Rho and Interest Rate Sensitivity
Rho and Interest Rate Sensitivity
Rho measures how much an option's price changes when interest rates change by one percentage point. While typically the smallest of the major Greeks, rho becomes significant for long-dated options and in environments with substantial rate movements.
Definition and Key Concepts
What Is Rho?
Rho is the expected change in option price for a 1% (100 basis point) change in the risk-free interest rate:
- Call rho is positive: Calls gain value when rates rise
- Put rho is negative: Puts lose value when rates rise
Example: A call with rho of $0.08 gains $8 per contract when rates rise 1%.
Why Rates Affect Options
Interest rates affect options through the cost of carry—the opportunity cost of capital:
- Call buyers: Instead of buying stock, they buy a call and earn interest on uninvested cash. Higher rates make calls more attractive.
- Put buyers: Instead of selling stock and earning interest on proceeds, they hold stock and buy a put. Higher rates make puts less attractive.
Rho Direction by Position
| Position | Rho Sign | Rate Rise Effect |
|---|---|---|
| Long call | Positive | Gain |
| Short call | Negative | Loss |
| Long put | Negative | Loss |
| Short put | Positive | Gain |
How It Works in Practice
Rho Characteristics
Rho and Time to Expiration: Longer-dated options have higher rho because there's more time for rate differences to accumulate.
| Days to Expiration | Relative Rho |
|---|---|
| 30 days | Very low |
| 90 days | Low |
| 180 days | Moderate |
| 365+ days | Significant |
Rho and Moneyness: ITM options have higher rho than OTM options because they have more intrinsic value affected by carry cost.
| Moneyness | Call Rho | Put Rho |
|---|---|---|
| Deep ITM | Highest | Most negative |
| ITM | High | Negative |
| ATM | Moderate | Moderate negative |
| OTM | Low | Low negative |
| Deep OTM | Near zero | Near zero |
Calculating Rho Impact
Single Option: Rho impact = Rho × Rate Change × 100 × Contracts
Example:
- 10 LEAPS calls with rho = $0.25
- Fed raises rates by 0.50% (50 basis points)
- Impact = $0.25 × 0.50 × 100 × 10 = $125 gain
Comparing Rho to Other Greeks
For short-dated options, rho is dwarfed by delta, gamma, theta, and vega:
| Greek | ATM 30-Day Call Impact (per 1% change) |
|---|---|
| Delta | ~$50 per $1 stock move |
| Gamma | Delta changes ~5% per $1 |
| Theta | -$5 per day |
| Vega | $10-15 per 1% IV change |
| Rho | $0.50-1.00 per 1% rate change |
For LEAPS, rho becomes meaningful:
| Greek | ATM 2-Year Call Impact (per 1% change) |
|---|---|
| Rho | $15-30 per 1% rate change |
Worked Example
LEAPS Call and Interest Rate Environment
You buy a 2-year LEAPS call on XYZ ($100 stock) when rates are 4%.
Initial Position:
- XYZ 2-year $100 call
- Premium: $18.00
- Delta: 0.58
- Rho: $0.22 per 1% rate change
Scenario: Fed Hikes Rates 1%
| Factor | Impact |
|---|---|
| Rho gain | +$0.22 × 100 = +$22 per contract |
| As % of premium | +$22 / $1,800 = 1.2% |
Scenario: Fed Cuts Rates 1%
| Factor | Impact |
|---|---|
| Rho loss | -$0.22 × 100 = -$22 per contract |
| As % of premium | -$22 / $1,800 = -1.2% |
For a $1,800 option, a $22 change is modest but not negligible over a 2-year holding period with multiple rate decisions.
Put Position Comparison:
XYZ 2-year $100 put:
- Premium: $14.00
- Rho: -$0.18 per 1% rate change
If rates rise 1%:
- Put loses $18 per contract
- Combined with any price decline offsetting
Synthetic Long Stock via Options:
Buy call, sell put at same strike creates synthetic stock:
- Call rho: +$0.22
- Short put rho: +$0.18
- Net rho: +$0.40 per 1% rate change
- This approximates the interest cost of carrying 100 shares
Risks, Limitations, and Tradeoffs
Rho Is Usually Dominated by Other Greeks
For typical options trades (30-90 DTE), rho's impact is minor compared to delta and vega. A 1% rate change might move an option $0.50, while a 1% underlying move or 1% IV change moves it $5-15.
Rate Changes Are Gradual
Unlike underlying prices that can gap, interest rates typically change in 25-50 basis point increments at scheduled Fed meetings. The impact accumulates slowly rather than creating sudden P/L swings.
Model Assumptions
Standard rho calculations assume a parallel shift in the yield curve. In reality:
- Short-term and long-term rates can move differently
- Credit spreads can widen while risk-free rates fall
- Options on futures may have different rate sensitivities
Dividend Interaction
For stocks with dividends, the net carry cost involves both interest rates and dividend yield. Higher dividends reduce call values and increase put values, similar to the effect of lower interest rates.
Common Pitfalls
-
Ignoring rho for LEAPS: Long-dated options are significantly affected by rate expectations.
-
Not adjusting for rate environment: A 5% rate environment has different rho dynamics than a 0% environment.
-
Assuming rates are stable: Fed policy changes can shift rates substantially over a LEAPS holding period.
-
Confusing nominal and real rates: Inflation expectations also affect markets; rho captures nominal rate sensitivity.
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Over-weighting rho in short-dated trades: For weekly or monthly options, rho is typically irrelevant.
Checklist for Rate Sensitivity
- Calculate position rho for options over 6 months to expiration
- Assess current rate environment and Fed expectations
- For LEAPS, factor potential rate changes into position sizing
- Recognize that call rho is positive and put rho is negative
- Compare rho impact to expected delta, theta, and vega impacts
- For synthetic positions, understand combined rho exposure
- Monitor Fed meeting dates when holding long-dated options
- Adjust expectations if rate environment shifts significantly
Next Steps
Understanding individual Greeks is essential, but real positions combine multiple legs. See Position Greeks vs. Individual Leg Greeks for how to aggregate and manage Greeks across complex positions.
For volatility sensitivity that often dominates rho, review Vega Exposure to Implied Volatility Changes.