Oh No, Here Comes Rho!
Vol #92: August 5th, 2022
The diamond industry promises that big things come in small packages. Investors too would do well to heed this reminder that small changes can create big impacts.
As benchmark interest rates are being aggressively tweaked (+75 basis points each of the last two Fed meetings), we’re seeing big impacts as markets adjust to this new paradigm. The Fed Funds target rate has changed 2.25%, and we’ve seen certain assets move 10x that. Growth stocks have been pounded like it’s the year 2000, and the dollar is strengthening to levels not seen for 20 years.
In the options pricing model, when interest rates change, we call this exposure “rho”. It’s the greek that describes how much an option’s price will change given a 1% increase in interest rates. Calls have positive rho, and puts have negative rho.
The way I remember the impact of rho is by thinking about what the pricing model uses for a stock price. Options are priced based on where the underlying will be at expiration (with some arbitrage boundaries if there is early exercise as with American style options). Implied volatility gives us the expected range, and the implied interest rate gives us the forward value of stock.
In the arbitrage replication theory of Black Scholes pricing, the forward value of stock is a function of the risk free interest rate minus any dividends expected to be paid. The higher the interest rate, the higher the forward value, thus calls get richer and puts get cheaper.
On our show earlier this week, Lex from Tradier explained a different, complementary intuition. If you’re long calls and short puts you have a “combo” on; this mimics the exposure you get from a long underlying position. To hedge this, you need to sell stock and put on a “reversal”. This reversal is 100% delta neutral (save special situations for the 201 class), and your only risk is the cost of carry - i.e. the interest rate or dividend changing.
Short stock exposure collects interest, because you’ve sold stock and now have a pile of cash sitting in a bank earning yield. (Assuming the stock is not hard to borrow.) If interest rates go up, you’re going to make more money on your short stock, so long calls and short puts have positive exposure to interest rates - positive rho.
For most stocks and underlyings, the interest rate is closely tied to the risk free rate of return. Something like the Fed Funds, Eurodollar, or Treasury bill rate. Market forces will pin this implied rate to what the largest participants are paying as a cost of capital.
My friend Ari (author of the fantastic blog “Don’t Take My Word for It”) shared with me a joke he has around the office. “It’s the cost of carry” is their go-to response for explaining something funky in the markets.
Stock and strike price are easy inputs into the model, and even volatility can be interpolated because it’s symmetrical to calls and puts. But when your model needs a different kind of jiggering, it’s usually the cost of carry.
This immediately made me think of the concept of “dark matter” - the hypothetical substance which supposedly accounts for over 85% of the universe’s makeup. Scientists first stumbled across this because absent *something else*, there was no way that galaxies and universes would behave as they do, or even have formed at all.
Interest rates and the cost of carry are the dark matter glue that holds asset pricing models together. Options traders look to determine the forward price of stock, and cost of maintaining the position. It’s the same as when investment bankers perform a discounted cash flow analysis, it all comes down to interest and growth rate assumptions.
During the last major bull market in crypto, interest rates for tokens were fairly elevated compared to traditional markets. While the Fed Funds rate was effectively 0%, Bitcoin and Ethereum derivatives were pricing in interest rates that nearly hit 30% annualized figures.
Some of this was due to the speculative leverage that futures contracts offered. Because participants could get up to 100x leverage on a future, there was a lot of hot money demand that separated the prices of derivatives from their underlying. An “easy” trade to make if you had the capital, was selling futures and buying spot to watch those values converge and capture an arbitrage profit.
A big part of the difference was the relative cost of capital in the different ecosystems. With numerous hoops to jump through to get between the TradFi and DeFi world, capital had different prices. The options markets or borrow/lend markets offered a better perspective on what the “risk free” rate of return was in DeFi.
During this time period to get models to “fit”, interest rates were typically in the 6-10% range, which paralleled what centralized exchanges like Gemini were paying lenders of stablecoins. Digital dollars and tokens were both in demand, so the forward price of those assets responded accordingly. This is no longer the case, as various structural factors like reduced access to leverage combine with slackening retail demand.
As interest rates change, so does the hurdle rate for capital expenditures and investments. Higher interest rates means higher cost of capital, whether it's a direct cost from borrowing those funds, or an opportunity cost compared to the risk free rate of return.
The higher interest rates get, the more expensive these decisions become. While rho is a lowly and oft forgotten options greek, it not only tells us what the market thinks about inflation expectations and the cost of capital, but it can have second order effects on trading and pricing.
Like every other business, options dealers are faced with capital allocation decisions. Most professionals are trading on some kind of leverage, i.e. borrowed capital to fund their haircut and margin requirements. Assuming their books are well hedged, and they have a sustainable edge in the marketplace, this is a fantastic way to increase returns.
With rising interest rates, there come tougher decisions about where to deploy their resources. Capital intensive products may see liquidity drain from lit markets. Nuances in the haircut calculation like minimum contract charges may also cause liquidity providers to exit products and positions to improve their capital efficiency. Liquidity further out the term structure might also suffer as there is greater uncertainty about rates for long term positions. Rho is like volatility - even small changes can have a big impact on longer durations.
Other participants may also change their behavior in light of higher interest rates. Institutional managers who were content getting an extra percentage point on a yield strategy now have competition from high yield savings accounts. Does this make yield enhancement strategies like covered calls or condors more or less attractive? What would be the knock-on effects of additional or reduced volatility supply?
For nearly 15 years options traders have been able to effectively ignore rho. The maligned greek was relegated to special situations like hard to borrow stocks, and even there chunky orderflow and the murky shadows of stock loan meant rates were treated more like straddles than implied volatility numbers.
How fast interest rates move up and for how long they stay there has captivated the attention of every market participant. It might not be as sexy as delta, gamma, or vega, but as Powell and company flap their wings, be sure to know your rho.