QLD Projection: 56.9035443400289 QLD Close: 52.6699981689453
QLD Projection: 53.7158176075328 QLD Close: 52.6699981689453
QLD Projection: 54.2554285321917 QLD Close: 52.6699981689453
RSQ1: 0.99873149394989
RSQ2: 0.998972177505493
Well, the calulcated values for our QLD projections are essentially a perfect fit with rsquares equivalent to 1 with a little error.
Continuing on the results in Covestor, I finally took the plunge and decided to start using QQQQ Calls and Puts for my directional bets on the NASDAQ 100 Equity Index only for me personally. To do that, I needed a way to calculate an exact position size, and I think everyone should find the enclosed spreadsheet useful for creating synthetically leveraged positions in any security given that you know certain characteristics about the underlying price, excercise price, interest rate, expiry date, security volatility (think 90 days is fine), and the dividend rate, which is inconsequential in our excercise on the Q's.
I have enclosed a basic spreadsheet of how I derive my position sizes in options. Holding to the fact that at 192% of equity, I am sythetically leveraged 4 to 1 on the index, basically, the missing factor in calculating the number of option contracts to purchase is dependent on the delta of the option. Using 90 day volatility as the volatility benchmark, and a basic option pricing calculator from
www.otrader.com.au, I input the underyling's security price of 42.99, strike price of 43, interest rate around 0.5% but really 0, expiration date of 11/21/2009, underlying volatility as 2.5468 and a nearly infintesimally low dividend rate of 0.0408. I can use the black scholes or binomial model using any amount of steps. Both based on the Call Price of 1.02, which I bought at the very end of the day but more on that later, the put price closed at 1.01. The Black-Scholes Derived delta for the call was 0.3414 and the delta for the put was -0.6557.
Compiling all this together, you can take the spreadsheet and create your synethic options positions with much less capital than a typical stock would require. Right now I have a hypoethical $100,00 portfolio in the sheet assuming you desire to make a leverage factor of 5 with.
Ceteris Paribus, then, your ideal number of options that will allow you to perfectly replicate a 5 to 1 leveraged position on the underlying is exactly equivalent to:
(Portfolio Size*Leverage Factor)/(Delta of the Option Times the Current Security Price of the Option Times 100).
The reason for this is because delta, even as it is stated in the spreadsheet, will tell you at any given time the option you own will be exactly equivalent to owning 0.3414 times 100 shares of the underlying in the case of the call, or 0.6557 times -100 shares of the underlying for the put for every option contract.
The same logic would be applicable to futures position sizing for large portfolios.
I did not take any significantly large position in the options tonight, but by tomorrow, one way or the other, covestor will consider that as 100% of my portfolio, so even though the option is insignificantly large, if it's down 8% on the open, which I'm pretty sure will happen, well, in the equities section it will show that as my performance being down 8%, but it's not accurate. Don't be fooled. As I hope this exchange and explanation has helped, the matter of leverage seen through my Cash <i>and</i>Equities performance is more representative of what I've done.
Anyway, that said, I've never actually seen this explained on the internet. I was only able to put the puzzle together at Level II of the CFA curicullum where I actually learned how to use the greeks, and I guess you can probably add Vega and Gamma for even more accuracy, but in practice it won't really affect your hedges or the amount of options you buy as you'll be rounding up to the nearest whole integer.
So, I'm long the $43 QQQQ Calls expiring November 21st, and I still anticipate taking a large position in QLD. I'm finding that options, at least on the Q's, have greater liquidity, certainly much better liquidity than the QLD and QID options that nearly always have ten to five cent spreads even when the market is open, worse during the open, too.
That'll put it in perspective for a lot of people. I hope people like and use the spreadsheet. It's not that complicated. Put in a security price, delta, portfolio size, desired leverage factor, and boom, you'll get the amount of options it would take to create that synthetic portfolio with a fraction of the amount of capital rather than outright purchase of the underlying. These positions should stay pretty consistent for at least the next three to four days, but after that rebalancing because of the time to expiration premium will be required. You could even say it's required on a daily basis, but my trades should only last at the most 2 weeks. For much larger positions and longer horizons leaps are available, and using this spreadsheet as a guide I think will help.
Understanding that leverage doesn't have to be greater than 1 is equivalent to attmepting to create a synthetic portfolio of the underlying with a fraction of the amount of capital required. So, if you want to look at how to build a portfolio out of Google that is forty percent of your portfolio with the $500 strike March 2010 Options, be it by selling put options, or buying call options, the answer I get by using 90 day volatility in GOOG, an interest rate of 0.5%, expiry of the option, Underlying at 554.21, portfolio size at $100,000 and a leverage factor equivalent to 0.4 meaning 40% of our portfolio, you would either have to sell 1.02 rounded to 2 put options, or 2.438338 rounded to 3 call options to create your position in google.
I don't believe it takes advanced software to calculate greeks. It really doesn't, and I've not actually seen a case where the theoretical value of the option actually calculates a legitimate value. The free software at the link above is perfectly capable of calculating a delta, which is essentially all you need to know to build a portfolio of options with.
I do not endorse or recommend any of these transactions for anyone. They were only examples of how to create a synthetically leveraged portfolio of any position size or percent of equity.
So, I think that helps. There's a lot more to options than a gambling casino as I've seen them used on the site. They serve a great purpose for creating and hedging these kind of positions.