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By Michael DePalma, Ashwin Alankar 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. AllianceBernstein Limited is authorized and regulated by the Financial Conduct Authority in the United Kingdom.

Michael DePalma and Ashwin Alankar are Co-Chief Investment Officers of Tail Risk Parity Services, and Philip Chasparis is Quantitative Analyst of Global Diversified Strategies, all at AllianceBernstein, L.P.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

Source: How Low Can The 30-Year Treasury Yield Go?