-Borrow the shares from someone (can be demanded back at any time)
-Sell them on the open market for S0
-At some date t, buy asset back on the open market for St
-Profit is S0- St
What is a repurchase agreement?
Think of it as 2 things:
-Posting your stock as collateral AND
-Getting a loan and agreeing to pay a set percentage of interest + loan amount
-Total interest = repurchase price - initial sale price
What is the law of one price?
-If 2 portfolios have the exact same assets and payoff likelihoods, then portfolios should be the same price
Assuming a financial asset can be stored costlessly and provides no income, what is the price of a forward? What are 2 other key assumptions for this equation?
F = FV(S0) = x(1+r)t where r is the EAY of the risk-free interest rate
-Can be traded with no transaction costs
-Can be short sold
If the price of the forward contract is less than S0 how can you make money risk-free?
Buy the forward contract and sell the stock
Payoff = S0- PV(F)
If the price of the forward contract is greater than S0, how can you make money risk-free?
Sell the forward contract and long the stock
Payoff = PV(F) - S0
Walk me through a forward pricing arbitrage if calculated F < S(0). How could you make $1MM today?
1) Buy in the spot market at S, sell in the forward market at calculated F
2) Find arbitrage profit per unit Quoted F - calculated F and discount amount back to PV
3) Determine amount to trade in to reach goal: 1MM/PV(profit/unit) = # of units
4) Determine amount to borrow/invest risk-free S*#ofUnits + $1MM (borrow $1MM to realize arbitrage at present)
Consider a forward whose underlying pays a predictable income (e.g. dividend). What is the value of the forward?
F = FV(S) - FV(income)
Suppose you buy a 2 month forward on the S&P with S=1175, 2-month interest rate = 3%, and dividends = $2/month. What is value of forward?
FV(S) = 1175(1.03)^(2/12) = $1180.803
FV(inc) = 2(1.03)^(1.5/12) + 2(1.03)^(.5/12) = $4
F = $1176.793
Consider a forward whose income is a known number of additional units of underlying assets. What is the value of the forward?
F = S[(1+r)^t]
Where r = risk-free rate (EAY) and
d = growth rate of underlying
Consider a forward contract on swiss francs and the dollar. Suppose the 2-year interest rate on the USD is 3.86% and the interest rate on francs is 5.36%. The spot price for francs is .7703. What is the value of the forward?
F = (.7703)[(1.0386)^2]
= .7447 USD per Swiss franc
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