Risk Perversion Revisited and the Idea of Inflation Risk Arbitrage

Today, while perusing a favorite site of mine, Minyanville, I came across a great op-ed piece that touches on an idea of risk perversion that I very very poorly examined a few months back (I just reread it and stared blankly at the screen).  A few months older and maybe wiser, this article helped me better drill down on the ideas in my head and I would like to comment on and add to his analysis. 

The op-ed piece is basically an assault on the recent government bailouts and moral hazard surrounding fiscal and monetary involvement in the markets.  He writes,

As a result of my values and life experiences, I chose conservative personal finances. Due to my preference for security and prudence, I forgo the opportunity for larger gains and windfalls in exchange for the lower risk and security. It used to be that I could live with this trade-off. However, the last decade (and last few years in particular) have made this choice increasingly difficult. Not only have risky investments been deliberately supported by government policy, but less risky paths have been infected by overspill from the risk-taking activities; worse yet, my very own government is treating me as a sucker. I mean openly, which is kind of new.

This gets at the heart of the idea of risk perversion - a phenomena where investors accept misunderstood view of risk which spreads throughout the market and through processes such as reflexivity becomes dogma.  A great example of this is "home prices always go up".  This slowly infiltrated the real estate market over the past few decades and caused many of would-be renters to leverage themselves beyond their means and rationality in order to invest in an asset that they thought was risk free.  In doing so, the massive shift of renters to buyers caused this assertion of risk to appear to be correct by many statistical measures over extended time periods - up until recently. 

Extending this to the Modern Portfolio Theory definition of risk budgeting between the risk-free and the the risky asset leads to more interesting conclusions.  The risk-free asset, usually defined by a Treasury Bill, is supposed to be, well free of investment risk.  Since fixed income investment risk is made up primarily of purchasing power (inflation) risk, default risk, interest rate risk, and liquidity risk.  Since T-Bills are highly liquid, usually held to maturity, and virtually default-free, this leaves us with only inflation risk.  Inflation risk is a very sneaky risk, because it is not usually evaluated post-facto.  Although CPI measures can be subtracted to get a real rate of return.  An investor who invests $950 and receives $1000 a year later usually doesn't factor in the fact that his $1000 can only now buy $980 worth of goods and services, mainly because  that is not what it is used for as the investment proceeds are reinvested and 2% inflation over one year is hardly noticeable.  Although this should be and usually is considered before such an investment is made, it is usually not evaluated directly afterwards.  It is usually years later, when inflation begins to compound that these effects are realized and evaluated.  Additionally, under a normal yield curve environment, inflation should gradually push yields up therefore compensating the investor for inflation as he/she reinvests.  Should inflation risk get out of control, risk-averse investors soon find themselves taking on no risk and taking a loss to do so - which is not a characteristics of a healthy economy and capital market.

The slutty stepdaughter of Modern Portfolio Theory is the Capital Asset Pricing Model (CAPM), which has been used and sometimes abused by almost everyone in Finance over the past quarter century.  When choosing to diversify between the risk-free and risky asset, this formula gives an expected rate of return for an individual investment:

Expected Rate of Return = Risk Free Rate + Beta*(Expected Market Return - Risk Free Rate)

E(r) = R(f) + B*[R(m) - R(f)]

Let's assume that this risky asset is the S&P 500 SPDR (SPY), with a Beta of 1 the equation quickly reduces to what we would expect.   

E(r) = R(m)

I mentioned earlier that under NORMAL conditions inflation risk on the risk-free-rate of return is not really evaluated, however a inverted yield curve and inflationary period where year over year inflation (as measured by CPI and PCE) has increased more than the risk free rate.  The chart using CPI shows this to be a very recent and rare phenomena - occurring post-bubble from 2002 to mid 2005

and using PCE as inflation benchmark....

Well what does this all mean?

First, the obvious observation is that for a substantial period of time, the real risk free rate of return was actually negative.  During this time period, the risky asset dramatically outperformed the risk-free asset as the market roared back from the post bubble collapse. This is important because a large pool of investors allocated to the risk-free asset experienced a relatively substantial negative real return over an extended time period.  Up until 2003, any time that this phenomena existed or got close to existing it was immediately corrected. As the always appropriate George Dub once said, "Fool me once shame on me.  Fool me twice shame on you." I add, "Fool me three times and I'm a fool."

Next we should look at how this all factors in to the CAPM model, substituting the risk free rate, with the factoring inflation into the expected market return and risk free rate

R(e) = R(f) - i+ B*[R(m) - i - R(f) + i] = R(f) - i + B*[R(m) - R(f)] = R(e) - i

Therefore as expected we can conclude that by adjusting the various input returns for inflation we get an expected return that is adjusted for inflation. 

So, then we can conclude based on CAPM, adding inflation into the calculation does not fundamentally change anything, however the fact that the risk free rate of return is negative will affect how one allocates between the two portfolios. 

A fundamental concept of CAPM is that an investor should be compensated based upon the time value of money and risk.  The time value of money is represented by the first half of the expression, R(f), whereas risk is represented by the second half, B*[R(m) - R(f)].  If the real risk free rate is negative, the investor is not compensated for the time value of money, but rather PENALIZED for it, since he is not taking any risk.  Therefore the rational investor will not allocate towards it unless of course he is being compensated even less for risk. 

Whereas the time value portion of the equation is very straightforward and can be almost perfectly analyzed ante-facto, the risk portion is very difficult to analyze before investing.  Forecasts must be made based for market return and assumptions for beta. 

If an investor assumes that at the very least, he will be compensated more for allocating towards the risky portfolio and should be compensated at least at level equal to inflation risk for investing in the risky portfolio, thus substituting inflation, i, for R(m), the the second half of the equation changes to

-B*(R(fr)), where R(fr) is the real risk free rate

Then the new equation can be constructed where

R(e) = R(fr) - B*R(fr)

In a situation where the real risk free rate is negative, the equation is always maximized when the investor allocates away from the risk-free portfolio.  Only when inflation expectations turn positive will an investor in this situation ever allocate different.

Another important feature of all of this is that if real risk free rates are negative both market risk as well as any types business or financial risks of the risky portfolio that are added to expected market returns above inflation are irrelevant.  In any case he will choose the risky portfolio, if he believes both the risk free rate will remain negative and that risky returns will at least equal inflation. 

Thus, the perversion of risk.  Facing a negative return on the risk free asset, the investor is FORCED to either take a loss or take risk - sometimes much more than he or she would like or will get paid for.  Although inflation risk is the same for both portfolios, it becomes much more "rational" to risk loss to make a gain then to accept loss with almost 100% certainty, thus inflation risk is proportionally much higher in the risk free portfolio than in the risky portfolio although it is the same in magnitude in both.  In its crudest form, this may be  the framework that has perpetuated much of the madness that many of us have griped about for a few years now.  The relative risk free asset has been the one that doesn't take your money but gives you a shot at making money by taking risk - if that does not make sense then you are not alone.

The fact that investors would only need inflation to pass through earnings is what created a risk free asset from a risky asset.  Although this has not happened throughout history, I hypothesize that a debt infused economic boom devoid of real wage growth and characterized by rampant consumption and the outsourcing of fixed labor costs would almost exclusively be inflationary and any earnings growth should be equal to inflation plus any operating gains or losses.  If the credit fueled demand caused the price of Good A to increase almost 10% in the store and globalization and other factors only caused costs to increase 2%, the company selling widgets should grow its earnings by about 8% - add financial leverage to the situation and these earnings increase even more - offsetting any input cost inflation.

Essentially, this phenomena spawned what appeared to be a very profitable trade for many who picked up  it.  Inflation risk was priced differently in two very liquid markets.  In the risk-free market taking on inflation risk generated a negative expected return, whereas in the risky market it generated an expected return that greater and presumably could be magnified proportional to market risk as well other underlying investment risk.  Therefore the "astute investor" - and I use that term loosely - thought that they were simultaneously buying and selling inflation risk and capturing the spread - let's call it inflation risk arbitrage.   Obviously this thought process wasn't so technical, but has simplified by many notable investors and journalists who recommend that equities are the only way or easiest way to keep up with inflation and nurtured by famous investors such as Joel Siegel, who claimed that over time stocks offer greater return for much less risk.  The fact that many years passed where "safe" investors started to realize that they were losing money helped perpetuate such a trade and change the entire market's outlook on risk. 

The reality of the situation is that the risk profiles have not changed.  Inflation masked business risk and financial risk for risky investments as the special, global, credit driven, [insert whatever you want here] inflationary environment enabled companies to increase profit margins enough that any volatility in earnings, sales, or poor capital investment, went relatively unnoticed - which feeds into the idea that liquidity and volatility are polar opposites.  As liquidity dried up, many investors in financial and consumer discretionary stocks were introduced to business and financial risk that they unknowingly or perhaps were "forced" to take on.  This wiped away a few years inflation gains in only a few months.  The fact that bailouts are now punishing those who did not realize this even complicates the situation further. 

The probability distribution that describes business risk has a much higher kurtosis than that which describes inflation risk (bigger more infrequent observations).  This enabled the risk it to lurk underneath unnoticed and unseen and create what seemed to be a risk free arbitrage. When receiving a fixed payment inflation risk is easily approached ante-facto and managed.  When expecting to sell sometime in the future at a higher price, inflation risk is more or less embraced and hoped for.  Investors who thought they were capturing some sort of spread (whether they outwardly realized it in such technical terms or not) hoped to end up on the bright side of an inflation trade.  It wasn't until they got burned that they found out what they were really capturing was extra risk premium that was defined by infrequent and large (or severe) observations.  This trade was able to carry on for quite some time as many conservative investors after one or two years of investing in T-Bills, woke up to the fact that they were losing money and prices going up everywhere. 

To finish up touching upon the op-ed piece, the moral hazard of all these bailouts is not only that it encourages wild risks to be taken, but also does not allow for the pain and reflection that is associated with a loss and for the real reasons for that loss to be explored.  Loose monetary and fiscal policy and too much credit in the system enabled a dangerous situation where risk-averse investors lost money to take no extra risk rather than lend money to earn a return.  Poor oversight and suspect conflicts of interest enabled this to spiral into many years of perceived risk perversion and a damaged market psyche.

Comments

[Bond investor]

ZB, you have an impressive intellect. We should both try to get higher-paying jobs...

A couple thoughts:
1. You're right on the mark with ex ante and ex post inflation. Just look at the TIPS market -- you often pay too much for ostensible inflation protection. You may *think* you're getting protection, but if you sell your TIPS after what you think is a "high" CPI print, you will often be disappointed because the market is trading on expected future inflation.

2. The fat-tailed distributions for taking equity risk versus the somewhat normal distributions for inflation risk suggest (to me, at least) that stock risks are understated, and journalists like the annoying Jack Hough of SmartMoney should get their heads examined. Using the average arithmetic return to justify a 100% stock portfolio is cold comfort to those who bought in March 2000. The 7-year return on stocks vs. bonds is about even, and bonds had a much less bumpy ride.

3a. You correctly (I think) eliminate default and liquidity risk from owning T-bills, and conclude that only inflation risk remains. Yet you also acknowledge that inflation is a long-term, creeping phenomenon that really only begins to bite over several years. By definition, T-bills are not a multi-year investment. Further, they are too easily affected by the Fed's monetary policy, which often lags the market. I think you're just arguing for an upward-sloping yield curve. Those worried about preserving purchasing power against inflation should be in longer-term bonds (either nominal or TIPS, depending upon their forecast), not short-term bonds.

3b. There is another "risk" that should be priced into T-bill rates: the real rate of interest. People will charge a borrower *something* for deferring consumption above the rate of inflation. Historically, that's been about 2%. Morgan Keegan economist Dr. Rataczjak has covered this in detail in his weekly commentaries (can't find the cite -- sorry).

4a. People that say "I can't just own bonds, I must speculate in stocks, credit, houses, energy, etc. to keep up with the real inflation I experience" may be mistaking a change in the mix of goods and services they buy vs. a general increase in prices that really would be worrisome inflation. My elderly money mgt clients complain about rising health care costs, but that's a demographic shift, not "inflation." Conversely, they see falling prices in apparel, telecom, or declining-demand goods like newspapers as "good budgeting" on their part, not "deflation." For more info, Google "Inflation: The Cost-Push Myth" by Dallas Batten of the St. Louis Fed back in 1981.

4b. Yale's Robert Schiller (of home price index fame) has been way out in front on the problem you described and that I discussed in 4a. The major problem with good- or service-specific price increases is that historically there's been no easy, reasonably-priced way to hedge. Now that the CME trade housing-price derivatives, you can hedge away your home's price decline. (Imperfectly, to be sure, but better than nothing.) It's too bad that going long the Health Care Spyder isn't a better hedge against rising health care costs...

[ZeroBeta]

I appreciate the kind words bond investor. As you have been my most faithful reader, I apologize for the long absence. The combination of being busy, mild writers block, and time spent working on a website that proved too difficult took too much time away from my blog. Thanks for checking back, I appreciate the loyalty.

1. The TIPS market is similar. I think the TIPS market suffers from a very fat tail liquidity risk. It is not that deep and each issue is relatively small. Since it is a type of "insurance", if things get deflationary, TIPS investors can lose tons of money as I would think many conservative investors, would flood the market after seeing this fall and swap into a vanilla Treasury Bond with a more stable risk distribution.

2. I couldn't agree more. I think we are going to come to a major liquidity crisis in the equity market in a few years as investors realize that they have been valuing equities improperly for the past 10 - 20 years beleiving that "stocks go up over time" and there will be someone who is willing to pay. If interest rates begin to creep up, Treasuries will be much more attractive than 1% dividend yields and people will realize that an investment should be valued on some sort of earning stream for THE INVESTOR not for the company who merely pockets the earnings through obscene compensation, or the government through higher tax rates than dividend tax rates.

3a. True but many people invest in T-Bills through some sort of money market fund which just rolls them over rather than going to auction. So I'm making assumptions based on the term structure of interest rates. Obviously, reality is much more complex. Those worried about inflation would go to longer term bonds or TIPS, but I think equities have offered a much more attractive risk profile and have been invested in instead.

3b. I think its an interesting measure but would think it is dependent upon many other phenomena such as wage inflation, wealth effects and many other consumer type data. Also, since the savings rate is negative, one would say that this is not really a choice being made any more and actually dependent on inflation and short term rates - which would introduce tons of model mispecification. Although interesting to look at, I believe it is very hard to add that into an analysis without introducing tons of bias, but will look into it.

4a. People don't really understand inflation in general. They don't see stock price returns as inflation, but gas prices as such. It is also underscored by the major difference between consumer and investor behavior. With price inflation, inflation is seen as a cost and usually attributed to some conspiracy, but price deflation is attributed to some skill - whether it be they are a good shopper or that a politician is a good politician. On the other hand, asset inflation is seen as a skill. People who pick a great stock or buy a house that increases in price did it because they were clever and are a sophisticated investor, whereas asset deflation is seen as a cost or better yet, a crisis. The recent bailouts and this whole subprime crisis show this quite nicely. The same is true with wage inflation as is with investment inflation. The best example of this is property taxes - the cost associated with your property. You think you are skillful when your house doubles, but think its a travesty and the government needs to change when your taxes double as well. It also relates back to the whole preference for gratificaiton now versus in the future. With investments we immediately accrue what paper gains we have and wish to defer our losses. We realize all cost increases or decreases dynamically, therefore would rather spend our money on what is certain - the now, then take the chance of realizing the losses that have been deferred into the future.

4c. I don't think a market could develop around this, and would really help anything - possibly make things worse. Most services and products are either intangible or depreciating in nature, therefore the futures market would never be as deep as the actual market. Nobody wants to speculate in the widgets market and have to buy futures on widgets and have to hold inventory. Futures markets develop because speculators are willing to trade commodity futures because commodities are assets and many people buying them are willing to accept payment in that commodity in the future. I just don't see how you can receive a "healthcare service" in the future and how anyone within the market could participate. The housing one works because of the amazing amount of derivatives based on home prices that banks hold.

[Bond investor]

ZB, thanks for the reasoned response and always-interesting content. Let's dig a little deeper...

1. So if TIPS have major tax, liquidity and structural shortcomings, why are they among the best performers among bonds this year? (Although nominal 20-30 yr cpn Tsy and STRIPs have outperformed Vanguard Infl-Prot Secs Fd) I think it's just coincidence that the *trailing* 12-month CPI and a flight to Treasuries occurred at the same time. I will have to check CPI vs. spread-widening trends historically. My gut tells me that the Fed and bond markets used to be less pre-emptive and expectational, so trailing CPI might peak at a different time as your typical flight to Treasuries. Also, most recessions are not credit-induced (like this possible one might be), but due to other shocks: Internet mania, Gulf War + tax hike, hyperinflation + oil embargo + structural change from mfg to service economy.

2. You're concerned that stocks (particularly low-dividend ones) may not be good investments in an age filled with skepticism about stock exit-strategies (like Baby Boomers retiring/dying) and the value of that final "liquidating dividend" in a Dividend Discount Model. I wholeheartedly agree! I also think the converse may be true -- if the real interest rate and the level of inflation both fall, then the equity risk premium may be exposed as being not large enough. (Actually, I think we're saying the same thing!)

3a & b. I'll try to dig up the Morgan Keegan piece on this, but I agree that it's just a hypothesis -- the effect is nonzero, but whether it's more significant than the forces you outlined, I dunno.

4a. You hit the nail on the head with loss aversion and mental accounting of "money I made" vs. "money *they* take away" (taxes, retailers, et.) It will be very interesting to see how loss aversion affects the housing market. NYTimes Business, of all places, has a good article on this today, about the LA suburb of Paramount, where house sales of any kind, at any price, has fallen -78% YOY! Refusing to take a loss on a house will only prolong the housing recession.

4b. I agree that without an active speculator community able to take the other side of a trade, the hedges Shiller would like available will remain illiquid or never be created. Where I live, there *is* a firm that specializes in "retail" sized gasoline forward contracts for non-agricultural buyers. So if you commute an insane amount to work in a big honkin' SUV, you can buy "insurance" on gas prices forward for months or years. You purchase at a price above the spot price, and buy in gallons, which can be "redeemed" at most gas stations in my metro area. The problem that I see is that the firm will be left with a lot of out-of-the-money options on old contracts. Yes, they paid more up front, and hopefully the firm earned money on the float, but if their "insured-price" gallons are out-of-the-money, such as if gas prices fall, then they can just pay in cash like regular Joes at the service station.

[ZeroBeta]

Bond Investor thanks for the response. what do you do for a living? Do you have a blog by the way?

1. With the end of the curve at less than 5%, CPI at 3%, the yield curve reverting and steepening, and the Fed cutting interest rates with oil and food at all time highs, wouldn't you rather be in TIPS than sitting on the end of the curve? I think it DID offer a better risk return for fixed income money, however its a bit of a crowded trade with a ton of retail/401k money flowing in. My dad asked me about them the other day, and immediately told him not to buy them. The average guy hearing about inflation on the news and in the paper, unaware and unable to hedge against it sees a Vanguard Inflation Protected Treasury Fund and piles in. Plus ETF's that invest in TIPS have also become very popular.

2. Yeah its the same thing just the other way around, but i think its almost inevitable. At some point boomers will need income, so one of two will have to give. With low interest rates they get crappy treasury yields and with no low dividend yields its the same thing. So either they begin to sell stocks and buy bonds (perpetuating the bagholder scenario), or stocks begin to issue dividends to retain capital. Either way the they get marked to market.

4b. Yeah but I think any type of insurance perpetuates inflation in the asset being insured and simply misallocates resources. Health insurance is a perfect example. It has enabled people to access health care they don't need bidding up costs of both insurance and healthcare - eventually to a price where most people can't afford either. The government, which has a very strong insurance lobby to no surprise, steps in because of political reasons and further adds to the problem. The only type of insurance that has fixed premium payments is that which insures something that is not a financial asset or good - such as life insurance. A less vanilla example is index puts to hedge market risk. As the ability to hedge against this supposedly risk that can't be hedged (up to a point in IV profitably) causes a bias on stock prices to move up as there is less stock selling and more put buying and investors get nervous, and increases the cost of the volality hedge beyond what the actual volatility will be. Eventually, when things get too out of control (like now) the government must step in and provide liquidity to prevent a crash, which is essentially what a put option provides (since it is a contractual agreement to sell stock at higher price). This further inflates the cost of the asset. Cars wouldn't be as expensive as they are if people didn't have to buy the insurance and gas prices would be lower. In an insurance contract risk is simply transferred, and if the eventual reinsurer is the Federal Government, it is automatically inflationary as it increases the liabilities and decreases the currency.