An Interest in Rho!


RhoOption Rho explains to us the amount an option value would change for a change in the risk free rate of interest. It is normally regularized to show the change in the value of an option for a percentage change in interest rate.

A unique way to understand the concept of Rho is to remember the basic assumptions of most option pricing models used in stock market. It’s mostly assumed that an asset that is paid upfront against cash must offer a return at least equal to the risk free interest rate.

Have a discernment on how Rho works in stock market?

In stock market, another assumption is made that for a stock option, the underlying price will increase in twelve months by a minimum of risk free interest rate. The assets must be more risky as against the risk free interest rate, so they should offer returns at least at par to risk free rate.

Let’s consider a call option with a strike price of hundred rupees, which expires in twelve months time, on a spot price of hundred rupees. Now, let’s imagine that the risk free interest rate is 5%. You might infer that this is an at the money option as its strike equals the spot price. However, it is actually not the case as the option is struck not at the spot price but on the future price of the spot. In simpler terms, the value of this call, which has twelve months to go relates to where the spot price is expected to priced in twelve months time and not where it is currently trading at. Hence, at the money calls in this situation is the 105 rupees call as that is the forward price of the Rho in stock market spot.

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Now, let’s go back to the definition of Rho again. Rho is nothing but the change in option price against the change in the interest rates. It is quite clear from the example that if the risk free rate increases from five to ten percent, it is going to increase the value of the call option. The interest rate increase has the effect of pushing the forward spot rate up and this pushes the calls further towards in the money. The put options with strike price of hundred rupees would instead become further out of the money and therefore would lead to a drop of its value. In general terms, we see that the calls have positive rho while puts have negative. If you are long on the calls and short on the puts, even at the same strike price, you would lead to a positive exposure versus the interest rates.

Also Read : Alpha, the God of Active Investments!

In stock market, the risk with rho can be added across options that have exposure to the same interest rates. However, immense care should be taken to match the rate of interest with duration and type. Only the options with the same expiration and currency can be added with regards to rho risk. It is simply because the rate of interest varies by currency and duration. An interest rate yield curve is variable and highly specific to the currencies. Brokerage Firms with varied option portfolios can reduce the hedging cost by aggregating rho across the portfolios rather than hedging one at a time.

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