Rho

What Is Rho?

Rho is the rate at which the price of a derivative changes relative to a change in the risk-free rate of interest. Rho measures the sensitivity of an option or options portfolio to a change in interest rate. Rho may likewise allude to the collected risk exposure to interest rate changes that exist for a book of several options positions.

For instance, in the event that an option or options portfolio has a rho of 1.0, for each 1 percentage-point increase in interest rates, the value of the option (or portfolio) increases 1 percent. Options that are generally sensitive to changes in interest rates are those that are at-the-cash and with the longest opportunity to expiration.

In mathematical finance, amounts that measure the price sensitivity of a derivative to a change in an underlying boundary are known as the "Greeks." The Greeks are important devices in risk management since they permit a manager, trader, or investor to measure the change in value of an investment or portfolio to a small change in a boundary. More important, this measurement permits the risk to be isolated, hence permitting a manager, trader, or investor to rebalance the portfolio to accomplish an ideal level of risk relative to that boundary. The most common Greeks are delta, gamma, vega, theta, and rho.

Rho Calculation and Rho in Practice

The specific formula for rho is muddled. Yet, it is calculated as the principal derivative of the option's value with respect to the risk-free rate. Rho measures the expected change in an option's price for a 1 percent change in a U.S. Treasury bill risk-free rate.

For instance, expect that a call option is priced at $4 and has a rho of 0.25. Assuming that the risk-free rate rises 1 percent, say from 3 percent to 4 percent, the value of the call option would rise from $4 to $4.25.

Call options generally rise in price as interest rates increase and put options generally decline in price as interest rates increase. In this way, call options have positive rho, while put options have negative rho.

Expect that put option is priced at $9 and has a rho of - 0.35. In the event that interest rates were to diminish from 5 percent to 4 percent, the price of this put option would increase from $9 to $9.35. In this equivalent scenario, expecting the call option referenced over, its price would diminish from $4 to $3.75.

Rho is bigger for options that are in-the-cash and abatement consistently as the option changes to become out-of-the-cash. Additionally, rho increases as the opportunity to expiration increases. Long-term equity anticipation securities (LEAPs), which are options that generally have expiration dates that are greater than one year away, are undeniably more sensitive to changes in the risk-free rate and, in this manner, have bigger rho than more limited term options.

However rho is a primary input in the Black-Scholes options-pricing model, a change in interest rates generally overallly affects the pricing of options. Along these lines, rho is generally viewed as the least important of all the option Greeks.

Features

• Rho is typically viewed as the least important of all option Greeks.
• Rho measures the price change for a derivative relative to a change in the risk-free rate of interest.