A Negative Interest Rates Thought Experiment

Toto, I have a feeling we’re not in Kansas anymore

Dorothy in Wizard of Oz

With a negative yielding investment, the price you pay exceeds the sum that you will get back at maturity plus the income you receive in the interim. If you buy a negative yielding bond you are guaranteed to lose money. If the rate you receive on bank deposits is negative, you are guaranteed to lose money.

Negative interest rates are becoming kind of a big deal:

Most negative yielding debt is government debt, which is ironically considered “safe”, at least in first world countries. With government debt, you know what cash flows you will receive during the holding period, and what face value amount of principal you will receive upon maturity. With everything else, cash flow is uncertain and principal is always at risk. Indeed the yield on government debt functions as a proxy for the “risk free rate” , which is a critical input in financial models investors use to make strategic decisions throughout financial markets.

Conservative investors generally prefer to hold a lot of government debt in order to meet future needs. Pensions, banks, and insurance companies are required to hold a minimum percentage of their assets in government debt so they can safely meet obligations to their stakeholders.

Negative interest rates cause a lot of surprising second order impacts throughout the world impacting how people do business.

Options Pricing

The Black Scholes model is one of the pillars of modern finance. It uses the risk free rate as an input but it cannot compute when the risk free rate is negative. It requires users to calculate a logarithm. Yet the logarithm of a negative number is undefined/meaningless. Here is a paper that explored the implications in more detail. Maybe people can use the old Brownian motion models, but there isn’t going to be universal agreement right away on what to use.

Any switchover will create unintended consequences throughout the investment world . Lots of funds hold over the counter options or swaps which must be valued using models in the time between their initiation and expiration or exercise. This valuation impacts the number that appears on the statement of investors. To the extent that investors have asset allocation targets around what percent of the entity’s assets can be invested in what, this will have secondary impacts in other markets. A lot of large firms have to totally change their valuation policies which is never easy to do because valuation departments are plenty busy with their jobs as it is. Markets aren’t going to close just so they can rewrite their valuation policies.

Also, in cases where a swap or OTC option contract requires collateral to be posted as the pricing changes throughout the life of a contract, both sides of the contract need to agree on valuation methods. When interest rates are positive, Black Scholes is a noncontroversial options I doubt contractual language was written in a way that accommodate for a world where Black Scholes would completely stop working.

Currently, more banks are trading a wide number of options without a reliable price. Each bank could handle this problem by performing its own solution, but the lack of a shared approach could lead to serious legal issues.

Source

This stuff is all theoretical but it has real cash impact throughout the world. What types of risks can be hedged will impact how capital can be allocated. How capital is allocated directly impacts what ideas get funded.

Now lets consider the real world impact on different groups of investors.

Stimulating TINA

In theory, negative rates should stimulate the economy. If investors only invest in safe assets, nothing else will get funded. Retirees need income from investments to live, foundations need to earn enough to safely withdraw funds, etc etc. If the bank charges them to hold their cash, they will invest more in real estate, high yield debt, and venture capital etc. They will have to take no more risk because “there is no alternative”(TINA).

However, when you look at how negative rates will impact pensions, banks and insurance companies, its hard to escape the conclusion that they might have a destructive, rather than stimulative impact on financial markets.

Pensions

People live longer than they can work.  To prevent a social catastrophe, countries have different ways of providing for old people.  Pensions are a big part of the financial markets According to CFA society:   Willis Towers Watson’s 2017 Global Pension Assets Study covers 22 major pension markets, which total USD 36.4 trillion in pension assets and account for 62.0% of the GDP of these economies.

 In the US people pay into Social Security, which provides a bare minimum standard of living to old people. The Social Security Fund is only allowed to invest in US Treasury Securities. If Treasuries yielded negative, the Social Security Fund will erode over time, meaning it won’t be able to meet its bare minimum obligations to retirees.  

Social Security by itself barely provides enough to live on. A lot of people in the US and around the world also have pensions through their jobs as well.  The impacts of negative rates get more nuanced and even weirder when you consider how these work.  

First of all, extremely low interest rates worsen pension deficits.  Future obligations must be discounted backwards. Lower discount rate leads to higher obligations in the present day.   On the other side of their balance sheet, they must make an actuarial assumption about future returns on their investments.    From what I’ve seen they often make aggressive return assumptions. To try to justify higher return assumptions, they put what they can into riskier investments.  To this extent pension funds are partially in the TINA Crowd.

Pensions are generally also obligated to put a certain amount of assets into “safe assets”  which are the first thing to start yielding a negative rate. As a result, this negative rate will create a destructive feedback loop.

Gavekal had this story of a Dutch Pension as an example: 

One day he was called by a pension regulator at the central bank and reminded of a rule that says funds should not hold too much cash because it’s risky; they should instead buy more long-dated bonds. His retort was that most eurozone long bonds had negative yields and so he was sure to lose money. “It doesn’t matter,” came the regulator’s reply: “A rule is a rule, and you must apply it.”

Thus, to “reduce” risk the manager had to buy assets that were 100% sure to lose the pensioners money.

Pension funds get caught in a feedback loop that will erode their capital base. For example say they buy a 5 year zero coupon bond at €103:

The €3 loss will reduce the market value of assets by €3. Holland also has a rule that pension funds must buy more government bonds the closer they get to being underfunded. Yet buying such negative-yielding bonds and keeping them to maturity ensures losses, making it more likely the fund will be underfunded, and so forced to buy more loss-making bonds (spot the feedback loop). Soon the fund will be distributing returns from capital, rather than returns on capital. Hence,it is not inflation that will destroy pension funds, but the mix of negative rates and rules that stop managers from deploying capital as they see fit. These protect governments, not pensioners who are forced to buy bad paper.

So negative rates will exacerbate the global retirement crisis. Oops.

Banks

What about banks?  Negative rates also destroy their capital base, and leave them with less money to actually lend out in the economy.  This hits at the heart of how fractional reserve banking works.

According to Jim Bianco at Bloomberg:

For every dollar that goes into a bank, some set amount (usually about 10%) must go into a reserve account to be overseen by the central bank. The rest is either lent out or used to buy securities.

In other words, the fractional reserve banking system is leveraged to interest rates. This works when rates are positive. Loans are made and securities bought because they will generate income for the bank. In a negative rate environment, the bank must pay to hold loans and securities. In other words, banks would be punished for providing credit, which is the lifeblood of an economy.

Gavekal explains how this leads to an eroding capital base (using the same 5 year zero coupon bond as the pension example above):

As a leveraged player, let’s assume it lends a fairly standard 12 times its capital. This capital has to be invested in “riskless” assets that are always liquid. In the old days, this would have been gold or central bank paper exchangeable into gold. Today, the government bond market plays the role of “riskless” (you have to laugh) asset, which has no reserve requirement. As a result, banks are loaded up with bonds issued by the local state. Now let us assume that a bank has just lost €3 on the zerocoupon bond mentioned above. The bank’s capital base will be reduced by €3. Based on the 12x banking multiplier, the bank will have to reduce its loans by a whopping €36 to keep its leverage ratio at 12. Hence, the effect of managing negative rates while also respecting bank capital adequacy rules means that the capital base can only shrink.

Insurance Companies

One of the main ways that insurance companies make money is by collecting premiums in advance of paying out any claims.  Hey are able to invest these premiums, collecting a float premium. Of course they are limited in how much risk they can take with the money they are holding to pay out any possible claims.  Regulators generally require them to put a certain amount in a “risk free “ asset like government debt, and the rest in riskier assets. If government debt is negative yielding, we again get to a destructive feedback loop that has major second order impacts.

From the Gavekal note:  

The insurance company could raise its premium by the amount of the expected loss from holding the bond (not very commercial), or it could just underwrite less business. Either way, it will have less money to invest in equities and real estate. Simply put, either the insurance company’s clients will pay the negative rates, or the company itself will do so by increasing its risks without raising returns. This means that either the client pays more for insurance, and so becomes less profitable, or the insurance company takes a hit to its bottom line.

People will have to pay more premiums for less insurance coverage.

Long term, negative rates will exacerbate the retirement crisis and basically destroy the business models of banks and insurance companies as we know them. This doesn’t automatically mean negative interest rates can’t persist. Perhaps there are other ways to provide for old people (ie higher taxes on a shrinking economy?) Banks and insurance companies can find other ways to make money. Regulators might respond, by changing rules or creating various incentive programs.

In this post I only covered only a few of the second order impacts of negative interest rates. Negative interest rates make the capital asset pricing model give nonsensical infinite results. I think CAPM is mostly bullshit anyways, but enough people use it that it has a reflexive impact on asset pricing. Unwinding it won’t be easy. I didn’t even touch on how negative rates can screw up the plumbing of financial markets: repo markets, securities settlement , escrow etc. Not enough people have really thought this all through. Many of the assumptions that have historically driven investor behavior will no longer hold if negative rates persist.

Maybe interest rates will normalize again. It will wipe out a few of the most overleveraged players, but the financial system will recover quickly. On the other hand, if negative rate do persist, get ready for a slew of unintended consequences in places you didn’t expect.

See also:

Mysterious by Howard Marks at Oaktree

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