Introducing Rho, the Interest-Rate Greek

optionsguy posted on 04/15/10 at 09:39 AM

In this back-to-basics series Brian Overby reviews the Greeks, factors to help you gauge the impact of various changes on option contract prices. Today's post discusses Rho, the Greek measuring how interest-rate changes can influence option prices.

Rho measures the amount a theoretical option's price will change for a corresponding one-unit (percent) change in the interest rate used to price the option contract. Rho is less important for those who trade near-term options, but rho does need to be watched by those who trade longer-term options.

Rho mainly addresses cost-of-carry issues, or weighing the opportunity costs of tying up your cash in a long-term option versus other available choices. As a source of steady income available over longer stretches of time, dividends are also very close cousins to interest rates and will similarly affect Rho.

Let’s consider an example: a 50 strike call option, with the stock trading at 50 so it's a perfectly at-the-money (ATM) option. Let’s further assume we have 60 days to expiration, the risk-free interest is 5%, there are no dividends involved with this option, and implied volatility is currently 25%. The price of the option is $2.25 and rho would be equal to .045 or 4 ½ cents.  If nothing else in the marketplace changes EXCEPT the interest rate used to price the option increases one percentage point from 5% to 6%, the call option should only increase in value by approximately 5 cents. In other words, a 1% jump in interest rates should theoretically bump the call option's price from $2.25 to $2.30.

That’s theory, but in practice if the Fed were to increase rates by a percentage point, most traders’ prime concern would be where the market was heading next, as opposed to any minimal effect on their option contract.

That said, we're in a historically low interest-rate environment today and finally emerging from a protracted recession. Chances are good that interest rates could move higher in the near-term, so it's worth understanding how such a change might impact your option positions.

Our example above used a call option with positive rho. Typically calls have a positive rho value, while puts have negative rho. That suggests an increase in interest rates will cause calls to become more expensive and puts to become less expensive. Dividends create the opposite effect: if the dividend amount increases, puts will typically increase in price while calls decrease in price. To learn more about how the carry costs of calls and put work please read one of my most popular blogs about early exercise. Carry costs play a big part in early exercise, and this blog goes into great detail as to why.

Using the Options Calculator from our Tools menu, let's review a "here and now" example with 3M (MMM), a large-cap stock with a dividend. You'll notice rho for the call is at 0.0334, or .03 if we round, and the put is -0.0508 or about -0.05.

Right now the put is just in-the-money and trading for $3.00; the call is just out-of-the-money and trading for $1.65. Rho suggests that, in theory, the call would gain 3 cents and the put in theory would lose about 5 cents for a 1% increase in interest rates. To put that into perspective, that's around 1% of the price for these 38-day option contracts. Now let's compare these numbers to a LEAPS option.

These option contracts use the same underlying stock, 3M, and strike price, but it has 647 days to expiration. Because of the time factor, these option prices increased in value to 8.51 for the call and 11.21 for the put. (The reason the put costs so much more is because the stock does pay a decent dividend, and several dividends will be paid over that 647-day time period. It makes sense if you think about it from the put owner's point of view. When a dividend is paid, the stock price is decreased by the amount of the dividend, and puts benefit from a decrease in price. So the actual price of the put increases in anticipation of all the potential dividends being paid over the time period.)

What can you take away from the above? You can readily see how important a dividend can be, but also look at how it affects rho. Rho is larger for the put - around 79 cents - versus the call, around 52 cents. But if we just consider these amounts on a percentage basis, rho accounts for almost 7% of the option's price - in other words, interest-rate swings as measured by rho matter much more to these LEAPS prices than to their 38-day option equivalents. You see why LEAPS option traders need to focus much more on interest rates and dividends than near-term option traders.

Next week's post will round off our series on the Greeks with a closer look at rho. We'll discuss rho's close relationship with vega, the volatility Greek, and explore other factors to keep in mind when interest-rate changes are afoot. Stay tuned!

Regards, Brian Overby
TradeKing's Options Guy

[image: Giardini di Mirò, Live @ Rockin'Rho, 17.09.2006 by zabriensky what? on Flickr]

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Even though the Greeks represent the consensus of the marketplace as to how the option will react to changes in certain variables associated with the pricing of an option contract. There is no guarantee that these forecasts will be correct.

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Posted by optionsguy on 04/15/10 at 09:39 AM


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