# How Low Can the 30-Year Treasury Yield Go?

Posted by **Michael DePalma** (pictured) and** Philip Chasparis** of AllianceBernstein (NYSE: AB)

Even as the US Federal Reserve has continued to taper bond purchases and hint at eventually tightening monetary policy, long-term US Treasury yields have not only continued to fall, but outperformed all other maturities from two-year to 10-year bonds. Investors shouldn’t bank on them falling much further.

As of May 21, the yield on the 30-year Treasury bond was 3.4%, about half a percent *lower* than it was at the beginning of the year. There are a number of explanations; among them is demand from pension funds. Equities, credit sectors and other risk assets have enjoyed a lengthy rally since the depths of the global financial crisis, moving many pension funds much closer to fully funded status. To lock in these gains, many pensions are hedging their liabilities by purchasing 30-year Treasury bonds.

Pensions buy, prices go up, yields go down and Treasuries get richer. It makes sense.

**“Insurance” Prices Are Remarkably Efficient**

But how rich is the long bond at this point? One way to look at the question is to assess how much pension funds are willing to pay to use the 30-year bond as “liability insurance.” In the 1970s, Nobel Laureate Robert Merton introduced the notion that investors care about hedging their investments. If hedging is valuable, and nothing valuable is free, then there must be a cost. In capital markets, this cost is embedded in the prices of assets used as hedges, which become more expensive.

As it turns out, the pricing of insurance has been pretty consistent across the financial and real markets. For example, if insurance is priced efficiently, we expect the cost of insuring an asset with annualized volatility of 20% to be twice as high as the cost of insuring an asset with volatility of 10%. Half the risk, half the insurance cost. Armed with this assumption, we can check whether the real numbers bear out this efficiency.

Let’s say an investor uses an at-the-money put option to insure against losses on the S&P 500 Index, which has a volatility of 16%. Based on the Black-Scholes option-pricing model, the option costs a little more than half a percent, or 56 basis points, per year over 30 years.

Insuring a home typically costs about 40 basis points of the home value per year, using the Federal Housing Finance Agency’s median home value of $198,000 and an annual insurance premium of $800, according to Home Insurance LLC. That price tag is noticeably less than that of insuring the S&P 500 Index. But bear in mind that home values are about 35% less volatile than the S&P 500. So, if we make an adjustment to produce an apples-to-apples comparison by equalizing risks, home insurance works out to a price of about 60 basis points per year. That’s remarkably similar to the price to insure financial assets (Display).

**Checking the Long Bond’s Price Tag Today**

These relationships give us insight into when pension funds might find these bonds too rich for their blood. If the insurance premium embedded in the price of long Treasuries is too high, pensions will step back their hedging demand for these assets and look for other, cheaper forms of insurance.

Long-dated pension liabilities are, for all intents and purposes, benchmarked or priced against the 30-year Treasury bond and/or long-maturity highly rated corporates, both of which are about as volatile (risky) as the S&P 500 historically. Given how efficient insurance prices seem to be, it’s unlikely pension funds will pay much more than the cost to insure against equally risky S&P 500 assets to hedge their liability exposure. As we show above, this cost is about 55 to 60 basis points per year.

Now, how does this insurance estimate square with Treasury yields today? Let’s assume that a reasonable yield for the 30-year Treasury would be roughly equal to the long-term growth rate of gross domestic product in nominal terms. Forecasts vary, of course, but seem to hover around the 4% mark. If we subtract 60 basis points or so to account for the insurance cost of hedging pension liabilities, we get a 30-year Treasury yield of 3.4%. That’s about where it’s trading today.

Is that rich or cheap? We’d say about fair, given the demand from pension funds hedging liabilities.

So, we don’t think it’s prudent to bet on yields falling much lower than they are today. Sure, a geopolitical shock or some other flight-to-safety factor could come into play to put more downward pressure on yields. However, it seems unwise to think pension funds will suddenly become willing to shell out more for 30-year Treasuries as liability insurance than what the market typically charges to hedge equally risky assets. They’d be more likely to move on to second-best insurance substitutes—or possibly do without insurance altogether.

This leaves the long Treasury bond with what we view as a very lopsided return profile: a low upside in terms of positive returns and the possibility of sizable losses if hedging demand falls off.

*The views expressed herein do not constitute research, investment advice or trade recommendations and do not necessarily represent the views of all AllianceBernstein portfolio-management teams. *

Michael DePalma is Chief Investment Officer of Tail Risk Parity Services and Philip Chasparis is Quantitative Analyst of Global Diversified Strategies, both at AllianceBernstein, L.P.

Could you please explain how you get the cost for an ATM put on the S&P as 0.56%? It seems that it would be a lot more than that. For example a 3 month ATM put option currently costs around 3% (at presumably similar vol levels to 16% or maybe lower).

Good question, VK.

Since the liability hedging cost analyzed in this piece is the cost to hedge the value of 30-year liabilities today for the next 30 years, the relevant cost to protect the current equity value over the next 30 years is a 30-year at-the-money (ATM) put option.

Assuming an implied volatility of 23% (the term structure of volatility is upward sloping to capture term premium risk, so it’s higher than shorter-dated at-the-money options), and assuming reasonable levels of interest rates and dividends based on the forward market, a 30-year ATM put option costs about 17%, which is equivalent to 17%/30 = 56.6 basis points per year.

You’re absolutely correct that the strategy of rolling 3-month ATM put options costs a lot more, because this strategy isn’t just protecting the current value of equity—it’s protecting any future appreciation in the value of equity.

For example, if the price of the S&P 500 Index today is $100, a 30-year buy and hold ATM put option will ensure that at the end of 30 years the value is no less than $100. However, if in three months the S&P 500 Index appreciates to $150, the strategy of buying a new 3-month ATM put option every three months (in this case, the first one struck at $100 and, once expired, buying a new one struck at $150) will ensure that your value does not fall below $150.

So, you’ve locked in the $50 appreciation following a 3-month rolling ATM put option strategy where a one-time static 30-year ATM put strategy at t=0 will not lock this in. Extending this example, if you purchased a 1-month ATM put option and rolled this over each month, it would cost more than the 3-month ATM put rolling strategy.

Thanks for the explanation. Seems to me its not a very practical hedge.

a) As someone pointed out on the Pragcap page:

http://pragcap.com/how-low-can-the-30-year-treasury-yield-go/comment-page-1

the delta will be less than 1 and so it doesn”t prevent mark to market draw-downs in the interim. That is dissimilar from an insurance.

b) Secondly, if the index moves up in the short term (or say in the first 5-10 years which is more than likely despite recessions, etc), the hedge becomes pointless (for the remaining time) and one would want to roll the hedge up. I”m not sure about the parallels with home insurance on this point. It seems to me that home insurance would need to rolled up as well and it would not be as expensive.

There might be an optimal roll frequency, maybe annual or something, but then that would be quite expensive. Any roll interval beyond a year seems impractical in hedging against short term losses.

Thanks for the explanation though. At least I know now how you got to 0.56%.

Actually the delta should be 0.5 to start with so one would need two puts. But, then delta would vary and one might need to delta hedge if the “insurance” is supposed to protect against interim drawdowns.

Again, great questions/comments, @VK:

The idea of liability hedging is to lock in your liabilities and hence your funded status today. This means that your funded status won’t become any better, but at the same time won’t become any worse. So if you lock in your funded status at 90%, your funded status will never fall below 90% and never increase above 90% when your liabilities are due 30 years from now.

So, how does this map to an insurance equivalent? It would be a policy that protects your current investment value today. This is very different from an insurance policy that protects the future appreciation of your investment. For that, you would you need a rolling put buying strategy that resets the strike price to a higher level, just as you indicated. Because such a strategy protects future realized growth, it’s much more expensive—it protects against interim drawdowns, as you noted. A static 30-year ATM put ensures that over the next 30 years the value of your equity investment will never fall below where it is today. Hence, it protects your current investment value against any drawdowns that cause value to fall below today’s value.

Now, what a pension fund might do when funded status is 85% is lock some of this funding in by moving away from some of the return-generating assets to long-duration fixed income. When the remaining return-generating assets outperform and funded status grows to 90%, the pension fund would lock in some of this, and so on—until they’ve fully locked in (in an ideal world) 100% funded status. Each time they lock in a portion of the funded status, this is akin to buying a static ATM put option, where the strike of the first option is at the 85% funded level, the strike of the second is at the 90% funded level, and so on.

Drawing the analogy to equity markets, if you had $85 in equities, a similar hedging strategy would be to lock in some of this value by buying some 30-year puts struck at $85, and when equities rally to $90 buy some more 30-year puts to lock in this value, and so on, until the full value is protected at an average protected value of $100. The put portfolio would be a static portfolio where the positions aren’t rolled but are instead held for 30 years when payouts are due.