The Standard and Poor's 500, or simply the S&P 500, is a stock market index tracking the performance of 500 large companies listed on stock exchanges in the United States. On the other hand, the SPY-ETF is an exchange-traded fund (ETF) created to provide individuals with an investment vehicle to invest in the stock market. SPY-ETF tracks the S&P 500 index by holding a portfolio of stocks in companies in the S&P 500, producing returns on investments roughly in line with the S&P 500 index. Assume that the S&P 500 index level follows a normal distribution with a mean index level of 4,325 points and a standard deviation of 272 points. Suppose you are an analyst working in a Hedge Fund, and your manager provides the following investment rules:

• If the reported S&P 500 index level falls in the top 30% of the point distribution, sell 10% of the assets in the SPY-ETF.
• If the reported S&P 500 index level is below 3,985 points, buy additional shares of the SPY-ETF.

a)What is the probability you will buy additional shares of the SPY-ETF? In other words, what is the probability that the S&P 500 index level falls below 3,985 points?

b)

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What is the minimum index level that the S&P 500 should reach in order to sell 10% of the assets in the SPY-ETF? Here are the investment rules provided by the manager:

• If the reported S&P 500 index level falls in the top 30% of the point distribution, sell 10% of the assets in the SPY-ETF.
• If the reported S&P 500 index level is below 3,985 points, buy additional shares of the SPY-ETF.

c.) Suppose that the opening S&P index level is 4325 points or more; what's the probability that you will sell 10% of the assets in the SPY-ETF before the market closes?

Answer rating: 100% (QA)

a To determine the probability of buying additional shares of the SPYETF we need to calculate the probability that the SP 500 index level falls below ... View the full answer