Leveraged fund optionality and the “least cost bearer of risk”

Traded financial derivatives, it is often claimed, permit markets to find the “least cost bearer of risk”. But if this is true, what exactly does it mean? Who are the least cost bearers of risk? Highly diversified investors with very strong balance sheets? It’d be natural to think so. But think again. Perhaps the least cost bearers of risk are aggressivley speculative investment funds intentionally leveraged to the point where the potential upside is very large, and the corresponding downside triggers bankruptcy.

Recall that any leveraged, limited-liability entity can be understood as a call option. If a business owes the bank $1M, but its assets — including the present value of expected future profits — are worth less than that $1M, it can declare bankruptcy. Its owners hand over all assets to the bank, and walk away without paying off the loan. On the other hand, if equityholders believe the business is worth more than a million, they pay off the bank, or rollover the loan, depending on the operation’s current liquidity and available investment opportunities. Thus, the value of this entity to equityholders can be described by the red curve below.

Investments whose returns are like options have an unusual property. Usually, investors hope to minimize risk and maximize returns in their investment choices. But the expected return of an option increases with the risk (or volatility) of the underlying asset. Consider the case of an idealized entity operating entirely on borrowed cash. It holds $1M in assets, all borrowed, no owners equity. On the graph above, it sits at the point where the dotted line intersects with the red line. Suppose equityholders had a choice, hold the million dollars cash, or flip a coin in a bet that either doubles their money or loses it all. An unleveraged, risk-averse investor always prefers sure cash to a fair coin-flip. But a very leveraged investor who has the option of shifting costs to the lender, takes the coin-flip. If she loses the flip, she loses nothing, the lender takes the cost. If she wins, she’s turned other peoples’ money into a cool million for herself.

A 100% leveraged entity is a zero-cost bearer of risk. The downside of any potential investment is immaterial. Only the probability-weighted magnitude of the expected upside matters. A 100% leveraged entity prefers volatility to safety, even if the “average” outcome of a gamble is not particularly good. Even if the coin in the previous example were rigged so that the fund loses 2 out of 3 flips, equityholders still prefer to play than to hold cash. Since creditors bear the losses, the only cost to a bad gamble is the opportunity cost of better gambles that might otherwise have been undertaken.

In the real world, very few entities get to borrow all their assets, hold all gains, but walk away from any losses by defaulting. It’s a great deal for the borrowers, but a crappy one for lenders, who strive to prevent these kinds of perverse incentives from arising. Lenders typically require borrowers to hold significant equity. A typical borrower sits at the intersection of the red and green lines. At this point on the curve, equityholders absorb most losses, as well as any gains on their investments, and the possibility that some of their losses will be borne by lenders if they lose absolutely everything is unlikely to be particularly relevant. Also, business bankruptcy often exacts nonmonetary costs that mitigate predatory behavior by borrowers. Controlling equityholders of failing businesses lose reputation, their jobs, see their friends lose jobs and retirement security, face lawsuits, etc. Finally, lenders often protect themselves with “covenants” that remove control from equityholders as the degree of business leverage increases, to prevent borrowers from taking big chances after they’ve borne great losses.

But, nevertheless, the world is a diverse place, with lots of different kinds of businesses and creditors. While very few entities enjoy 100% leverage, some businesses fall much closer than others to the dotted line on the graph above, some businesses have more non-monetary costs associated with bankruptcy than others, some businesses have more restrictive covenants than others. Leverage is no longer as simple a concept as funds borrowed from a diligent local bank. Bonds can be sold to the public, to naive foreign investors, to foreign central banks. In markets awash with liquidity, borrower reputation may substitute for balance sheet due-diligence in the decision to extend credit.

The trading of financial derivatives is supposed to transfer risk exposure to its least cost bearer. In light of the foregoing discussion, what might a least cost bearer look like? As we’ve seen, entities that are nearly completely leveraged, that fall near the dotted line on the graph above, face a low, or even negative, cost to bearing risk! This is counterintuitive, since these are the sorts of entities that face the greatest likelihood of bankruptcy. But that is exactly the point. Bankruptcy transfers the cost of risk gone bad to others. The least cost bearer of risk is an entity with few nonmonetary costs associated with failure, and a reputational or strategic capacity to take on leverage without surrending its ability to take risk. It should be no surprise to anyone following financial markets that this sounds a lot like a highly regarded hedge fund. Think Long-Term Capital Management.

The point of this essay is that LTCM-style meltdowns are not aberrations, but are a rational, structural consequences of a financial system in which the returns of some entities have high optionality, offering the possibility of high-returns for a low sums put at risk of total loss. LTCM should not be regarded as a failure or lapse of judgement on the part of its managers or investors. Its failure was a “normal accident”. Assuming independence of returns across investments, the rational investor should diversify her holdings among a very large number of funds with LTCM-style leverage and high appetites for risk, as these offer far superior return to risk than traditional investments. Many, perhaps most, of these investments would go south, and end up worthless. But the returns on the high-leverage, high-risk funds that succeed will much more than make up for these setbacks. On average, lenders bear most of the risks and equityholders enjoy most of the gains. It’s a good deal for investors.

If highly leveraged funds are good deals for investors, than hedge-fund managers ought to be competing to create them. (We’ve not touched on the much maligned “2 & 20” fee structure of many hedge funds. That adds additional optionality to hedge fund incentives, but it is only icing on the cake.) Funds should be competing to maximize their leverage without compromising their capacity to take-on risk, leap-frogging one another down the slope of a graph towards that dotted line. Speculative derivative positions often offer both risk and leverage in convenient packages whose “rocket-scienceness” helps to obscure both aspects, and make it possible for a fund to take on yet more.

Of course there is a problem here. Somebody ends up bearing all the risk that leveraged funds can write off via defaults. What is rational behavior for each individual fund or investor may turn out not to be so rational, if failures turn out to be correlated rather than mostly independent. If several funds default away large losses, the funds’ creditors may in turn default, wiping out other funds’ gains and increasing the likelihood of futher defaults. In a typical “tragedy of the commons”, rational behavior by investors and managers can lead to a systemic crisis.

Update History:
  • 12-Jun-2006, 10:am p.m. EET: Changed “tragedy” to “crisis” in last sentence to avoid double-use, and removed the overdone word “grave”. Fixed two spelling errors.

2 Responses to “Leveraged fund optionality and the “least cost bearer of risk””

  1. Fullcarry writes:

    Another thought provoking post! Lately I have been thinking alot about the perverse effect that signs of overt inflation has on the leveraged community. Since leveraged money isn’t necessarily concerned about inflation but only inflation induced Fed action, inflation hedges and derivatives get pressured whenever overt signs of inflation emerge.

    I am pretty sure that the preponderence of leveraged money in the economy is going to have perverse non-intuitive effects going forward. Your post is a nice framework for thinking about this.

  2. Fullcarry — your point about inflation measures is interesting to think about. Inflation that is not widely recognized to be inflation is indistinguishable from growth, especially for securities like stocks, that mostly “pass-through” rising prices. In an ideal world, high but anticipated inflation would have no effect on valuations, as an inflation-induced “earnings growth” effect would be offset by a an increase in required rate of return. But if there is inflation that is not recognized and anticipated, and not reflected in interest rates, stock values would rise. Until, of course, markets recognize the unacknowledged inflation and update their return requirements, at which point, valuations would fall. So as you say, covert inflation is “good”, but overt inflation is “bad” for stockholders. Leverage magnifies this effect, as rising interest rates due to market recognition of inflation increases interest costs at the same time as it decreases leveraged asset valuations. That could lead to a bad cycle of selling due to leverage constraing intensifying leverage constraints for others…

    Inflation is notoriously difficult to define, but an interesting approach to inflation would look at value as a share of GDP. Has the value of your investement as a share of GDP declined? If so, by this measure, it has lost value due to inflation. To retain value by this measure, and investment must grow by at least nominal GDP.

    What’s interesting is that under this (unorthodox) inflation measure, long-term “real” returns on capital are cannot be much more than 0%. Why? If long-term returns are above zero, and returns are reinvested, returns as a share of GDP would grow without bound to 100%. This form of “real” return can be above 0% only by the percentage of returns consumed rather than reinvested in equilibrium. Approximating normal returns by this measure as near 0, various other inflation measures can be weighed by looking at why and how much they are lower than this measure, and to what degree we believe the difference is justified. Our measure is the one relevant to an actor wishing to maintain her relative share in an economy’s wealth. Other measures implicitly make a claim that an investor can be at least as well off as she had been while owning a smaller share of GDP. Conventional measures are more optimistic, in a sense, since they permit more people to have smaller shares of an bigger pie. But the question of what matters to people — absolute vs relative wealth, and what exactly it means for a dollar to really “go farther” — are tough questions.