Rho as an advantage when interest rates rise

by Jay Pestrichelli on December 16th, 2013

It has been a long time since anyone has really talked about the effect of interest rates on the price of options. That is because in the current environment there is nothing to speak of with rates of 0% to 0.25%. However, in normal environments, interest rates do impact the price of options and that is calculated using the Greek Rho.

Investopedia defines Rho as: The rate at which the price of a derivative changes relative to a change in the risk-free rate of interest. Rho measures the sensitivity of an option or options portfolio to a change in interest rate.

For example, if an option or options portfolio has a rho of 12.124, then for every percentage-point increase in interest rates, the value of the option increases 12.124%.

Why does this occur? The change in options prices comes in the comparison to using an option to represent a position vs. actually buying 100 shares of it. For example, we know that the equivalent of buying 100 shares of SPX (S&P 500) at today’s price of \$1790 (which isn’t actually possible) would take \$179,000. However, buying a deep in the money option would require only 25% to 30% of that amount. That leaves 75% to 70% of the cash free to earn interest. Knowing this, the options market can charge a little more premium for that deep in the money call.

As said earlier, Rho has had little effect on call prices because interest rates have been so low. However, if we all agree that rates are more likely to go up than go down, it would stand to reason we would want to hold positions that benefit from rising rates. Said another way, we want to be long Rho.

Take for example, the SPX DEC 2015 1325 Call. It has about 2 years to expiration, is in the money by \$462, and has less than \$5 of time value. With the SPX at 1787 this option will cost about \$465 per contract or \$46,500. The Rho for this option is 26.42. That means that every 1% that interest rates rise, this option will make \$2,642 (100*Rho).

This is a way to get long interest rates and leave a large portion of your assets in cash away from market risk. Remember, you only needed \$46,500 to gain the exposure of \$178,700 of market value. Being long 1 contract of an SPX option so deep in the money will feel exactly like owning 100 share of the SPX – if that was possible. The \$132,200 you didn’t need to invest is available to either now earn interest or be put to work on other opportunities.

Constructing a position
By the way, there is the added benefit of holding an option like this as it will gain dollar for dollar on the way up, but not lose dollar for dollar on the way down when the move was dramatic enough. If there was to be a large market selloff, the rate of change of this option with regard to the market price decline would be less.

For example if the market dropped 20% over the next 6 months, a portfolio that was long at 1787 would decline to 1431 for a \$35,600 (100*{1431-1787})loss. However, this option bought for \$465 would be worth \$185, a loss of only \$28,000. This loss avoidance becomes even more dramatic the farther down the market drops.

A position like this 1325 long-dated call is one that has plenty of exposure but is still considered hedged. After all, you can’t lose more than you spent on the price of the option. If you thought the exposure of \$46,500 (the max loss) on a \$178,700 investment was still too risky, you can always hedge it by buying puts at a higher strike price. Choosing a strike price at 10% lower than current market (1600) would run \$130 or \$13,000 over the 2 year period. This works out to be an annualized cost of 3.6%. This leaves nearly \$120,000 free in cash to invest elsewhere or earn interest.

And if that seems to expensive for the hedge, go ahead and sell the 1325 put to offset some of the cost of the protection. If you already didn’t plan on being long below the 1325 call level, why pay for protection below that. Selling the 1325 put would bring in \$5,200. This would reduce the annualized cost of hedging to 2.2% and there is no upside limitation. The max loss now of this combination is \$26,800 or 15%

That got complicated quick, so here is a summary of the positions we just entered:

SPX @ 1787
Long 1 1325 DEC2015 Call for \$465
Long 1 1600 DEC2015 Put for \$130
Short 1 1325 DEC2015 put for \$52

Net cost of \$543
Max gain: No Limitations
Max loss: \$268 @ SPX of 1600
Breakeven of SPX @ 1867 (4.4%)
Days to expiration 731
Annualized cost of hedging 2.2%

So for 2 years you have a max loss of only 15%, no limitations on upside gain, a cost of hedging only 2.2% per year and stand to gain if interest rates rise, and about \$125,000 of free cash available for other opportunities.

All in all, not a bad way to set yourself up for the next couple of years.

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