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I’m all about keeping a healthy dose of skepticism. The financial world is notorious for attracting fraud and scams that trap gullible investors.

But I also know that certain things are verifiably good for everyone, despite their reputation.

Take high-frequency trading (HFT). HFT firms rapidly buy and sell shares to fill our orders. They make a few cents, or even fractions of a penny, on each trade. By executing millions of orders, they make big money.

This has sparked some controversy and harsh criticism because it can seem as though these firms are front-running our orders. They buy solely to sell to us. They mark up the prices and profit on the difference.

This all sounds bad. But before you run off imagining HFT firms as organized mobsters running the show, I can assure you they’re not.

HFT actually works to our benefit, and in return, market makers capture low-risk gains for their service. So, it’s a win-win for both sides. And I have concrete math to prove it.

## Put-Call Parity Keeps Prices in Line

Not only do HFT firms enable us to trade options on any stock by adding liquidity to the market, they’ve also lowered the cost of trading under what it would be with other systems.

That’s because a critical equation keeps prices in check — the put-call parity equation.

HFT firms use the put-call parity equation to limit their risks when buying and selling to execute our orders. It states that the value of a put and the stock is equal to a call and some cash.

Here’s the formula:

P + S = C + PV(A)

P = price of put with strike price A.S = price of stock.C = price of call with strike price A.PV(A) = net present value of the option’s strike price.

Now that we know the theory behind the formula, let’s look at an example.

On Monday, Apple Inc. (AAPL) was trading at about \$140.65. The \$141 call expiring on October 28 was trading at \$5.45. The \$141 put expiring on October 28 was trading at \$6.10.

Let’s plug these numbers into the formula:

P + S = C + PV(A)

For our purposes, let’s rewrite it to:

P + S = C + (A / (1 + R) ^ T)

Where R is the interest rate a broker charges on a margin loan and T is the length of the loan in years.

For this example, the variables are:

P = \$6.10S = \$140.65C = \$5.45A = \$141R = 3.83% or 0.0383 in the formula.T = 0.049 since the option expires in 18 days.

For this example, I’m using the interest rate charged by Interactive Brokers.

Plugging in our values, we get:

\$6.10 + \$140.65 = \$5.45 + (\$141 / (1 + 0.038) ^ 0.05)  (1)

Let’s reduce:

\$146.75 = \$5.45 + (\$141 / 1.002)  (2)

\$146.75 = \$5.45 + \$140.72   (3)

\$146.75 = \$146.17     (4)

As you can see in line 4, the two values on both sides of the equation end up being close for me, off by just 0.4%.

That can be explained by the fact that I don’t have true real-time data. HFT firms collocate servers at the exchange. They use gold-tipped cables to minimize delays. They have true real-time data.

Their interest rate is also lower than the one I used. And they don’t ignore the dividend to simplify the calculation.

If you stuck with me through the math, you now know exactly how to confirm prices are fairly marked.

I’ve done this calculation hundreds of times. It’s always the same. The prices match the formula within 1% almost every time. For an illiquid stock, the difference might be 2%.

This means we get fair prices when we trade. And if we don’t, an HFT firm will jump in and take the mispriced option. With this formula, they can earn a quick, risk-free profit.

If the AAPL call was trading at \$5.10, for example, the formula wouldn’t balance. So, an HFT firm could buy the cheap side of the equation and short the expensive. They immediately lock in a risk-free gain.

That threat makes mispricing rare. So, I don’t ever expect to spot one. Arbitrage traders would jump into the market and push the mispriced option back in line with the put-call parity equation.

I benefit from all this knowing I can trade any option, on any stock.

Andrew Keene also applies this idea in Trade Kings.

Andrew is a former market maker — in fact, he was the No. 1 market maker for Apple options on the trading floor at the CBOE — and he’s an expert at trading on volume and open interest.

So many years as a market maker taught Andrew to pay attention to order flow. Eventually, he realized he could design scanners that tap into this order flow, and signal trade opportunities. And he started sharing those signals with his followers in a live, one-of-its-kind Trade Room.

This Trade Room is free to join until tomorrow’s close. And just this week, Andrew’s scanners have produced over 18 signals… with gains reaching as high as 198%.

Regards,

Amber HestlaSenior Analyst, True Options Masters