Rho – The Forgotten But Important Options Greek

Options traders and frat bros share an important commonality. OK, because of the high overlap between the two groups there are many more than one, but I was referring to their knowledge of the Greek alphabet.

Yet even within the world of options greeks, some are more important than others. Delta, which is the change in an options value for a given move in the underlying’s price, seems to take first place. Gamma (the change in an option’s delta for a given move in the underlying’s price) and theta (the change in an options price over time, aka “decay”) follow closely behind. Options writers profit from theta, and those who are long options are implicitly betting that a stock will move sufficiently to allow the position’s profits from gamma will outpace their losses from theta (we paid particularly close attention to that relationship when managing our market-making portfolio). Vega (the sensitivity of an option’s price to changes in implied volatility) is also quite important, particularly around earnings season when traders adjust their volatility assumptions leading up to and after an earnings report.

Somewhere hiding off to the side of the screen is rho. Rho is the sensitivity of an options price to changes in interest rates. For years, rho could be largely ignored because interest rates were low and at or near zero. If delta is the Zeus on the options market’s Olympus, rho might be Momos, the largely forgotten goddess of satire.

But they say that timing is everything in comedy, and timing certainly plays a key role when trading options. With interest rates showing historical levels of volatility while broadly rising, now is the time for us to pay some attention to rho.

It is important to remember that options prices utilize the forward price of the underlying security. If you buy an option with three months to maturity, pricing models consider what the stock is likely to be worth in three months’ time. If we buy the stock now, we must lay out sufficient funds to pay for it. If we enter into an agreement to buy the stock sometime in the future we can deposit those funds into an interest bearing account. This is why we typically see futures curves rise from left to right (aka “contango”).

When interest rates are zero, we are largely indifferent to whether we invest the money now or later. As a result, the forward values of many stocks were essentially the same as their current values. When rates are zero, the future value of $50 is still $50. When rates are 3%, the three-month forward value of $50 is $50.375.ⁱ This means that even if the stock hasn’t moved, any options with a three-month expiration would have to adjust their forward price by $0.375. If we are talking about a stock or ETF with a $300 value, that amount is $2.25. That change is what rho is trying to capture.

Once rho becomes a factor, it tends more meaningful for higher priced stocks and longer dated options. We see that the effect of rate changes are greater in absolute dollar terms if the underlying is higher priced. We also see that forward values change more over longer periods of time. In the example above, the forward value of $50 over one year would be $51.50 vs a three-month $50.375.

Prior to the recent rate hikes, rho had only been meaningful for stocks that were hard to borrow. If a stock is hard to borrow it can depress its forward value. In that case a buyer can receive interest payments for owing the stock that are greater than those received for foregoing the purchase. That interest rate differential can be quite substantial, and rho needs to be a meaningful when trading options on hard to borrow stocks – or those that suddenly become hard to borrow. But the vast majority of shares are considered “general collateral”, meaning that the relevant interest rate is the prevailing Fed Funds rate.

Most investors will realize that dividends also affect the forward price of a stock. If we forego owning a stock over an ex-dividend date we are not entitled to that payment. Options prices typically reflect the effect of dividend payments via lower forward values. Anyone who trades options on a dividend payer needs to be vigilant about dividend payments and ex-dates.

As options greeks go, rho is still less meaningful than many of its peers. If you’re not trading options on high priced indexes, or sticking to shorter dated options on stocks that are not hard to borrow, the effects of rho can be relatively minimal. But rho can no longer be ignored; if you’re scrolling through the options greeks it may behoove you to mouse all the way over to check on rho too.

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i 50.375 = 50 * (1 + .03/4), with 4 being the factor for ¼ of a year. If we were trying to calculate for one month, we would divide by 12.