Hedged Option Portfolios

| ## ...there are 6 basic positions Buy a share (a.k.a. go long) Sell a share short. Buy a call. Buy a put. Write a call. Write a put. Each position can be described by the payoff at a variety of prices of the underlying security. For example, if you buy a share of stock, your profit is Purchase Price minus Selling Price. If you buy a call options, your profit is Stock Price at expiration minus Call Price minus Excercise Price. Caveat: If Stock Price at expiration is less than the excercise price, then the holder elects not to excercise the option and the profit is just -Call Price.

## ...what is a hedged position?

Consider the profit situation when you own (or go long) 1 share. The potential loss is fairly large - equal to the amount paid for the share. Of course the potential gain is infinite. But suppose your knowledge of the firm or its markets convinces you that it's precariously poised. The next few days could an incredible announcement - probably something disasterous, although the test results might possibly confirm that the firm's earlier rosy predictions. In either case, you know something is up and you have suspicions. Now if you add to your existing portfolio of 1 share, a put option - the right to sell 1 share at a pre-specified (or Strike) price, you have a hedge portfolio. If the firm goes bust your share is worthless but you get back an amount equal to the strike price. So your loss is limited. If the fantastic happens and the firm becomes the next darling of Wall Street your payoff is less by whatever you paid for the put, but still infinite. You're hedged.

## ...visualizing hedged portfolios

This visualization lets you invest in 3 securities of any of the 6 basic types. The surfaces use a red-green colormap with green showing the most likely outcomes (where likely is computed using a specified average and standard deviation assuming a log normal distribution of price fluctuations). Then you can view the overall behavior of your selected portfolio. This signature is shown semi-transparently in white if you select Securities + Signature in the Common page.

When you select Signature only or Signature colored by N(x) the visualization shows the zero payoff plane with a semi-transparent black surface. Portions of the signature above this plane make the investor happy, portions below make her sad.

## ...what are some common hedges?

- Top Straddle... Write 1 call and 1 put. The signature will show a right-side-up tent with (the big end pointing down).
- Top Vertical Combination... Write 1 call and 1 put. By varying the strike prices you can change the bluntness and width of the top of the signature so that you profit over a wider range of outcomes than with a Top Straddle.
- Bottom Straddle... Buy 1 call and 1 put. The signature will resemble and upside-down tent. The interpretation of this is that the investor has no idea what will happen except that she's sure any price change will be very big. She's betting that the situation at expiration will be very different from the situation today.
- Bottom Vertical Combination... Buy 1 call and 1 put and vary the strike prices to modify the
- Bullish Vertical Spread... Buy 1 call with a low strike price and 1 put with a high strike price.
- Bearish Vertical Spread... Buy 1 call with a high strike price and 1 put with a low strike price.
- Butterfly Spread... Buy 2 calls - 1 with a very low strike price and 1 with a very high strike price - and 1 put with a moderate strike price. The investor is betting against any major changes in the market value of the firm's stock.