Question

Suppose you won the lottery and had two options: (1) receiving $0.1 million or (2) taking a gamble in which, at the flip of a coin, you receive $0.2 million if a head comes up but receive zero if a tail comes up.

1. What is the expected value of the gamble? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $550,000 should be entered as 0.55.
   million
   
2. Would you take the sure $0.1 million or the gamble?
   -Select-Take $0.1 millionTake the gambleItem 2
   
3. If you chose the sure $0.1 million, would that indicate that you are a risk averter or a risk seeker?
   -Select-Risk averterRisk seekerItem 3
   
4. Suppose the payoff was actually $0.1 million - that was the only choice. You now face the choice of investing it in a U.S. Treasury bond that will return $108,000 at the end of a year or a common stock that has a 50-50 chance of being worthless or worth $240,000 at the end of the year.
   
   1. The expected profit on the T-bond investment is $8,000. What is the expected dollar profit on the stock investment? Round your answer to two decimal places. Write out your answer completely. For example, 0.25 million should be entered as 250,000.
      $
      
   2. The expected rate of return on the T-bond investment is 8%. What is the expected rate of return on the stock investment? Round your answer to two decimal places.
      %
      
   3. Would you invest in the bond or stock?
      -Select-BondStockThis depends on the individual's degree of risk aversion.Item 6
      
   4. Exactly how large would the expected profit (or the expected rate of return) have to be on the stock investment to make you invest in the stock, given the 8% return on the bond? Round your answer to two decimal places. If no exact answer can be obtained, enter 0.
      %
      
   5. How might your decision be affected if, rather than buying one stock for $0.1 million, you could construct a portfolio consisting of 100 stocks with $1,000 invested in each? Each of these stocks has the same return characteristics as the one stock - that is, a 50-50 chance of being worth zero or $2,400 at year-end.
      
      1. Investing in a portfolio of stocks would definitely be an deterioration over investing in the single stock.
      2. Investing in a portfolio of stocks would definitely be an improvement over investing in the single stock.
      3. The situation would be unchanged.

Answer 1

Suppose you won the lottery and had two options: (1) receiving $0.1 million or (2) taking a gamble in which, at the flip of a coin, you receive $0.2 million if a head comes up but receive zero if a tail comes up.

What is the expected value of the gamble? Round your answer to two decimal places.

Expected Value = Amount when Head * Probability of Head + Probability of tail * Cash flow when Tail

Expected Value = $0.2 Million * 50% + 50% * 0

Expected Value = $0.10 Million

Would you take the sure $0.1 million or the gamble?
Take $0.1 million

Because cash flow under both are equal so taking risk does not worth when you get same expected cash flow

If you chose the sure $0.1 million, would that indicate that you are a risk averter or a risk seeker?
Risk averter

Suppose the payoff was actually $0.1 million - that was the only choice. You now face the choice of investing it in a U.S. Treasury bond that will return $108,000 at the end of a year or a common stock that has a 50-50 chance of being worthless or worth $240,000 at the end of the year.

The expected profit on the T-bond investment is $8,000. What is the expected dollar profit on the stock investment? Round your answer to two decimal places.
Expected Profit from Stock Investment = Amount when Worthy * Probability + Probability * amount when Worth less - Investment

Expected Profit from Stock Investment = 240000 * 0.50 + 50% * 0 - 100000

Expected Profit from Stock Investment = $20000

The expected rate of return on the T-bond investment is 8%. What is the expected rate of return on the stock investment? Round your answer to two decimal places.
Expected Return on Stock Investment = Profit / Investment

Expected Return on Stock Investment = 20000 / 100000

Expected Return on Stock Investment = 20%

Would you invest in the bond or stock?
This depends on the individual's degree of risk aversion

Exactly how large would the expected profit (or the expected rate of return) have to be on the stock investment to make you invest in the stock, given the 8% return on the bond?

0 because the stock is a risky asset but bond investment is a risk free asset. it depends on risk aversion of the investor to compute the return required from stock investment to make it comparable with bond

How might your decision be affected if, rather than buying one stock for $0.1 million, you could construct a portfolio consisting of 100 stocks with $1,000 invested in each? Each of these stocks has the same return characteristics as the one stock - that is, a 50-50 chance of being worth zero or $2,400 at year-end.

Investing in a portfolio of stocks would definitely be an improvement over investing in the single stock.

because correlation will help to reduce the risk of the portfolio

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