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The Limits to Trusting the Robots

October 20, 2017 1 comment

After another day on Thursday of stocks starting to look mildly tired – but only mildly – only to rally back to a new closing high, it hardly seems unusual any more. I have to keep pinching myself, reminding myself that this is historically abnormal. Actually, very abnormal. If the S&P 500 Total Return Index ends this month with a gain, it will be the second time in history that has happened. The other time was in 1936, as stocks bounced back from a deep bear market (at the end of those 12 months, in March 1936, stocks were still 54% off the 1929 highs). A rally this month would also mean that stocks have gained for 19 out of the last 20 months, the longest streak with just one miss since…1936 again.

But we aren’t rebounding from ‘oversold.’ This seems to be a different situation.

What is going on is confounding the wise and the foolish alike. Every dip is bought; the measures of market constancy (noted above, for example) are at all-time highs and the measures of market volatility such as the VIX are at all-time lows. It is de rigeur at this point to sneer “what could go wrong?” and you may assume I have indeed so sneered. But I also am curious about whether there is some kind of feedback loop at work that could cause this to go on far longer than it “should.”

To be sure, it shouldn’t. By many measures, equities are at or near all time measures of richness. The ones that are not at all-time highs are still in the top decile. Buying equities (or for that matter, bonds) at these levels ought to be a recipe for a capitalistic disaster. And yet, value guys are getting carried out left and right.

Does the elimination (with extreme prejudice) of value traders have any implications?

There has been lots of research about market composition: models, for example, that examine how “noise” and “signal” traders come together to create markets that exhibit the sorts of characteristics that normal markets do. Studies of what proportion of “speculators” you need, compared to “hedgers,” to make markets efficient or to cause them to have bubbles form.

So my question is, what if the combination of “buy the dip” micro-time-frame value guys, combine with the “risk parity” guys, represents a stable system?

Suppose equity volatility starts to rise. Then the risk-parity guys will start to sell equities, which will push prices lower and tend to push volatility higher. But then the short-term value guys step in to ‘buy the dip.’ To be clear, these are not traditional value investors, but rather more like the “speculators” in the hedger/speculator formulation of the market. These are people who buy something that has gone down, because it has gone down and is therefore cheaper, as opposed to the people who sell something that has gone down, because the fact that it has gone down means that it is more likely to go down further. In options-land, the folks buying the dip are pursuing a short-volatility strategy while the folks selling are pursuing a long-volatility strategy.[1]

Once the market has been stabilized by the buy-the-dip folks, who might be for example hedging a long options position (say, volatility arbitrage guys who are long actual options and short the VIX), then volatility starts to decline again, bringing the risk-parity guys back into equities and, along with the indexed long-only money that is seeking beta regardless of price, pushing the market higher. Whereupon the buy-the-dip guys get out with their scalped profit but leaving prices higher, and volatility lower, than it started (this last condition is necessary because otherwise it ends up being a zero-sum game. If prices keep going higher and implied volatility lower, it need not be zero-sum, which means both sides are being rewarded, which means that we would see more and more risk-parity guys – which we do – and more and more delta-hedging-buy-the-dip guys – which we do).

Obviously this sort of thing happens. My question though is, what if these different activities tend to offset in a convergent rather than divergent way, so that the system is stable? If this is what is happening then traditional value has no meaning, and equities can ascend arbitrary heights of valuation and implied volatility can decline arbitrarily low.

Options traders see this sort of stability in micro all the time. If there is lots of open interest in options around, say, the 110 strike on the bond contract, and the Street (or, more generally, the sophisticated and leveraged delta-hedgers) is long those options, then what tends to happen is that if the bond contract happens to be near 110 when expiry nears it will often oscillate around that strike in ever-declining swings. If I am long 110 straddles and the market rallies to 110-04, suddenly because of my gamma position I find myself long the market since my calls are in the money and my puts are not. If I sell my delta at 110-04, then I have locked in a small profit that helps to offset the large time decay that is going to make my options lose all of their remaining time value in a short while.[2] So, if the active traders are all long options at this strike, what happens is that when the bond goes to 110-04, all of the active folks sell to try and scalp their time decay, pushing the bond back down. When it goes to 99-28, they all buy. Then, the next time up, the bond gets to 110-03 and the folks who missed delta-hedging the last time say “okay, this time I will get this hedge off” and sell, so the oscillation is smaller. Sometimes it gets really hard to have any chance of covering time decay at all because this process results in the market stabilizing right at 110-00 right up until expiration. And that stabilization happens because of the traders hedging long-volatility positions in a low-volatility environment.

But for the options trader, that process has an end – options expiration. In the market process I am describing where risk-parity flows are being offset by buy-the-dip traders…is there an end, or can that process continue ad infinitum or at least, “much longer than you think it can?”

Spoiler alert: it already has continued much longer than I thought it could.

There is, however, a limit. These oscillations have to reach some de minimus level or it isn’t worth it to the buy-the-dip guys to buy the dip, and it isn’t worth reallocation of risk-parity strategies. This level is much lower now than it has been in the past, thanks to the spread of automated trading systems (i.e., robots) that make the delta-hedging process (or its analog in this system) so efficient that it requires less actual volatility to be profitable. But there is a limit. And the limit is reach two ways, in fact, because the minimum oscillation needed is a function of the capital to be deployed in the hedging process. I can hedge a 1-lot with a 2 penny oscillation in a stock. But I can’t get in and out of a million shares that way. So, as the amount of capital deployed in these strategies goes up, it actually raises the potential floor for volatility, below which these strategies aren’t profitable (at least in the long run). However, there could still be an equilibrium in which the capital deployed in these strategies, the volatility, and the market drift are all balanced, and that equilibrium could well be at still-lower volatility and still-higher market prices and still-larger allocations to risk-parity etc.

It seems like a good question to ask, the day after the 30th anniversary of the first time that the robots went crazy, “how does this stable system break down?” And, as a related question, “is the system self-stabilizing when perturbed, or does it de-stabilize?”

Some systems are self-stabilizing with small perturbations and destabilizing with larger perturbations. Think of a marble rolling around in a bowl. A small push up the side of the bowl will result in the marble eventually returning to the bottom of the bowl; a large push will result in the marble leaving the bowl entirely. I think we are in that sort of system. We have seen mild events, such as the shock of Brexit or Trump’s electoral victory, result in mild volatility that eventually dampened and left stocks at a higher level. I wonder if, as more money is employed in risk parity, the same size perturbation might eventually be divergent – as volatility rises, risk parity sells, and if the amount of dip-buyers is too small relative to the risk parity sellers, then the dip-buyers don’t stabilize the rout and eventually become sellers themselves.

If that’s the secret…if it’s the ratio of risk-parity money to dip-buyer money that matters in order to keep this a stable, symbiotic relationship, then there are two ways that the system can lose stability.

The first is that risk parity strategies can attract too much money. Risk parity is a liquidity-consumer, as they tend to be sellers when volatility is rising and buyers when volatility is falling. Moreover, they tend to be sellers of all assets when correlations are rising, and buyers of all assets when correlations are falling. And while total risk-parity fund flows are hard to track, there is little doubt that money is flowing to these strategies. For example one such fund, the Columbia Adaptive Risk Allocation Fund (CRAZX), has seen fairly dramatic increases in total assets over the last year or so (see chart, source Bloomberg. Hat tip to Peter Tchir whose Forbes article in May suggested this metric).

The second way that ratio can lose stability is that the money allocated to buy-the-dip strategies declines. This is even harder to track, but I suspect it is related to two things: the frequency and size of reasonable dips to buy, and the value of buying the dip (if you buy the dip, and the market keeps going down, then you probably don’t think you did well). Here are two charts, with the data sourced from Bloomberg (Enduring Intellectual Properties calculations).

The former chart suggests that dip-buyers may be getting bored as there are fewer dips to buy (90% of the time over the last 180 days, the S&P 500 has been within 2% of its high). The latter chart suggests that the return to buying the dip has been low recently, but in general has been reasonably stable. This is essentially a measure of realized volatility. In principle, though, forward expectations about the range should be highly correlated to current implied volatility so the low level of the VIX implies that buying the dip shouldn’t give a large return to the upside. So in this last chart, I am trying to combine these two items into one index to give an overall view of the attractiveness of dip buying. This is the VIX, minus the 10th percentile of dips to buy.

I don’t know if this number by itself means a whole lot, but it does seem generally correct: the combination of fewer dips and lower volatility means dip-buying should become less popular.

But if dip-buying becomes less popular, and risk-parity implies more selling on dips…well, that is how you can get instability.

[1] This is not inconsistent with how risk parity is described in this excellent paper by Artemis Capital Management (h/t JN) – risk parity itself is a short volatility strategy; to hedge the delta of a risk parity strategy you sell when markets are going down and buy when markets are going up, replicating a synthetic long volatility position to offset.

[2] If this is making your eyes glaze over, skip ahead. It’s hard to explain this dynamic briefly unless I assume some level of options knowledge in the reader. But I know many of my readers don’t have that requisite knowledge. For those who do, I think this may resonate however so I’m plunging forward.

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The Phillips Curve is Working Just Fine, Thanks

September 5, 2017 2 comments

I must say that it is discouraging how often I have to write about the Phillips Curve.

The Phillips Curve is a very simple idea and a very powerful model. It simply says that when labor is in short supply, its price goes up. In other words: labor, like everything else, is traded in the context of supply and demand, and the price is sensitive to the balance of supply and demand.

Somewhere along the line, people decided that what Phillips really meant was that low unemployment caused consumer price inflation. It turns out that doesn’t really work (see chart, source BLS, showing unemployment versus CPI since 1997).

Accordingly, since the Phillips Curve is “broken,” lots of work has been done to resurrect it by “augmenting” it with expectations. This also does not work, although if you add enough variables to any model you will eventually get a decent fit.

And so here we are, with Federal Reserve officials and blue-chip economists alike bemoaning that the Fed has “only one model, and it’s broken,” when it never really worked in the first place. (Incidentally, the monetary model that relates money and velocity (via interest rates) to the price level works quite well, but apparently they haven’t gotten around to rediscovering monetarism at the Fed).

But the problem is not in our stars, but in ourselves. There is nothing wrong with the Phillips Curve. The title of William Phillips’ original paper is “The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957.” Note that there is nothing in that title about consumer inflation! Here is the actual Phillips Curve in the US over the last 20 years, relating the Unemployment Rate to wages 9 months later.

The trendline here is a simple power function and actually resembles the shape of Phillips’ original curve. The R-squared of 0.91, I think, sufficiently rehabilitates Phillips. Don’t you?

I haven’t done anything tricky here. The Atlanta Fed Wage Growth Tracker is a relevant measure of wages which tracks the change in the wages of continuously-employed persons, and so avoids composition effects such as the fact that when unemployment drops, lower-quality workers (who earn lower wages) are the last to be hired. The 9-month lag is a reasonable response time for employers to respond to labor conditions when they are changing rapidly such as in 2009…but even with no lag, the R-squared is still 0.73 or so, despite the rapid changes in the Unemployment Rate in 2008-09.

So let Phillips rest in peace with his considerable contribution in place. Blame the lack of inflation on someone else.

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Come see our new store at https://store.enduringip.com!

The Gold Price is Not ‘Too Low’

August 1, 2017 2 comments

Note: We are currently experimenting with offering daily, weekly, monthly, and quarterly analytical reports and chart packages. While we work though the kinks of mechanizing the generation and distribution of these reports, and begin to clean them up and improve their appearance, we are distributing them for free. You can sign up for a ‘free trial’ of sorts here.


Before I start today’s article, let me say that I don’t like to write about gold. The people who are perennially gold bulls are crazy in a way that is unlike the people who are perennial equity bulls (Abby Joseph Cohen) or perennial bond bulls (Hoisington). They will cut you.

That being said, they are also pretty amusing.

To listen to a gold bull, you would think that no matter where gold is priced, it is a safe haven. Despite the copious evidence of history that says gold can go up and down, certain of the gold bulls believe that when “the Big One” hits, gold will be the most prized asset in the world. Of course, there are calmer gold bulls also but they are similarly dismissive of any notion that gold can be expensive.

The argument that gold is valuable simply because it is acceptable as money, and money that is not under control of a central bank, is vacuous. Lots of commodities are not under the control of a central bank. Moreover, like any other asset in the world gold can be expensive when it costs too much of other stuff to acquire it, and it can be cheap when it costs lots less to acquire.

I saw somewhere recently a chart that said “gold may be forming a major bottom,” which I thought was interesting because of some quantitative analysis that we do regularly (indeed, daily) on commodities. Here is one of the charts, approximately, that the analyst used to make this argument:

I guess, for context, I should back up a little bit and show that chart from a longer-term perspective. From this angle, it doesn’t look quite like a “major bottom,” but maybe that’s just me.

So which is it? Is gold cheap, or expensive? Erb and Harvey a few years ago noticed that the starting real price of gold (that is, gold deflated by the price index) turned out to be strikingly predictive of the future real return of holding (physical) gold. This should not be terribly shocking – although it is hard to persuade equity investors today that the price at which they buy stocks may affect their future returns – but it was a pretty amazing chart that they showed. Here is a current version of the chart (source: Enduring Investments LLC):

The vertical line represents the current price of gold (all historical gold prices are adjusted by the CPI relative to today’s CPI and the future 10-year real return calculated to derive this curve). It suggests that the future real return for gold over the next decade should be around -7% per annum. Now, that doesn’t mean the price of gold will fall – the real return could be this bad if gold prices have already adjusted for an inflationary future that now unfolds but leaves the gold price unaffected (since it is already impounded in current prices). Or, some of each.

Actually, that return is somewhat better than if you attempt to fit a curve to the data because the data to the left of the line is steeper than the data to the right of the line. Fitting a curve, you’d see more like -9% per annum. Ouch!

In case you don’t like scatterplots, here is the same data in a rolling-10-year form. In both cases, with this chart and the prior chart, be careful: the data is fit to the entire history, so there is nothing held ‘out of sample.’ In other words, “of course the curve fits, because we took pains to fit it.”

But that’s not necessarily a damning statement. The reason we tried to fit this curve in the first place is because it makes a priori sense that the starting price of an asset is related to its subsequent return. Whether the precise functional form of the relationship will hold in the future is uncertain – in fact, it almost certainly will not hold exactly. But I’m comfortable, looking at this data, in making the more modest statement that the price of gold is more likely to be too high to offer promising future returns than it is too low and likely to provide robust real returns in the future.

Pre-Existing Conditions and Fire Insurance

When it comes to health care, I continue to be amazed at the utter nonsense that gets tossed about when the discussion comes to insuring pre-existing conditions. The problem seems to be that no one who understands insurance has anything to say about health care legislation, because the question of why you may not want to guarantee issuance of insurance at a given rate no matter what pre-existing conditions the patient has is really not hard to understand. Consider this little vignette:

Caller: Hi, I’d like to buy some home insurance, please.

Agent: Sure, I’d be happy to help with that.

Caller: Does the insurance cover loss from fire?

Agent: Of course. That’s just one of many coverages you get with our insurance. Can you tell me a little bit about your house?

Caller: It’s three bedrooms, two baths. Worth about $300,000. What will the insurance cost me?

Agent: It depends on a few more pieces of information I have to gather from you, but about <pause> $800 per year.

Caller: That sounds great. Sign me up. Do you need my credit card?

Agent (laughing): Just a moment, sir! I need to get more information to give you an accurate quote. Can you tell me about the condition of your home?

Caller: You mean, right now?

Agent: Um…yes.

Caller: It’s on fire.

Agent: Your house is on fire?

Caller: Yep. Can we speed this up a bit?

Agent: Sir, we can’t insure your house against fire if it’s already on fire!

Caller: Why not? Just because it’s a condition that existed prior to my call?

Agent: Well, yes.

Caller: That’s outrageous! I demand you issue me insurance!

Agent (after conferring with management): Sir, it turns out we can offer you insurance on your home…

Caller: See? I knew you could be reasonable.

Agent: …for $350,000.

See, here’s the thing. Insurance is based on the principle of distributing money in a pool of similar risks from insureds who don’t experience the insurable event to those who do experience the insurable event. If someone enters the pool who has already had the insurable event, it’s simply a transfer – there’s no insurance. Person A needs $100,000 in surgeries, and gets an insurance policy that costs $1,000. Where does the rest of the money come from? It doesn’t come from the insurance company, and I think perhaps people don’t understand that point (and Republicans are truly abysmal at explaining it). The rest of the money comes from other insureds. Consider this situation: rather than get private insurance, you and twenty of your fraternity brothers from college – all about the same age and health – decide to form your own mutual insurance network. Everyone agrees that if anyone gets sick, the whole group will pitch in equally to pay the medical bills of the sick person. Now, suppose one person says “can we take my mom in as well? She has early-onset dementia and was just diagnosed with lung cancer. She’d be glad to join the group and pay an equal share, because fair is fair!” Do you think it is fair that mom pays the same amount?

The insurance company makes money if the money they pay out is less than the money they take in, but they also stand to lose if they underwrite the risks poorly and pay out more than they take in. And insurance companies don’t systematically rip people off by underwriting policies super-conservatively. In fact, the evidence seems to be that insurance companies rather frequently fall prey to pressures to move more product, and underwrite policies too aggressively.

The social-justice question can be separated from the health care insurance question. If you feel that everyone should have their medical bills covered, no matter what, then create a federal umbrella program for high-risk insureds and pay for that program with taxpayer funds. That’s explicit: let the cost of health insurance cover the actual cost of health insurance, which involves conditions the risk pool doesn’t have yet, and represent the welfare or charity – because that’s what it is, of course, when others pick up the expense of those unable to pay – as exactly that. After all, the federal government offers flood insurance to landowners who can’t get insurance at a “reasonable price” because the land floods all the time; that is a similar welfare situation in which taxpayers have decided they are willing to foot the bill because it’s a social good that people live or build on the flood plain. (I’m not sure why, but that’s the import of the federal flood insurance program). So there’s precedent for the government taking over pools that are too risky for private markets.

Again, this isn’t rocket science and it isn’t hard to explain. Why doesn’t someone get on television and explain it? How about a commercial using my script?

Categories: ACA, Analogy, Good One, Insurance, Rant

Good Models and Bad Models

I have recently begun to spend a fair amount of time explaining the difference between a “good model” and a “bad model;” it seemed to me that this was a reasonable topic to put on the blog.

The difference between a good model and a bad model isn’t as obvious as it seems. Many people think that a “good model” is one that makes correct predictions, and a “bad model” is one that makes bad predictions. But that is not the case, and understanding why it isn’t the case is important for economists and econometricians. Frankly, I suspect that many economists can’t articulate the difference between a good model and a bad model…and that’s why we have so many bad models floating around.

The definition is simple. A good model is one which makes good predictions if high-quality inputs are given to the model; a bad model is one in which even the correct inputs doesn’t result in good predictions. At the limit, a model that produces predictions that are insensitive to the quality of the inputs – that is, whose predictions are just as accurate no matter what the inputs are – is pure superstition.

For example, a model of the weather that depends on casting chicken bones and rat entrails is a pretty bad model since the arrangement of such articles is not likely to bear upon the likelihood of rain. On the other hand, a model used to forecast the price of oil in five years as a function of the supply and demand of oil in five years is probably an excellent model, even though it isn’t likely to be accurate because those are difficult inputs to know. One feature of a good model, then, is that the forecaster’s attention should shift to the forecasting of the inputs.

This distinction is relevant to the current state of practical economics because of the enormous difference in the quality of “Keynesian” models (such as the expectations-augmented Phillips curve approach) and of monetarist models. The simplest such monetarist model is shown below. It relates the GDP-adjusted quantity of money to the level of prices.

This chart does not incorporate changes in money velocity (which show up as deviations between the two lines), and yet you can see the quality of the model: if you had known in 1948 the size of the economy in 2008, and the quantity of M2 money there would be in 2008, then you would have had a very accurate prediction of the cumulative rate of inflation over that 60-year period. We can improve further on this model by noting that velocity is not random, but rather is causally related to interest rates. And so we can state the following: if we had known in 2007 that the Fed was going to vastly expand its balance sheet, causing money supply to grow at nearly a 10% rate y/y in mid-2009, but at the same time 5-year interest rates would be forced from 5% to 1.2% in late 2010, then we would have forecast inflation to decline sharply over that period. The chart below shows a forecast of the GDP deflator, based on a simple model of money velocity that was calibrated on 1977-1997 (so that this is all out-of-sample).

That’s a good model. Now, even solid monetarists didn’t forecast that inflation would fall as far as it did – but that’s not a failure of the model but a failure of imagination. In 2007, no one suspected that 5-year interest rates would be scraping 1% before long!

Contrariwise, the E-A-Phillips Curve model has a truly disastrous forecasting history. I wrote an article in 2012 in which I highlighted Goldman Sachs’ massive miss from such a model, and their attempts to resuscitate it. In that article, I quoted these ivory tower economists as saying:

“Economic principles suggest that core inflation is driven by two main factors. First, actual inflation depends on inflation expectations, which might have both a forward-looking and a backward-looking component. Second, inflation depends on the extent of slack (or spare capacity) in the economy. This is most intuitive in the labor market: high unemployment means that many workers are looking for jobs, which in turn tends to weigh on wages and prices. This relationship between inflation, expectations of inflation and slack is called the “Phillips curve.”

You may recognize these two “main factors” as being the two that were thoroughly debunked by the five economists earlier this month, but the article I wrote is worth re-reading because it describes how the economists re-calibrated. Note that the economists were not changing the model inputs, or saying that the forecasted inputs were wrong. The problem was that even with the right inputs, they got the wrong output…and that meant in their minds that the model should be recalibrated.

But that’s the wrong conclusion. It isn’t that a good model gave bad projections; in this case the model is a bad model. Even having the actual data – knowing that the economy had massive slack and there had been sharp declines in inflation expectations – the model completely missed the upturn in inflation that actually happened because that outcome was inconsistent with the model.

It is probably unfair of me to continue to beat on this topic, because the question has been settled. However, I suspect that many economists will continue to resist the conclusion, and will continue to rely on bad, and indeed discredited, models. And that takes the “bad model” issue one step deeper. If the production of bad predictions even given good inputs means the model is bad, then perhaps relying on bad models when better ones are available means the economist is bad?

Pension Fund Perils: Why Conventional Pairing of LDI with De-risking Glide Paths Produces Inferior Outcomes

February 9, 2017 1 comment

Milla Krasnopolsky, CFA and Michael Ashton, CFA[1]

Combined use of traditional Liability Driven Investment (LDI) and funded status responsive de-risking strategies should be decoupled or rebuilt. Embedded inconsistencies in the treatment of risks in these two elements of what has become a popular pension strategy cause irreconcilable conflicts in their execution and imperils the positive pension fund outcome.

This article provides a critique of the combined LDI / De-risking Glide Path strategy as currently implemented by many pension plan managers and also provides an example of an alternative solution that better improves pension plan outcomes.

deriskingboxApproaches to pension risk management have passed though many phases over the past 40+ years.  Higher rate environments of the 1980s made liability immunization programs with treasuries very attractive, but traditional 60/40 or balanced fund strategies persisted as the dominant strategy for pensions.  As rates began their secular decline, funding levels continued to deteriorate and while liability-driven investing became popular again in the beginning of the new millennium, significant levels of underfunding prevented most pensions from fully matching their assets and liabilities.  A variety of partial risk mitigation solutions began to emerge as the lower rate environment of the past 20 years forced institutional investors to be exposed to higher levels of market risk.  New asset classes were introduced into pension plan portfolios in order to achieve higher returns and higher levels of diversification.  Adverse market volatility was further reduced through creative solutions that incorporated smart beta and risk allocation strategies that delivered lower-volatility at similar levels of long term return.  Other strategies sold liquidity back to the market in order to generate additional return in a low yielding environment.  Some risk-based approaches also introduced interest rate derivative overlay programs to extend interest rate duration of total assets along with equity risk reduction programs to reduce equity market risk.  Finally, de-risking glide paths – and ultimately liability risk transfer to insurance companies – became in vogue as companies continued to struggle with their asset-liability risk and found it expedient to pay insurance companies to assume the problem for them.

In recent years, much has been written about whether pension funds have sufficient assets to support their liabilities, and clearly the source of much of this angst is that…many of them don’t.  One thing that is clear is that after decades of chasing new and creative solutions, the problem of underfunded pension plans is still here and the debate about who should manage the assets, and how they should be managed, continues with ever-increasing urgency.

This article represents our contribution to this debate, with a special focus on the asset allocation requirements for cost effective pension plan de-risking.

 

Two Shortcomings of Traditional LDI and De-risking Strategies, as Combined

Type of risk

At this point it is important to differentiate the assets that function as liability hedges and those assets that better assist with the process of de-risking as the plan glides towards a fully hedged status.  Long duration bonds function as the best hedge for the liabilities, and as the plan’s funded status improves and the de-risking process proceeds, the allocation to bonds increases.  While bonds and bond-like derivatives are a core staple of liability-driven investing (LDI) strategies, for most underfunded plans that have a goal of full funding with some help from asset performance it is economically infeasible to allocate 100% of the assets to the liability-matching portfolio.  A gradual increase in bond assets over time as funding status increases is part of the de-risking asset allocation process.  This is an important distinction between LDI and the process of de-risking.  If the liability-matching assets allow the plan to better lock in the current funded status level, then it is only the remaining assets that allow that plan to reach the next funded status threshold in order for the plan to de-risk further.  Traditionally, these non-LDI assets are exposed to a significant amount of equity beta, as the long-term expected compensation from taking equity risk is positive.  While it is thought to be true that, in the long term, equity beta risk is well compensated, the trouble is that in the shorter time horizon of de-risking process the equity beta is very much dependent on market valuations that are not related to the valuation of the pension liabilities. Therefore, it becomes a tactical rather than a strategic decision to hold equities for a de-risking plan.

While all pension models focus on longer-term horizons, pensions in a de-risking mode have a much lower risk tolerance in the short term.  This has caused many pensions to allocate assets to a variety of alternative investments in order to diversify away from equity beta risk.  However, this practice also introduces other risks to the plan, some of which are illiquidity, currency, and/or additional credit default risk.  So there is an inconsistency: while pension funds are known for taking the very long view when it comes to illiquidity, if the sponsors are pursuing an LDI/de-risking strategy the additional illiquidity is counterintuitive, given the objective to be dynamic and nimble in the de-risking process.

But assuming that potential illiquidity is at least somewhat of a concern to a pension fund manager, then the Hobson’s choice between equity risk or illiquidity likely means that underfunded pension plans that are pursuing joint LDI/de-risking strategies are still carrying too much equity beta risk, or are slowing down the de-risking process while equity risk is mitigated through other less liquid investments, or both. Pension fund managers and their advisors sense this, but tend to reach a type of asset allocation compromise where pension returns may be less optimal and de-risking results are less effective.

So if equity beta isn’t desirable as unrelated to the liability, and illiquidity of many other alternatives make them less-desirable for dynamic rebalancing into LDI assets, what is the most effective way to replace the equity beta for a de-risking plan?  What other forms of beta and/or alpha are appropriate in aiding in the process of de-risking?  From the standpoint of Markowitz efficient frontier generation, risk is a function of return variance and the covariance of the returns of the eligible portfolio elements. Beyond that, to the optimization routine risk is risk. That is, it doesn’t matter whether the risk comes from beta or from alpha.  From the standpoint of the de-risking process, when it comes to the non-LDI assets or return generating assets, alpha is preferred to most beta since alpha is more process-dependent as opposed to market-dependent.   In the shorter-term horizon of de-risking, non-LDI beta introduces more risk.  So our only choice seems to be some combination of liquid alpha and/or well compensated liquid beta that has some correlation to liabilities.  This particular beta may be different from how the liability matching or LDI assets are invested and doesn’t need to match the performance of the liabilities, but should have a positive correlation with liability performance.  That’s a tall order.

Some of the more publicized alpha alternatives are hedge funds, private investments in equity or debt of corporations, or real estate.  We don’t intend to dive into the merits and disadvantages of these or other alternative investments on a stand-alone basis but will only superficially observe their fit in a de-risking framework.  Many hedge funds return as much beta as alpha – indeed, the fact that there are successful hedge-fund replication techniques is virtual proof that many hedge funds are actually beta masquerading as alpha. The obvious visual correlation between hedge fund returns and equity returns, too, should make one suspicious that hedge funds are a pure source of alpha (see Chart, source Bloomberg, comparing the HFRI Fund of Funds Composite Index to the S&P 500).

hfriFigure 1: HFRI Fund of Funds Composite Index vs S&P 500

While those hedge funds or private investments that have a higher correlation to fixed income beta may benefit plans with a long time horizon, they suffer from varying degrees of illiquidity, which impedes the de-rising process as previously discussed.

While there may be other examples for a better alternative, we can provide one strategic example that better fits the combined LDI / de-risking criteria we have discussed in this article.

 The Better Alternative

We have addressed above the type of risk that pension funds do not want to have. But it behooves us as well to point out one type of risk that pension funds really ought to have, and yet tend to be underinvested in: inflation exposure, or more accurately real interest rates.

There is a competent literature about the importance of inflation-linked assets to the pension plan.[2] Importantly, inflation-linked assets are relevant even if the pension benefits are not themselves inflation-linked, since for most pension plans the formula which links the work history of active participants to their future retirement benefits implicitly means that pension benefit accruals for a particular employee are higher the more that employee earns. Since wages generally rise at least partly because of inflation, this implies that any pension fund with active participants still accruing benefits does in fact have some inflation exposure.

But the importance of inflation to the pension plan goes beyond that liability-side insight. Additionally, pension assets are exposed to inflation – and, especially, large changes in inflation – because on the asset side the majority of the assets of most plans are invested in equities and nominal fixed-income. Both of these asset classes are terribly exposed to increases in inflation, especially when inflation rises above 3-4%.[3]

We can go still further. While the effects just mentioned are well-established in the literature, one additional benefit from owning inflation-linked assets has not been discussed as far as we can tell, and that is this: the relative value of inflation-linked bonds, compared to nominal bonds, is related to the business cycle and/or level of interest rates level in the same way that corporate spreads are – but without default risk. The chart below (source: Bloomberg data) highlights the connection between credit spreads and 10-year breakevens.[4] This is important because for most pension funds, the relevant interest rate for discounting liabilities is not the risk-free Treasury rate, but a risky corporate rate; therefore, the liability has credit spread risk and an asset that co-moves with credit spreads – especially without actually having credit risk – is valuable.

creditvsbreaksFigure 2: Inflation spreads (“Breakevens”) vs Credit spreads

In our opinion, given a choice between equity beta and inflation/real rate beta, there is no choice: inflation-linked assets are clearly the more valuable risk for a pension fund to own.

Now, pension plans that are pursuing de-risking along with LDI are typically loathe to replace equity risk, given its advantage (over a full cycle, although not necessarily at any given point) in expected return, with real interest rate risk. But inflation-linked markets have an additional benefit, at least in 2017 – they are inefficient, and produce myriad opportunities to generate alpha along with their useful beta. Indeed, we have designed an investment strategy that addresses all of these requirements:

  • Historical return commensurate with equity returns, with slightly lower total risk
  • Beta from inflation-linked bond markets, which is relevant to pension fund liabilities
  • Risk sourced from useful beta, as well as alpha
  • Implied credit spread exposure, without actual credit risks, which is relevant to pension fund liabilities
  • Superior liquidity to “alts” such as real estate, private equity, or hedge funds – which is more consistent with the de-risking mandate

We call this strategy “Enhanced Systematic Real Return.” In a nutshell, this strategy holds the combination of inflation-linked bonds and breakevens that most efficiently adds inflation protection for a given level of interest rates, and adjusts these proportions based on the richness or cheapness of inflation-linked bonds to capture additional alpha.[5]

 

Magnitude of risk

After determining a different, if not more efficient risk vehicle for the non-LDI assets we now turn to the discussion of how much of this risk should be taken at every point of the glide path.  Should the risk allocation to return generating risk assets (i.e non-LDI assets) only depend on the dollars allocated to these investments or should the risk allocation be independent of dollars allocated and vary based on the level of leverage and/or asset composition?

Not All Risk is Bad

As we have already alluded, prudent risk has some place in the management of a pension fund on a glide path. Yet, as with the villain in the black hat, we have been conditioned to look at the word “risk” and recoil. But not all risk is bad. Certainly, with LDI approaches risk is a negative – after all, the goal of LDI is to maximize the funded status (difference between assets and liabilities), subject to a limit on the maximum volatility (risk) of the funded status. In that construction, there is no doubt that risk is bad, or anyway that less risk is better. But risk is not necessarily bad for de-risking.

This seems counter-intuitive. If we are trying to remove risk, doesn’t that imply that risk is bad? Yes – as we just said, risk is bad for the LDI-driven mandate. But the plan that takes less risk has fewer opportunities to reach de-risking thresholds. That is, the more that you de-risk the longer the next increment of de-risking takes. In this context, it is actually helpful to retain more rather than less risk in the non-LDI assets at each de-risking step.

Here is an analogy from basketball: consider the player who constantly heaves up three-point shots. He shoots a lower percentage from beyond the arc, and so the variance of his scoring is quite a bit higher than his variance shooting short jumpers or layups. Let us suppose that on average, he scores the same amount per game whether he shoots three-pointers or short jumpers. In an asset management context, we would say that this is a “non-optimized” shooter. He should aim for the same average scoring with lower volatility, right?

Now let us suppose that in a particular game, this player’s team is down by 18 points in the final quarter. The coach sends the player onto the court. If this coach is from the pension industry, he instructs his shooter to take only safe shots, because that is how he maximizes his Sharpe Ratio. But if this is actually a basketball coach, he orders his player to take as many three-pointers as he can. Why? He does this because in this situation, risk is good. A strategy of only taking safe shots is guaranteed to lose in this context; only a highly-volatile strategy has a chance of working.[6]

In the same way, prudent addition of volatility as the plan is de-risking helps to de-risk a plan that is under water. So we can see that there is a tension here, and one that is routinely ignored in most LDI/de-risking plans: more volatility is helpful for de-risking, but hurtful inasmuch as it departs from the LDI mandate to maximize the return/risk tradeoff for the funded status. This leads to the phenomenon that is common today, of “hurry up and wait.” As we noted previously: the more that a fund has been de-risked, the longer the next increment of de-risking takes. Each reduction of the proportion of return generating assets to total assets significantly increases the average time until the next de-risking point is reached, as the table below[7],[8] illustrates:

table1Table 1: Reducing return-generating assets will tend to increase time to next trigger

This is problematic. By de-risking, this plan is becoming too conservative as it approaches being fully funded. We can show that the plan reaches a fully-funded status more quickly when it prudently avoids full de-risking. What happens when we allow leverage, and maintain the total portfolio risk even as the bond allocation increases at each trigger? The following table shows the significant result:

table2Table 2: By maintaining portfolio risk to return-generating assets, de-risking proceeds apace.

 

Combining the Right Type, and the Right Magnitude, of Risk

When the pension plan pursues a strategy that focuses on risks sourced from alpha and the “right kinds” of beta sources that will tend to match the liability, and de-risks in a way that recognizes that some risk helps the de-risking task, then the combined result can be powerful. The chart below (Source: Enduring Intellectual Properties, Inc) compares this new approach with the “classic” LDI plus de-risking approach. The dashed lines represent the “classic” approach, while the solid lines represent an approach that uses our “Enhanced Systematic Real Return” strategy as a substitute for the equity risk of the traditional strategy. In each case, this imaginary pension fund starts year zero at 60% funded, and liabilities grow with the Bloomberg/Barclays/Lehman U.S. Long Government/Credit Index. Also in each case, the top line represents the 90th percentile outcome of the Monte Carlo simulation; the bottom line represents the 10th percentile, and the middle line represents the median outcome.

comparativeglidepathsFigure 3: Proper types and magnitudes of risks produce preferable pension outcomes.

There are several facets of this chart worth noting.

Importantly, observe how the median outcome line is linear with our approach, but flattens out with the traditional de-risking approach. This phenomenon is the visual counterpart to Tables 1 and 2; it illustrates how the closer one gets to being fully funded with a traditional glide path, the slower the funded status converges. Our approach, as highlighted in Table 2, is designed to remove that effect. The benefits of that approach aren’t only felt on the median outcome, but are apparent on every path as the funded status moves above 75%.

Also, observe that the superior “good” outcomes aren’t “paid for” by much worse “bad” outcomes. After all, we could have had even better “good” outcomes if we took lots of extra risk. But in that case, the benefit would have come at a price, and we would see it manifesting in much worse “bad” outcomes. The outcomes here are actually skewed to the positive side.

Finally, although you cannot tell this from the illustration, you should know that this simulation assumes that stocks and bonds have expected returns that are somewhere near their historical mean returns. Unfortunately, presently this seems a generous assumption for the traditional approach. It seems more likely that, going forward, pension plans which are invested heavily in equities will be drawing from a distribution with worse-than-average characteristics due to the high starting valuations. Ditto, of course, for fixed-income…but at least bonds affect both sides of the LDI equation.

Summary

LDI and de-risking glide paths can be combined under certain conditions, but current implementation practices create inconsistencies in how risks are treated and do not facilitate achievement of strategic goals.

Asset beta risks that do not match liability beta risks are useful only in a tactical setting, and then only if they are associated with exceptional returns (that is, the market is cheap tactically).

More effort is required to search out new sources of liquid alpha and beta that facilitate the de-risking process. We have produced one that we believe is useful in this context.

As the plan de-risks along the glide path, the level of risk in the non-LDI assets should be adjusted to preserve a quantum of variance that is useful in the de-risking process, as opposed to just mechanically adjusting allocation dollars in a simple glide path.


[1] Milla Krasnopolsky is an investment strategist and investment manager. Milla held previous positions as a Managing Director of Fixed Income Markets and Strategic Solutions at General Motors Asset Management and as a Principal and Senior Investment Consultant at Mercer Investments.  Michael Ashton is the Managing Principal of Enduring Investments and CEO of Enduring Intellectual Properties, Inc.

[2] For the iconic example, see Siegel and Waring, “TIPS, the Dual Duration, and the Pension Plan” (Financial Analysts Journal, September/October 2004).

[3] Remarkably, the myth that common stocks confer some inflation protection has survived decades of contrary experience, both before and after Zvi Bodie’s classic “Common Stocks as a Hedge Against Inflation” (Journal of Finance, Vol. 31, No. 2, May 1976), in which he concluded forcefully “The regression results…leads to the surprising and somewhat disturbing conclusion that to use common stocks as a hedge against inflation one must sell them short.”

[4] The 10-year simple “breakeven” is merely the yield difference between the 10-year nominal Treasury yield and the 10-year TIPS real yield; it represents roughly the amount of future inflation at which an investor would be indifferent between the two types of bonds.

[5] It would be inappropriate to discuss the fine details of this strategy in a thought piece such as this. However, we thought it important to point out that demand for a solution with these characteristics is not hopeless or uninformed. There does exist at least one such solution, and probably others!

[6] This idea isn’t exactly alien in finance: if you own an out-of-the-money option, a higher implied volatility increases your delta while if you own an in-the-money option, a higher implied volatility decreases your delta. It’s just alien in pension fund management.

[7] Both Table 1 and Table 2 represent simplified examples where LDI hedging assets and pension liabilities are proxied by the same long-duration bonds, and future pension contributions are excluded from the analysis.

[8] Table is based on a Monte Carlo simulation of a pension fund that begins with the indicated funding status and allocated as shown until it reaches the next de-risking trigger. Returns for stocks and bonds are simulated; the correlation from the last five years is used. The importance of the table isn’t derived from the precision of the assumptions, but from the illustration of the increased difficulty in reaching the next de-risking increment when the fund is already de-risked substantially.

A (Very) Long History of Real Interest Rates

December 23, 2016 5 comments

One of the problems that inflation folks have is that the historical data series for many of the assets we use in our craft are fairly short, low-quality, or difficult to obtain. Anything in real estate is difficult: farmland, timber, commercial real estate. Even many commodities futures only go back to the early 1980s. But the really frustrating absence is the lack of a good history of real interest rates (interest rates on inflation-linked bonds). The UK has had inflation-linked bonds since the early 1980s, but the US didn’t launch TIPS until 1997 and most other issuers of ILBs started well after that.

This isn’t just a problem for asset-allocation studies, although it is that. The lack of a good history of real interest rates is problematic to economists and financial theoreticians as well. These practitioners have been forced to use sub-optimal “solutions” instead. One popular method of creating a past history of “real interest rates” is to use a nominal interest rate and adjust it by current inflation. This is obvious nonsense. A 10-year nominal interest rate consists of 10-year real interest rates and 10-year forward inflation expectations. The assumption – usually explicit in studies of this kind – is that “investors assume the next ten years of inflation will be the same as the most-recent year’s inflation.”

We now have plenty of data to prove that isn’t how expectations work – and, not to mention, a complete curve of real interest rates given by TIPS yields – but it is still a popular way for lazy economists to talk about real rates. Here is what the historical record looks like if you take 10-year Treasury rates and deflate them by trailing 1-year inflation:

dumbrealThis is ridiculously implausible volatility for 10-year real rates, and a range that is unreasonable. Sure, nominal rates were very high in the early 1980s, but 10%? And can it be that real rates – the cost of 10-year money, adjusted for forward inflation expectations – were -4.6% in 1980 and +9.6% in 1984? This hypothetical history is clearly so unlikely as to be useless.

In 2000, Jay Shanken and S.P. Kothari wrote a paper called “Asset Allocation with Conventional and Indexed Bonds.” To make this paper possible, they had to back-fill returns from hypothetical inflation-linked bonds. Their method was better than the method mentioned above, but still produced an unreasonably volatile stream. The chart below shows a series, in red, that is derived from their series of hypothetical annual real returns on 5-year inflation-indexed bonds, and backing into the real yields implied by those returns. I have narrowed the historical range to focus better on the range of dates in the Shanken/Kothari paper.

skreal

You can see the volatility of the real yield series is much more reasonable, but still produces a very high spike in the early 1980s.

The key to deriving a smarter real yield series lies in this spike in the early 1980s. We need to understand that what drives very high nominal yields, such as we had at that time in the world, is not real yields. Since the real yield is essentially the real cost of money it should not ever be much higher than real potential economic growth. Very high nominal yields are, rather, driven by high inflation expectations. If we look at the UK experience, we can see from bona fide inflation-linked bonds that in the early 1980s real yields were not 10%, but actually under 5% despite those very high nominal yields. Conversely, very low interest rates tend to be caused by very pessimistic real growth outcomes, while inflation expectations behave as if there is some kind of floor.

We at Enduring Investments developed some time ago a model that describes realistically how real yields evolve given nominal yields. We discovered that this model fits not only the UK experience, but every developed country that has inflation-linked bonds. Moreover, it accurately predicted how real yields would behave when nominal yields fell below 2% as they did in 2012…even though yields like that were entirely out-of-sample when we developed the model. I can’t describe the model in great detail because the method is proprietary and is used in some of our investment approaches. But here is a chart of the Enduring Investments real yield series, with the “classic” series in blue and the “Shanken/Kothari” series in red:

endreal

This series has a much more reasonable relationship to the interest rate cycle and to nominal interest rates specifically. Incidentally, when I sat down to write this article I hadn’t ever looked at our series calculated that far back before, and hadn’t noticed that it actually fits a sine curve very well. Here is the same series, with a sine wave overlaid. (The wave has a frequency of 38 years and an amplitude of 2.9% – I mention this for the cycle theorists.)

endrealsine

This briefly excited me, but I stress briefly. It’s interesting but merely coincidental. When we extend this back to 1871 (using Shiller data) there is still a cycle but the amplitude is different.

endreallong

So what is the implication of this chart? There is nothing predictive here; about all that we can (reasonably) say is what we already knew: real yields are not just low, but historically low. (Current 10-year TIPS yields are higher than our model expects them to be, but not by as much as they were earlier this  year thanks to a furious rally in breakevens.) Money is historically cheap – again, we knew this – in a way it hasn’t been since the War effort when nominal interest rates were fixed by the Fed even though wartime inflation caused expectations to rise. With real yields that low, how did the war effort get funded? Who in the world lent money at negative real interest rates like banks awash in cash do today?

That’s right…patriots.

1986-004-223Frankly, that makes a lot more sense than the reason we have low real interest rates today!

Categories: Good One, Investing, Theory, TIPS
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