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- StudyBlue
- Michigan
- University of Michigan - Ann Arbor
- Finance
- Finance 380
- Carmel
- Class 2: Pricing Futures and Forwards

Andrew Z.

What is short selling?

-Borrow the shares from someone (can be demanded back at any time)

-Sell them on the open market for S_{0}

-At some date t, buy asset back on the open market for S_{t}

-Profit is S_{0}- S_{t}

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

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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(S_{0}) = 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 S_{0} how can you make money risk-free?

Buy the forward contract and sell the stock

Payoff = S_{0}- PV(F)

If the price of the forward contract is greater than S_{0}, how can you make money risk-free?

Sell the forward contract and long the stock

Payoff = PV(F) - S_{0}

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__]

[(1+d)^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__]

[(1.0536)^2]

= .7447 USD per Swiss franc

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