Rho: interest rates

Rho tells you how much an option’s price changes when interest rates move by one point, say from 4% to 5%.

Picture the dashboard of a car. Delta is the speedometer and theta is the fuel gauge. Rho is the smallest dial in the corner. Most days you can ignore it, but on a long trip it starts to matter. For options, a long trip means a contract that lasts a year or more.

Our $100 call with 30 days left has a rho of 0.041. A full point rise in rates adds about $0.04 a share, or $4 a contract. The same call with two years left has a rho of 0.960, about 23 times as much.

Why rates move option prices at all

Buying a call is a way to own the upside of a stock without paying for the stock yet. You pay the strike later, only if you choose to. Until then, that money can sit in Treasury bills and earn interest.

On our call, that is $100 kept in the bank for 30 days. At 4% it earns about $0.33. That is small, so the effect on a one-month call is small. Over two years the interest adds up, and so does the effect.

Puts go the other way. A put pays you the strike in the future. Higher rates make money you receive later worth less today, so puts get cheaper as rates rise.

How much it moves

Slide the rate from 0% to 8%. That is a bigger swing than most years ever see. The 30-day call goes from $2.86 to $3.19. The 2-year call goes from $14.03 to $21.68.

Switch the chart to puts. The 2-year put falls from $14.03 to $6.89, losing more than half its price.

When to pay attention

Rates rarely move a full point in a month. Implied volatility can move that much in an afternoon. For our 30-day call, one point of volatility is worth $0.11 a share and one point of rates is worth $0.04. For short-dated options, rho is small next to delta, theta and vega.

It matters for long-dated options, often called LEAPS, which run a year or more. If you hold those while the central bank is raising or cutting rates, check rho alongside the other Greeks.