Rho

Explained:

rho


 
   

Rho is one of the Greek factor sensitivities used by traders to measure market risk exposures in derivatives portfolios. It measures a portfolio's linear exposure to changes in the risk-free interest rate.

Let and be current values for the portfolio and underlier (here superscripts 0 indicate the current time t = 0. See the notation conventions documentation). Formally, rho is the partial derivative of the portfolio's value with respect to the risk-free rate:

[1]

This technical definition leads to an approximation for the behavior of a portfolio.

[2]
 
   

where is a small change in the risk-free rate, and is the corresponding change in the portfolio's value.

Suppose a portfolio has a rho of USD –2.3MM. If the risk free rate rises 5 basis points ( = .0005), the portfolio should lose about

2.3MM (.0005) = USD 1150 [3]

For most portfolios, sensitivity to the risk-free rate is minor compared to possible sensitivities to underliers or implied volatilities. For this reason, rho is a less significant Greek.

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copyright © Glyn A. Holton, 1996

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