The reason meteorologists aren’t held accountable for their rain or snow predictions is that weather forecasts are made in terms of probability statements rather than absolute outcomes. This is why we forget the thunderstorms that failed to materialize and forgive the snowstorms that nobody predicted – a 60% chance of rain turns into a sunny day; a 30% chance of flurries culminates as a blizzard. While a probability statement provides an out, it also is a barometer of confidence. And, in the case of financial forecasts, the market itself provides such a measure.
While 2013 has been a fantastic year for equity markets and risk assets in general, a dark cloud looms on the horizon. At some point, the Federal Reserve (Fed) will initiate its plan to taper; the beginning of the end of the latest round of quantitative easing will commence and the support for U.S. Treasurys and mortgage-backed bonds will fade. Rates must rise, “they” say. But does the “market” have a view?
Actually, rates have already risen a great deal since the beginning of May, with the process accelerating after May 21 when Bernanke mentioned the possibility that the Fed could begin to scale back its latest round of quantitative easing later in the year. As the chart below shows, the 10-year Treasury rate began May at 1.63%, reaching its high for the year on September 5 at 2.99%, before settling back into a range. It is currently 2.87%. Likewise, the 30-year fixed mortgage rate has risen from 3.40% to 4.52%. A change like this would cause the monthly payment on a $200,000 loan to jump from $886.96 to $1,015.75. The immediate concern is more than abstract – it is a bread-and-butter issue.
So how high can rates go? What is the chance that the 10-year Treasury rate will reach 3.50% by the end of 2014? This question can be answered by posing another – one focused on probabilities:
What probability does the market assign to the 10-year Treasury rate jumping above 3.50% in three months, six months, and one year?
To answer this question, we need to look to the options markets. Specifically, we can focus on the delta of the option. For options (financial securities that give the holder the right, but not the obligation, to buy or sell an underlying asset at a specific time and at a specific price), the Greek letter delta denotes the sensitivity of the option’s price to movements in the price of the underlying asset. An at-the-money option will have a delta of about 0.50, meaning that for every $1 move in the underlying asset, the option will move by about 50 cents. An option that is very far out-of-the-money (unlikely to pay off) will have a delta very close to 0. An option that is very far in-the-money (highly likely to pay off) will have a delta very close to 1.
Aside from an option’s sensitivity to movements in the underlying asset, the delta has another very intuitive interpretation. It can be shown to be mathematically equivalent to the risk-neutral probability that the underlying asset price will fall above or below a certain threshold. For example, an option with an exercise price equivalent to the current market level has about a 50-50 chance of paying off. An option that is very far out-of-the-money will have a very low probability of returning anything.
For example, as I write this, the S&P 500 Index is at 1,801. The March 2014 put option (an option to sell) with an 1,800 exercise price has a delta of 0.50, indicating that the market is assigning about a 50% chance that the S&P 500 Index will be below 1,800 at the option’s maturity in March 2014. Using the delta, the chance that the S&P 500 will be less than 1,700 is 24% and the chance it will be less than 1,600 is 12%.
A natural question is whether the risk-neutral probability corresponds to the actual probability. The short answer is that options markets probably overstate the actual chance of a certain level being reached. This is because the option seller should expect to receive a risk premium. Nevertheless, the probability provides a base as well as an upper bound to estimate the chance that certain levels will be breached. (As an aside, the probability that a certain level will at least be touched prior to a set date is 2 times the delta probability.)
Translating this same process to the 10-year Treasury rate, the current probability that the 10-year Treasury rate will be greater than 3.50% over the following horizons is as follows:
Probability that the 10-year Treasury will be greater than 3.50%:
- 3 months = 12.92%
- 6 months = 28.38%
- 1 year = 41.45%
Source: Bloomberg – December 6, 2013
Using the options data, we can also derive the market-implied probability distribution of 10-year Treasury rates:
Probability Distribution of 10-Year Treasury Rates:
Source: Bloomberg – December 6, 2013
So options traders are pricing in about even odds that the 10-year Treasury rate will be greater than 3.29% in one year and a 25% chance it will be greater than 4.00%. There is a 10% chance that the 10-year Treasury rate will explode up to at least 4.75% in one year. Since the current 10-year Treasury rate is 2.87%, the probability distribution is greatly skewed to the upside. Options traders are affirming anecdotal fear.
We can rely on the market’s forecast or we may apply our own. In any event, the consensus view is that rates are on an upward trajectory, and using options data, we can quantify the potential magnitudes with associated probabilities of various forecasts.
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