An investor has $40,000 in U.S. equities, $20,000 in european equities, $30,000
ID: 2819601 • Letter: A
Question
An investor has $40,000 in U.S. equities, $20,000 in european equities, $30,000 in U.S. bonds and holds $10,000 in cash. He is worried about two major events in the near future: (1) If Federal Reserve raises the interest rate in the next FOMC meeting, the value of his U.S. bonds and stocks drop by $3000 and $5000 respectively. The investor thinks the Fed will raise the rates with a probability of 40 percent. (2) Two presidential candidates are campaigning for an upcoming election in Italy. Mr. P is viewed as a president with business friendly policies and Mr. F is campaigning with controversial policies that might slow down growth. If Mr. P becomes the president, the value of U.S. and european equities will increase by $4000 and $5,000 respectively. if Mr. F wins the election, the value of U.S. and european equities will drop by $7000 and $8,000 respectively. The latest polls in- dicate that Mr. P wins the election with a probability of 55%. A financial advisor found an insurance policy that insures the current value of the portfolio, regardless of Fed's decision and the election results. In other words, the value of the portfolio remains constant at $100,000. Find the maximum amount that the investor is willing to pay for the insurance. The utility function of the investor is represented by U(Y) = vp over final wealth (Y). Note: There are 4 states of the world relevant to the investor. Setup the prob- aving lem such that the investor is indifferent between having insurance and not h insurance. Then solve for the maximum insurance premium.Explanation / Answer
1. Investors present wealth = 20,000+30,000+40,000+10,000 = 100,000
If the FOMC hikes rates, his wealth will be = 35,000 +20,000 + 27,000 + 10,000 =92,000
2. If P wins, his wealth will be = 44,000 +25,000 +30,000+10,000 = 109,000
If F wins, his wealth will be = 33,000 +12,000 + 30,000+10,000 = 85,000
Satate 1:FOMC hiking rates and P wins election = 0.4*0.55 = 0.22
State 2: FOMC hiking rates and F wins election = 0.4*0.45 = 0.18
State 3: FOMC not hiking rates and P wins election = 0.6*0.55 = 0.33
State 4: FOMC not hiking rates and F wins = 0.6*0.45 = 0.27
His final wealth value = 0.22*(109000+92000)/2 +0.18*(92000+85000)/2 + 0.33*(100000+109000)/2 + 0.27*(100000+85000)/2 = 97,500
His insurance premium = sqrt(97,500) = $312.25
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