Futures? Stocks? Which is a better investment, or are they the same? (Part 2)
In a previous blog post, we discuss various reasons why the basis in bitcoin prices exists when we compare the futures price to the cash price. They range from country of jurisdiction of the exchange, investor level of sophistication and so on. Are there more fundamental reasons why the basis should exist? For example, if we consider more financial-based futures, such as futures referencing the S&P 500 stock index, is there a logical reason why they should differ in prices compared to the underlying stocks?
In the case of the example of S&P 500 stock futures, the difference between the futures prices and cash prices can also be attributed to 2 reasons: risk-free interest rate and dividends. A futures investor typically has to put up a significantly lower amount of capital to get the same exposure as a cash stock investor, and this is excess capital which can be invested in government securities to earn a risk-free rate of return. As a result, the futures price should be higher than the cash stock price, and in fact, the fair futures price should be exactly equal to the spot cash stock price compounded by this risk-free interest rate for the duration equal to the time to expiration of the futures (to ensure no arbitrage, in technical lingo!). This is usually referred to as the time-value of money. Of course, in the last 10 years, interest rates on government securities, especially shorter-term ones, have been pretty much close to zero, so this factor has not played an important role and may have faded from investors’ memories.
Similarly, a futures investor will not be paid dividends which a cash investor is entitled to. Consequently, the futures price should be lower than the cash stock price. In fact, the fair futures price should be exactly equal to the spot cash stock price discounted by the annualized dividend rate for the duration equal to the time to expiration of the futures (again, to ensure no arbitrage!). To be exact, if we denote S as the initial cash price, F(T) as the fair futures price with T denoting the time to expiration, r as the annualized risk-free rate of return and q as the annualized dividend rate, F(T) should be equal to Sexp[(r-q)T] if we do not want to introduce arbitrage. Alternatively, another approach that is used by practitioners is to look at the difference between the market futures price and the cash stock price, calculate an implied rate of financing, and compare it to the risk-free and dividend rate to determine if the futures price is trading too high or too low relative to the cash stock price (which can introduce a “basis” trading opportunity).
Now, using the same framework, what happens if we compare a bitcoin cash investor to a bitcoin futures investor? Owning a bitcoin does not provide a steady stream of dividends in the conventional sense so, q, as denoted above, should be equal to zero. What should the equivalent of r, the risk-free interest rate, be? The bitcoin futures investor can deposit his excess bitcoin at various lending platforms which pays about 4–5% for one year. Should we plug r equal to 4% or 5% into the formula above to calculate the corresponding fair futures price to see if we may have a basis trade opportunity? The answer lies in the definition of r which is the “risk-free” interest rate, and any company, no matter how well-funded, is unlikely to have the same credit quality as the U.S. government (which has the ability to “print” money), and hence should not be considered “risk-free”. Even depositing money at a bank is not risk-free, as there is certainly a chance that the bank can fail (remember 2008?). Also, even though most cash deposits are covered by FDIC insurance, the maximum amount covered is only USD$250,000. Certainly, typical bitcoin platforms out there that accept bitcoin deposits are not publicly traded so their financials are not well-understood, and there is also not an equivalent of FDIC insurance for such deposits. Hence r should not be equal to the 4–5% that you can receive from such platforms.
What might be a better approach if you are sitting on bitcoin and you are thinking about doing a basis trade against bitcoin futures, but you still want to be able to earn a yield from your bitcoin holdings without taking on too much counterparty risks from such traditional platforms? At Digital Gamma, we have introduced a collateralized tri-party repo (TPR) agreement where initial margin is collected from both parties by Digital Gamma, the amount of which is market-dependent and computed based on statistical quantification of bitcoin volatility. Would this be a better approach for you to earn some yield from your bitcoin holdings via a collaterialized repo transaction if you are concerned about uninsured counterparty risk when you are sizing up such basis trades?
