and risk indices of the investment options are given below. Stock Fund Money Market Fund 2% 0.04 12% Return Risk(unit/S) 0.25 Investor needs an annual income of $14000 Formulation: Dec Var: S- $to be invested in Stock Fund, M-.. in MM Obi. Function: Min (Total Risk) Min .25S+.04M Constraints: Budget: SM Return(Income): 0.12S+0.02M $14,000 Questions: (a) Average return (portfolio return) Şreturn/Sinvested (b) If you would like to achieve an additional $1000 income, would the total risk increase or decrease? (c) If you have an additional $1000 to invest, would the total risk increase or decrease? (d) Now, suppose the investor gives additional $1000 to invest. Thus, you have now $201,000. Total Risk-. <= $200,000

Answer 1

Q1 : We can see from the second constraints section that the final value of return is 14000 and budget is 20000 and both are binding with no slack. Hence average return = 14000/20000 = 7%

Q2 : We can see from the second constraints section that the shadow price for Returns is 2.1. This means that for every $1 increase in required return the risk (objective function) would increase by 2.1. Thus if an additional $1000 income is required, the total risk would increase (by an amount equal to 1000*2.1 = 2100)

Q3 : We can see from the second constraints section that the shadow price for Budget is -0.002. This means that for every $1 increase in budget the risk (objective function) would decrease by -0.002. Thus if an additional $1000 budget is available to invest, the total risk would decrease (by an amount equal to 1000*0.002 = 2)

Q4 : The shadow price for Budget is -0.002 and the current risk is 29000. Hence if additional 1000 is available to invest then the total risk is 29000-1000*0.002 = 29000-2 = 28998