Question
Heading a portfolio I want to introduce a business analytics tool used in finance called the cash flow table. Let us use the forward contract
Heading a portfolio
I want to introduce a business analytics tool used in finance called the cash flow table. Let us use the forward contract as an example.
- Form a portfolio: we form a portfolio consisting of a forward contract F, some amount of the underlying asset I will call a stock, and cash.
- Notation:
Time = t (today)
Time = T (maturity)
S^(t) price of a share of stock today
Q quantity of the stock (Notes: Q < 0 if the stock has been sold short; Q is an odd notation but traditional)
S(t) value of stock holidays which is QS^(t) today
S(T) value of stock holding
Cashflow of Portfolio
Holding | Worth today(t) | Worth at maturity(T) |
Forward | $0 | (d) |
Stock | (a) | (e) |
Cash | (b) | (f) |
Total | (c) | (g) |
Forward contract:
At maturity T the holder of the contract can buy Q shares of stock for the price F. The contract has no value today.
Hedging the portfolio (Today)
The holder sells Q shares she does not have (called short selling). This raises S(t) = Q S^(t) in cash(b), but a negative cash value in stock of -S(t) = -Q S^(t) . (a) what does this total to for today (c)?
Maturity
The value of the stock is S(T) = S^(T) for which she paid F for. What is the net profit (Loss), that is difference between S(T) and F (d) ?
The stock cash value is -QS^(T) = - S(T) remember she owes Q shares of stock not the S(t) in cash they produced when sold. If S(T) < S(t), she does not get cash back since -S(T) > -S(t). She returns the shares to the sellers, who enjoy/regret profit or loss in the transaction.
What about the cash at maturity? This is the time value of money. If she made a deposit of S(t) dollars at t what that cash be worth at time T(f)? Sum the column to get (g)
Equate ( c ) and (g) to force no arbitrage.
You are done!
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