Suppose that there are two securities RAIN and SUN.
Subject: Business / Finance
Question
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Q1
Suppose that there are two securities RAIN and SUN. RAIN pays $100 if there is any
rain during the next world cup soccer final. SUN pays $100 if there is no rain. Suppose that the world cup soccer final is 1 year from today, and suppose that RAIN is trading at a price of $23 and SUN is trading at a price of $70.
(a) If you buy 1 share of RAIN and 1 share of SUN, what is your payoff after 1 year depending on the weather?
(b) What does the No-Arbitrage Condition imply about the price of a 1-year zero-coupon bond? (Assume no trading costs.)
(c) Suppose that a 1-year zero-coupon bond is trading at $90. Show how you would set up a transaction to earn a riskless arbitrage profit. (Assume no trading costs.)
(d) Suppose that trading zero-coupon bonds is costless, but trading RAIN and SUN each cost $2 per $100 face value. Can you still make an arbitrage profit?
Q2
Consider a market in which currently two assets are traded: (1) A stock, currently selling for $40, which is expected to increase in value by 40% or decrease in value by 20% every year. (2) A zero-coupon risk-free bond with one year maturity that costs $100 and offers 2% annually compounded interest. Suppose the financial institutions are considering the sale of the third asset with maturity of one year whose value at maturity equals max(S-40, 0)? S is the value of the stock at the time the asset matures and max(x, y) equals the greater of the two values x and y.
a) What should be the fair price of this asset today?
b) Suppose the price of this asset today equals $4. Is there anything you could do to make arbitrage money and implement your “Bora-Bora dreams”? Show formally the arbitrage strategy.
Q3
This question requires data collection. You can find all numbers on finance.yahoo.com.
The questions concern Microsoft (ticker: MSFT).
(a) What are the current price and the current price-earnings ratio?
(b) What is the current plowback ratio?
(c) What is the growth rate of earnings for the next 5 years according to the analysts?
Hint: look for annual growth rates under “analyst estimates”
(d) What is the beta of MSFT? Hint: look for “key statistics”. If the risk-free rate (Rf) is 1% and the market risk premium E[RM ?Rf ] is 11%, what is the required rate of return on MSFT according to the CAPM?
(e) Assume that Microsoft will have earnings and dividends that will grow at the analysts forecasted rate forever after; i.e., the Gordon growth model (GGM) applies. What is the price-earnings ratio that the GGM predicts for Microsoft?
