Wednesday, September 06, 2006 8:54:52 AM
Understanding Rho
Brian Overby
August 18, 2006
To finish off the series on the Greeks, here are a few fast facts on the interest rate Greek rho. Rho is defined as 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 can be an issue for investors that prefer to 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 options. As a source of steady income available over longer stretches of time, dividends are also very close cousins to interest rates and will affect Rho.
Let’s consider an example: a 50 strike call option, with the stock trading at 50. 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. This means if nothing else in the marketplace changes except the interest rate used to price the option would increase by 1% to 6%. The call option would only increase in value by approximately 5 cents, this means the option would trade for $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.
Rho reacts similarly to vega when it comes to changes in the price variables. The two things that create exposure to a change in interest rates/rho are the length of time until expiration, naturally, and the price of the underlying. Longer-term options will usually have larger rho numbers compared to shorter term. Rho also tends to get larger the more expensive the underlying is.
A few things to take with you about rho. Rho deals with carry costs. The call has a positive rho value, while puts have negative rho values. Stated another way, an increase in interest rates will cause calls to become more expensive and puts to become less expensive.
Dividends paid by the underlying are also a part of carry costs. The payment of a dividend offsets the carry cost. So the dividend payouts tend to have an opposite effect from the one described above: if the underlying security increases the dividend or decides to start paying one, calls usually become less expensive and puts tend to become more expensive.
If you’re a fan of LEAPs on large blue-chips in particular, rho is something to make note of, it can represent a large portion of the option’s price.
Brian Overby
August 18, 2006
To finish off the series on the Greeks, here are a few fast facts on the interest rate Greek rho. Rho is defined as 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 can be an issue for investors that prefer to 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 options. As a source of steady income available over longer stretches of time, dividends are also very close cousins to interest rates and will affect Rho.
Let’s consider an example: a 50 strike call option, with the stock trading at 50. 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. This means if nothing else in the marketplace changes except the interest rate used to price the option would increase by 1% to 6%. The call option would only increase in value by approximately 5 cents, this means the option would trade for $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.
Rho reacts similarly to vega when it comes to changes in the price variables. The two things that create exposure to a change in interest rates/rho are the length of time until expiration, naturally, and the price of the underlying. Longer-term options will usually have larger rho numbers compared to shorter term. Rho also tends to get larger the more expensive the underlying is.
A few things to take with you about rho. Rho deals with carry costs. The call has a positive rho value, while puts have negative rho values. Stated another way, an increase in interest rates will cause calls to become more expensive and puts to become less expensive.
Dividends paid by the underlying are also a part of carry costs. The payment of a dividend offsets the carry cost. So the dividend payouts tend to have an opposite effect from the one described above: if the underlying security increases the dividend or decides to start paying one, calls usually become less expensive and puts tend to become more expensive.
If you’re a fan of LEAPs on large blue-chips in particular, rho is something to make note of, it can represent a large portion of the option’s price.
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