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.

1. 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.
2. 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!