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Stocks and Bonds: Managing Risk and Return Under the Beta Convexity Puzzle


Are we on the verge of a deflationary deleveraging cycle or has QE reflated us into an inflationary growth cycle? How this issue reconciles will be a function of which cycle prevails.

In July of 2012 I wrote in Trading the Wrong Playbook Bubble that negative interest rates took the discount out of the discount rate. The idea was that the reason so many asset managers (especially hedge funds) were underperforming was that while they were focused on the fundamental discount, the market was being commanded by the grossly underinvested flow:

"By manipulating the yield curve to generate negative interest rates, Fed policy has taken the discount out of the discount rate and thus removed the ability for markets to correctly price assets. Fed policy has essentially turned all assets into commodities subject not to valuation but simply the supply and demand for the securities."

Since the market reaction to tapering and the ensuing rise in real interest rates, market participants have started to reassess this idea that QE removed the discount mechanism in the discount rate. In Thursday's Bloomberg Economics Brief, a commentary by Guy Haselmann of Scotiabank titled "Fed's 'QE-Infinity' May Send Monetary Experiment Awry" was published:
"Price discovery had already been distorted by QE1 and QE2, but it was QE-infinity that demolished it. Financial assets are valued by aggregating the discounted value of future cash flows. Yet, when QE was not given an end date, the market had to accept ZIRP as extending infinitely into the future. Thus, the discount rate used to value those cash flows was assumed to be zero in perpetuity. Dividing a number by zero equals the empty set."

Pay attention, this is important. Haselmann continues:
"It was only when QE was viewed as actually having an end-date during 'taper talk' in May that a forward increase in interest rates was priced into the discount rate mechanism. This is why the market adjusted after May, leading to a more than 100 basis point increase in bond yields.

"Furthermore, QE-infinity destroyed the foundations of the capital asset pricing model (CAPM) by flipping the capital structure upside down. Interest rates had been forced to such artificially low levels that risk/return characteristics became skewed and an asymmetric distribution arose the closer interest rates and credit spreads got to the zero-bound. Government bonds, which converged to par, offered limited upside potential and greater risk. Equities became the preferred asset class simply because they provided uncapped price appreciation that bonds did not. Many asset managers even moved into dividend-paying stocks as a substitute for fixed income exposures. This shift in perception has had a material impact on asset allocation models, and has significantly increased systemic risk."

As I've been saying repeatedly, it's not the QE flow, per se; it's negative real interest rate discount that is governing asset prices. The inflation premium in the bond market, due to the massive QE liquidity injection, produced negative real interest rates. These negative discount rates had a profound impact on asset valuation, turning asset allocation into a guesswork nightmare.

This past week I accidently came across some research that expands on this asset-allocation conundrum and I think correctly questions the implication of how it gets resolved. On August 15, 2011, in the midst of what was the QE 2 asset correlation unraveling, former Morgan Stanley FX strategist Stephen Jen, now running his own macro hedge fund SLJ Macro Partners, and his colleague Faitih Yilmaz published a research paper titled "On the Beta Convexity Puzzle":

"AUD and CHF are not supposed to have appreciated simultaneously against the dollar. Neither should both gold and equities have been bought en masse in the last two years. Some assets are low-beta (i.e., winter assets: assets that tend to perform well in a recession or when investors are in fear), while other assets are high-beta (i.e., summer assets: assets that tend to perform well in a recovery or when investors are greedy). Until two weeks ago, both high- and low-beta assets had performed well against the US dollar. We call this the 'Beta Convexity Puzzle.'"

It is interesting to me that they discovered this dislocation in the currency market but also that it transcended asset classes. Essentially the beta convexity puzzle shows that since the onset of QE, both high-beta, pro-cyclical assets and low-beta counter-cyclical assets performed the same regardless of the economic growth trajectory the asset represents.

They conclude:
"AUD (a summer currency) and CHF (a winter currency) tended in the past to perform well at different parts of the business cycle. However, after the Great Recession, both currencies have performed well against the US dollar. Beyond currencies, we also observe that, until recently, investors were busy buying equities (a risk-on trade) and buying gold (a risk-off or uncertainty-on trade). These are highly unusual market traits, distorting the linear relationships between return and beta for the global asset markets. While the world has indeed changed since the financial crisis, we are not convinced that this 'beta convexity puzzle' is sustainable."

What is the difference between a high-beta and a low-beta asset?

In a general sense, assets can be broken down into two categories: pro-cyclical and counter-cyclical. Pro-cyclical assets are thought to be aggressive, high-beta securities with exposure to higher market volatility, generating most of their return from economic growth. Think stocks. Counter-cyclical assets are thought to be defensive, low-beta securities with little exposure to volatility, generating most of their return from income. Think bonds. Conventional asset allocation theory states that you should structure your portfolio to optimize your return relative to the amount of systemic risk (beta) you are willing to accept. The more units of beta risk you take, the more return you make. But what if the market didn't differentiate between the two?

In June of this year as the tapering debate began driving an unwind of short US dollar levered positions both in the US and in emerging markets, Jen and Yilmaz wrote a follow-up piece positing whether the beta convexity puzzle was getting resolved. In "Tapering by the Fed and the Beta Convexity Puzzle" they write the following:
"QE3 has been a 'success' as it has achieved its objective of artificially inflating the values of both bonds and equities. While its timing and the pace are uncertain, in theory, the Fed's prospective tapering may mark the beginning of the unwind in these asset price distortions, with simultaneous declines in both bonds and equities being a risk, if corporate earnings don't re-accelerate to compensate for the tapering effects.

"Since the tapering discussions began, global bonds and equities have experienced a sharp rise in volatility, and some of the assets (gold and the Nikkei (INDEXNIKKEI:NI225)) have experienced extraordinary declines in value. The chart below shows the asset returns relative to beta since April 2013. What used to be a convex relationship (the previous chart) has turned into a concave relationship (the chart below).
Beta Convexity Vs. Beta Concavity

"One major problem in portfolio management is the lack of a balance between bonds and equities. As discussed above, if bonds and equities are positively correlated, as are gold and oil, it is very difficult for portfolio managers to construct hedged or balanced portfolios. If we are right, that, as the Fed tapers, there is a transition period where a concave relationship dominates in the beta space, then it is not clear what one would buy if he/she cuts back on both bonds and equities. Of course, when the Fed normalizes its policies, we should in theory see the normal beta relationships, and not just convex or concave relationships. But getting from here to there, we fear that the Sharpe ratios in general will likely be inferior than they were in the past four years."

Beta Convexity

Click to enlarge

This beta convexity puzzle is not some new paradigm. This is a product of falling real (negative) interest rates. The rising inflation discount lowered real yields, pushing them negative, which raised the net present value of nominal cash flows. This revaluation trickled up the yield curve and down the risk curve. High yield bonds were priced like investment grade credits, and this translated into higher multiples for equity risk regardless of fundamental performance. Multiples have been the principal catalyst behind the rally in risk, and it's occurring in an environment of decelerating growth.

Five-Year Inflation B/E Vs. S&P 500 (INDEXSP:.INX)

This was the Fed's intention and it worked. The problem is that it severely dislocated asset class valuation, and it's not likely this will be without a cost. The Fed believes it can gently raise nominal rates by maintaining high inflation expectations and thus controlling real interest rates. This is why it decided against tapering and why it wants to extend guidance on when it plans to raise Fed funds. Inflation expectations had declined considerably and real yields tightened market conditions.

The market, on the other hand, may have different plans. This is the key to how this plays out. Can the Fed reengineer inflation expectations, or more importantly, convince the market that it is committed to its inflation target? Will the market reflate beta convexity?

How this gets resolved by the market is going to potentially dictate asset performance for the foreseeable future. Thus figuring out how to position for coming out of the other side is going to be the holy grail of asset allocation. Which wing survives the adjustment process? That depends on what dominates the cycle, deflation or inflation, and thus what happens to inflation premiums and real interest rates.

The whole macro debate is whether we are on the verge of a deflationary deleveraging cycle or whether the Fed's QE has successfully reflated us into an inflationary growth cycle. How this beta convexity puzzle reconciles will be a function of which cycle prevails. The convex and concave relationships that have governed beta and asset allocation will return to a linear relationship based on fundamentals.

As interest rates normalize, so too should beta convexity. The first stage of the normalization process was turning the beta convex relative performance into a concave relative performance. The next stage will likely see the emergence of the beta asset that will govern the coming cycle. Was the Fed successful in reflating economic growth that will be bullish for high beta, or will QE have failed to engineer an increase in aggregate demand, thus benefiting low beta? The market is going to answer this question, and I believe it's going to happen over the coming months.

Thus far coming out of the September no-taper decision despite the reflationary bias, inflation expectations have been muted and the performance has leaned towards low beta. Both the S&P 500 and gold (NYSEARCA:GLD) have reversed their initial rally. Bond yields are lower with nominal yields outperforming real yields. It's too early to draw any conclusions and there are a lot of moving parts, however the market has made a significant opening statement.

If the Fed is successful, real yields are going to push nominal yields higher and high beta is going to outperform low beta. If the deleveraging cycle persists and aggregate demand remains subdued, nominal yields will remain low, lowering inflation premiums and low beta is going to outperform high beta. The key metric will be inflation expectations embedded in the yield curve.

Twitter: @exantefactor
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