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Tuesday, March 11, 2008

The Black-Scholes Formula is Wrong! - Part 9/12 - How FSK Trades Options

I attempted to trade my options trading system for 2 years, 2006-2007. I didn't buy any options in 2008 and I suffered a 100% loss after having doubled my money at one point. I concluded my options trading system isn't worth anything. I've concluded that gold and silver are the best possible investment for non-insiders, where you should earn a 0% inflation-adjusted return.

The problem is that I got totally wiped out when the stock market declined. I might still buy some GLD LEAP options, betting on inflation. The problem with out-of-the-money GLD LEAP options is that insiders will try to push down the price of gold if it rises too rapidly, limiting my potential gain. I'm going to gradually move my savings to GLD and SLV and physical metal. In my IRAs, GLD and SLV are the best option; physical metal is best for my taxable accounts.

I've concluded that only insiders may exploit a defective monetary system for their own benefit. For non-insiders, physical gold and silver are the best possible investments, provided you can find a safe place to keep them.

Table of Contents

Part 1 - Overview and Background
Part 2 - Axioms
Part 3 - Formula Derivation
Part 4 - The Put/Call Parity Formula
Part 5 - The Volatility Smile
Part 6 - The Contradiction
Part 7 - Resolving the Contradiction
Part 8 - The Kelly Criterion
Part 9 - How FSK Trades Options
Part 10 - Only Fools and Hedge Funds Write Covered Calls
Part 11 - Other Options
Part 12 - Summary

Options are priced as if the expected gain in the stock is the risk-free interest rate.

Stocks return more than a money market account in the long run. There are short-term fluctuations. In the long run, there WILL BE inflation, although the money supply will sometimes abruptly contract due to the Compound Interest Paradox.

After observing that EVERY LISTED EQUITY OPTION IS MISPRICED, I decided to develop my own options trading system. If I made such an observation and didn't profitably trade off it, that would make me a wimp.

Instead of pricing options as if the expected gain is the Fed Funds Rate, I price options as if the expected gain is 6%-10%. Using this adjustment, all calls are underpriced and all puts are overpriced.

It doesn't pay to short naked puts as a retail customer. First, you are taking a risk much larger than the premium, if the stock does tank. If you collect $2 when selling the put, you gain at most $2 but you can lose $20 or more. Second, the margin rules for retail customers make a short naked put position impractical.

However, long calls are a good deal. Long-term out-of-the-money calls are the biggest bargain. My only margin requirement is that I pay for the call fully with cash. That is only slightly more than a professional options trader would pay in capital for the same unhedged position. My worst-case loss is 100%, the amount I paid for the call. Compare that with a short naked put, where I can lose 1000% more than the premium I collect selling the put. With a short naked put, I am at a huge disadvantage to a professional options trader when considering margin requirements.

I wrote a program that downloads stock and option price data from Yahoo Finance. For volatility assumption, I use the lesser of (1) implied volatility (2) 2 year historic volatility (3) my own volatility forecasting algorithm.

Most stocks offer options up to only 9 months. Certain stocks offer options up to 2.5 years. These options are called LEAPs. LEAPs are offered on most of the 1000 largest stocks by market capitalization. On the Options Clearing Corporation website, you can download a list of all stocks that offer LEAP options.

Long-term LEAP calls are the best deal. If the expected growth priced into the option is wrong, then the longest-term options are mispriced the most. I found that the longest-term LEAPs were the best deal, and strikes around 50% more than the current stock price tend to be most favorably priced.

The interest rate priced into a 2 year option is *LESS* than the 2 year bond yield rate. Options traders pay transaction fees. As they adjust their hedge, they have to pay transaction costs. When they short sell stock, they pay a short sale fee. I am taking an unhedged long call position. I don't pay hedging costs. I don't pay short sale fees.

Professional options traders tend to be net long calls. Most retail customers buy a stock and write a covered call and buy a protective put. The professional options trader has the opposite of this position, long calls and short puts. The errors in the options pricing model are in FAVOR of the professional options trader, and they don't notice much because they're hedged anyway. When I buy a call from a professional options trader, he is probably selling me calls that were already in his inventory, or he is hedging calls of similar strike and duration. I am saving the professional options trader the cost of hedging, so I can sometimes buy calls at a discount.

Some stocks are "hard to borrow". This means that there are people who want to short sell the stock, but they cannot find shares to borrow to short sell. Either they have to pay a higher short interest fee, or shares are completely unavailable. This shows up at a lower price for call options, since options traders have a hard time hedging; the interest rate priced into the option is lower. Sometimes, for a "hard to borrow" stock, the expected growth rate priced into the option is negative! The call options on a "hard to borrow" stock are cheap from a statistical viewpoint. However, the underlying stock may be overpriced, because there are people who want to short sell it and can't.

When I buy call options, I project an expected return of 100% or more. I've been experimenting with my options trading system for around 2 years. A few months ago, I was making a 40% annualized return. Recently, the market has crashed and now my annualized rate of return is -16.7%. Using the Kelly Criterion, I will stick with my options trading system. The last 2 years haven't been so good for the stock market, so that's a good return when you consider that I'm making highly leveraged bets that the market will go up. A few of the stocks I picked have increased substantially. Buying long-term out-of-the-money call options, one or two lucky picks make up for a bunch of 100% losses.

Trading options as a retail customer, I pay substantial spread costs and commissions. However, the theoretical profit is SO HIGH that I do it anyway. I'm disciplined and only risk 10% of my savings per year on options.

I can tell you my trading system without worrying about it ceasing to work. The put/call parity formula will guarantee that the expected gain priced into options remains unchanged. Options traders conducting volatility arbitrage will guarantee that implied volatility stays near expected future volatility. Further, I'm not giving you my full source code; you probably won't pick the same options I do. The heuristic "2 year LEAP options, with strike 1.5 times current stock price" is a pretty good approximation.

When I profit from my options trades, I'm not arbitraging the professional options traders. I'm arbitraging the Federal Reserve and its monetary policy. Professional options traders make the profit they expect when they sell me a call.

My options trading system allows the average person to receive the same MASSIVE GOVERNMENT SUBSIDY that banks and hedge funds receive. It is risky. You should only attempt this if you REALLY know what you're doing. Earning a 100% return on 10% of my savings boosts my overall investment returns by 10%. The past 2 years was a bad time to be making leveraged bets that the market will go up. There *WILL* be inflation, and eventually there will be another 2-year period where the market goes up 30%-50%.

There's one final word of warning. When buying long-term out-of-the-money call options, try to avoid companies that are going to be bought out. If a stock is bought out for cash, all the volatility evaporates. I can usually identify these by looking at implied volatilities.


Anonymous said...

this happens when people trade that dont know any math. why do you trade options if you dont have any idea about it? black scholes isn't wrong. it is right under the hypothesis made. your "contradiction" reposes upon your lack of understanding of the concept of risk neutral probabilities. i suggest you learn basic math and read a book about options before you trade again

Anonymous said...

The risk free rate in BS in practice means only two things. One is that when you buy stock you pay r as interest on bought stock. Another is that when you short shell you get r interest on money from sale.

That's it. Everything you wrote about BS is wrong, sorry.

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