Considering Rho When Planning Trades

Just having an opinion on a stock is only half the battle in options trading.Choosing the best way to trade a forecast can make all the difference to the success of a trade. Options give traders choices. And one of the choices a
trader has is the month in which to trade. When trading LEAPS—Long-Term Equity AnticiPation Securities—delta, gamma, theta, and vega are important, as always, but rho is also a valuable part of the strategy.

LEAPS Options buyers have time working against them. With each passing day,theta erodes the value of their assets. Buying a long-term option, or a LEAPS, helps combat erosion because long-term options can decay at a slower rate. In environments where there is interest rate uncertainty, however, LEAPS traders have to think about more than the rate of decay.Consider two traders: Jason and Susanne.

Both are bullish on XYZ Corp. (XYZ), which is trading at $59.95 per share. Jason decides to buy a May 60 call at 1.60, and Susanne buys a LEAPS 60 call at 7.60. In this example, May options have 44 days until expiration, and the LEAPS have 639 days.Both of these trades are bullish, but the traders most likely had slightly different ideas about time, volatility, and interest rates when they decided which option to buy. Exhibit 7.1 compares XYZ short-term at-the-money calls with XYZ LEAPS ATM calls.

To begin with, it appears that Susanne was allowing quite a bit of time for her forecast to be realized—almost two years. Jason, however, was looking for short-term price appreciation. Concerns about time decay may have been a motivation for Susanne to choose a long-term option—her theta of 0.01 is half Jason’s, which is 0.02. With only 44 days until expiration, the theta of Jason’s May call will begin to rise sharply as expiration draws near.But the trade-off of lower time decay is lower gamma. At the current stock price, Susanne has a higher delta.

If the XYZ stock price rises $2, the gamma of the May call will cause Jason’s delta to creep higher than Susanne’s.At $62, the delta for the May 60s would be about 0.78, whereas the LEAPS 60 call delta is about 0.77. This disparity continues as XYZ moves higher.Perhaps Susanne had implied volatility (IV) on her mind as well as time decay. These long-term ATM LEAPS options have vegas more than three times the corresponding May’s.

If IV for both the May and the LEAPS is at a yearly low, LEAPS might be a better buy. A one- or two-point rise in volatility if IV reverts to its normal level will benefit the LEAPS call much more than the May.Theta, delta, gamma, and vega are typical considerations with most trades. Because this option is long term, in addition to these typical considerations,Susanne needs to take a good hard look at rho.

The LEAPS rho is significantly higher than that of its short-term counterpart. A onepercentage-point change in the interest rate will change Susanne’s P&(L) by $0.64—that’s about 8.5 percent of the value of her option—and she has nearly two years of exposure to interest rate fluctuations. Certainly, when the Federal Reserve Board has great concerns about growth or inflation, rates can rise or fall by more than one percentage point in one year’s time.

It is important to understand that, like the other greeks, rho is a snapshot at a particular price, volatility level, interest rate, and moment in time. If interest rates were to fall by one percentage point today, it would cause Susanne’s call to decline in value by $0.64. If that rate drop occurred over the life of the option, it would have a much smaller effect. Why? Rate changes closer to expiration have less of an effect on option values.

Assume that on the trade date, when the LEAPS has 639 days until expiration, interest rates fall by 25 basis points. The effect will be a decline in the value of the call of 0.16—one-fourth of the 0.638 rho. If the next rate cut occurs six months later, the rho of the LEAPS will be smaller, because it will have less time until expiration.

In this case, after six months, the rho will be only 0.46. Another 25-basis-point drop will hurt the call by $0.115. After another six months, the option will have a 0.26 rho. Another quarter-point cut costs Susanne only $0.065. Any subsequent rate cuts in ensuing months will have almost no effect on the now short-term option value.