Rho is the amount a theoretical option's price will change for a corresponding one-unit (percentage-point) change in the interest rate used to price the option contract. Typically the interest rate used here would be the risk-free rate of return. The rate associated with investing in Treasuries is traditionally defined by market experts as virtually risk-free.
Rho addresses part of the cost-to-carry issue: weighing the opportunity costs of tying up your cash in a long-term option versus other investments. (Whether or not the underlying stock pays a dividend can also impact cost-of-carry. Read below to learn more about dividends.)
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 annual risk-free interest rate is currently 5%, there are no dividends pending with this option, and implied volatility is currently 25%. The price of the call option is $2.25, and rho is .045 or 4.5 cents. This means if nothing else in the marketplace changes except the interest rate increases by one percentage-point, the call option would increase by the amount of the rho. In this case, the price of the call would increase in value by about five cents, to about $2.30 ($2.25 + $0.045 = $2.295). Interest rates don't usually jump by a full percentage point at a time; a more likely occurrence is that they'd move a quarter-point (0.25%) or half-point (0.5%). For these fractional moves, multiply the rho by the amount of the interest rate change (either .25 or .50), and the result would be the theoretical impact on the option's price (about one or two cents). If interest rates declined instead of increased, the call price would be expected to decrease by the amount of the rho multiplied by the change in the interest rate.
Here are a few takeaways about rho you may find useful:
Rho and vega react similarly when it comes to underlying price and time. Two factors that increase vega, or volatility exposure, are increasing time until expiration and higher underlying prices. These same factors also increase the option's sensitivity to a change in interest rates. When compared to shorter-term options, longer-term contracts would usually have larger rho numbers, or higher sensitivity to interest rate shifts. Rho also tends to get larger the more expensive the underlying security gets.
Because rho relates to carry costs, calls usually have a positive rho value, while puts tend towards negative rho values. That is to say, an increase in interest rates would cause calls to become more expensive and puts to become less expensive. But keep in mind, this change in value has nothing to do with an investor's outlook on the market. This change is only a result of how options pricing models work when they factor in a change in interest rates.
To bring this concept home, consider this example: let's say you have $10,000 to invest. One choice is to invest it all in Treasury bonds, offering a theoretically risk-free rate of return. Another choice is to invest in $10,000 worth of stock _ let's say 100 shares of the same stock at $100 per share. And a third choice is to buy one ITM call option for $10 reflecting your interest to control 100 shares of stock. The call investment would be $10 x 100 = $1,000. This action would leave you with cash left over ($10,000 – $1,000 = $9,000).
If interest rates are high, the first alternative may be more attractive than the second because investing in Treasury bonds offers lower risk but still may offer a modest return when compared to investing in shares of stock. However, the third option can be a hybrid of the first two choices. This selection allows for the investor to participate in a market investment (call option) and also invest the left over money elsewhere (Treasury bonds). Although there is no guarantee that the call option (or the stock for that matter) would perform well, the return from the Treasury bond investment would boost the combined return when both investments are considered together.
The higher the interest rate, the more appealing the third choice becomes to investors. On the contrary, the lower the risk-free interest rate, the less attractive this combination investment turns out to be.If you're a fan of LEAPS options, rho can be a useful secondary or tertiary indicator to keep your eye on. LEAPS stands for Long Term Equity AnticiPation Securities; they're basically extra-long-term option contracts. We've already established that longer-term options usually have larger rho numbers and are therefore more sensitive to interest rate shifts.