Being a weblog devoted to a variety of topics. Including Mathematics. And Mathematical Finance. Sometimes with homework.

Friday, January 16, 2009

21-270: Things to Keep in Mind #2

Another common early mistake is to take the future value of a portfolio by netting out the initial cost. When we speak of value, we do not include any concept of profit; the value of a portfolio at any given time, t, is simply the sum of the time t values (prices) of the component securities. Note that short positions have values opposite in sign to their corresponding long position.

For example, suppose there exists a $4 European call and a $1.50 European put, both struck at $50 on a single share of the same stock initially trading at $50 and both expiring in one year. If we create a portfolio consisting in one call and a short position in two puts, the initial value of this portfolio is the sum of the values of the calls and the shorted puts: $4 + 2 x (-$1.50) = $1.

If, after a year, the stock goes up in price to $60 the puts are worthless and the call is worth $10 (why?). Many students will then calculate the time 1 value of the portfolio to be $10 + 2 x (- $0) - $1 = $9. This is incorrect; the value of the portfolio is simply $10 = $10 + 2 x (- $0).

Likewise. if the stock falls to $45, the portfolio will have value -$10, not -$11.

In general, absolute profit is not as useful of a number to think about as you might first believe. For one thing, it neglects the time value of money. Similarly, it's difficult to analyse without knowledge of alternative investments or a quantification of its associated risk.

No comments:

Blog Archive