Today, we’re looking at option rho, but first lets talk about the greeks more generally.
One of the most important concepts in Options trading is to understand the Greeks.
The Greeks are calculated measures that form a vital part of a trader’s risk management toolkit.
At their core, the Greeks measure how sensitive the value of a portfolio will be, given a change in an underlying parameter.
By using Greeks, options traders are able to isolate different component risks and then create and manage a portfolio that achieves a desired exposure objective.
The most common Greeks that are used by options traders are what are called the first-order derivatives delta, vega, theta, and rho.
Of these, rho is the least discussed and arguably least important – however, this is not to say the measure itself is not important.
Rho is seen as the least important because it rarely changes, owing to the fact that it measures the effect of interest rates on the price of an option and interest rates rarely change.
Since most traders are doing so on short-term timeframes, interest rates very rarely influence their trades and so rho is rarely considered.
However, there are periods of time, such as rapid market falls and recessions, where interest rates can change very quickly, sometimes every month for a period of months.
So while rho doesn’t often come into play, it is important to understand due to the influence it can have on option performance.
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What Is Option Rho?
Like the other Greeks, rho is found during the calculation of the option pricing model (which is a model that uses variables to theoretically value an option).
Since it’s determined using a standard set of calculations, the easiest way to find the value for rho is to look up the option chain which displays all the calls and puts for a given underlying asset and set expiration.
In most cases, your broker will provide this information to you but it is also found online for free on websites such as nasdaq.com.
So once you have this value from the option chain, what does it mean?
Option rho tracks the change in the price of an option as a result of changes in the risk-free interest rate.
The risk-free interest rate is the minimum rate of return you can achieve without taking any risk of loss of capital.
The risk-free interest rate is typically based on government bonds, specifically Treasury Bonds and Treasury Bills.
These are regarded as risk-free since the government will not default on its debt – after all, should it have a shortfall of cash to pay its debt obligations it can merely print more money.
When there is an increase in interest rates, a call’s premium will increase while a put’s premium will decrease.
Rho reflects this by being positive for both long calls and short puts, and negative for both short calls and long puts.
Other factors which can impact rho are:
The Price Of Stocks
The value of rho increases as the price of a stock increases as it will cost more to finance it.
Time To Expiration
Longer-term options will have a higher rho value compared to shorter-term options as interest rates rarely move substantially during short periods of time.
Volatility
The value of rho will be indirectly impacted by volatility, such that whenever the value of options change so too will rho.
For example, out-of-the-money options gain in value as volatility increases, thus causing rho to increase as well.
How Does Option Rho Impact Options Prices?
In order to determine how rho impacts the price of an option, apply the following formula:
New Price = Current Price + Rho x (Change in Interest Rates)
For example, say you currently own a long call trading at $3.75 and that the current risk-free interest rate sits at 3%.
After checking the option chain, you discover that it has a rho of 0.07.
In response to an overheating economy, the Federal Reserve raises rates to 5% – which results in the option price changing as follows:
New Price = Current Price + Rho x (Change in Interest Rates)
New Price = $3.75 + 0.07 x 2 = $3.89
In the event that interest rates went down 2% instead of up, simply put a negative sign in front of rho:
New Price = Current Price – Rho x (Change in Interest Rates)
New Price = $3.75 – 0.07 x 2 = $3.61
Option Rho and Cost of Carry
While rho is generally not front of mind for most investors, it comes into its own when considering the cost of carry.
Cost of carry is simply the costs that are incurred as a result of having an investment.
Typically, this cost is interest incurred as a result of margin or a loan that is used to purchase the security.
So for those investors using loans for their options purchases, rho plays a much more important role in pricing.
Conclusion
Option rho is the least discussed and arguably least important Greek, as it rarely comes into play for most investors.
Rho tracks the change in the price of an option as a result of changes in the risk-free interest rate.
If interest rates increase, the premium for a call will increase, while a decreasing interest rate decreases a put’s premium.
This is reflected in the value of rho with it being positive for both long calls and short puts, and negative for both short calls and long puts.
To determine rho, simply multiply it by the change in interest rates and then add it to the current price of the option to determine what the new price should be.
Rho is most important to those investors who need to consider cost of carry or are buying options with a very long timeframe.
Disclaimer: The information above is for educational purposes only and should not be treated as investment advice. The strategy presented would not be suitable for investors who are not familiar with exchange traded options. Any readers interested in this strategy should do their own research and seek advice from a licensed financial adviser.
