| No-arbitrage and Security prices
5. (10 pts) The promised cash flows of three securities are listed here. If the cash flows are risk-free, and the risk-free interest rate is 8%, determine the no-arbitrage price of each security before the first cash flow is paid.
NPV OF A= 600+600/1.08=1,155.56
NPV OF B= 0+1500/1.08=1,388.89
NPV OF C= 2000+0/1.08=2,000
6. (15 pts) Consider two securities that pay risk-free cash flows over the next two years and that have the current market prices shown here:
What is the no-arbitrage price of a security that pays cash flows of $1000 in one year and $1000 in two years? (5 pts)
Low of one price
Price= 900+840=1,740
What is the no-arbitrage price of a security that pays cash flows of $1000 in one year and $5000 in two years? (5 pts)
Price= 900+ (5,000/1,000)*840= 5,100
Suppose a security with cash flows of $500 in one year and $1000 in two years is trading for a price of $1300. What arbitrage opportunity is available? (5 pts)
No-arbitrage price= (500/1,000)*900+ 840=1,290
We can buy 1 shares of security A and 2shares of security B, it cost: 900+840*2=2,580.
Then sell two shares of the security (with cash flows of $500 in one year and $1000 in two years), revenue: 1,300*2=2,600
Profit=2,600-2,580=$20
7. (25 pts) An Exchange-Traded Fund (ETF) is a financial security that represents a portfolio of stocks, where the weight of each stock in the portfolio is its percentage market value. Consider an ETF for which each share consists of 4 shares of Disney (DIS), 2 shares of Walmart (WMT), and 5 shares of IBM (IBM). The current prices of the stocks are as follows:
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