Friday, January 23, 2015

Rebalancing and Risk

What is tail risk and how does it relate to the stability of the correlation matrix? 

How does it interact with rebalancing?

Is it possible to identify the benefit one gets from rebalancing based upon market developments?

How do oil price fluctuations and foreign exchange fluctuations relate to the benefit of rebalancing?

What are the implications for a US investor’s international holdings?

This posting advances the notion that instability in the correlation matrix is indicative of a rise in the potential tail risk.  Further, the potential for tail risk should inform an investor’s approach to rebalancing his or her portfolio.  The conclusions drawn in this posting may be unique to market fluctuations caused by oil price and exchange rate instability.  The posting does not attempt to look beyond potential consequences of oil price and exchange rate instability.  It concludes by looking at the investment implications of the central thesis regarding the relationship between the correlation matrix and potential tail risk.  Not surprisingly, the conclusions regarding the implications vary dependent upon one's home currency.  This posting focuses specifically on the implications for US investors.

In finance, “risk” is usually equated with volatility.  Sticking with that definition, tail risk would be extreme volatility.  It is important in financial markets because of the phenomenon known as the fat tail: basically, the probability of an extreme event is higher than what one would assume from a normal distribution.  According to that definition, tail risk is just the same as “risk.”  It is the probability that makes it significant.

A second definition of tail risk is a low probability event that has huge consequences.  The second definition does not quantify low probability.  Instead it focuses on the magnitude of the consequences.  However, it is silent on whether those consequences are the volatility of the variable concerned or some other event that is triggered as a result of the low probability event.  Volatility of the variable is illustrated by a tendency for the amount of change to go exponential when it approaches an extreme.  Triggering of some other event is illustrated by, for example, an extreme change in the price of a commodity forcing a government to default on its loans.

The final candidate as a definition of tail risk considers a phenomenon in finance that is extremely important.  It combines elements of the two previous definitions.  It is associated with, and perhaps a consequence of, extreme volatility.  When there is extreme volatility, it is often accompanied by a breakdown in the relationship between different financial assets.  In financial jargon, the correlation matrix breaks down. 

Being statistical measures, how well things are correlated are not a constant.  They fluctuate.  Thus, while a breakdown in the correlation matrix is often associated with tail risk as defined in the first and second definition, it also sometimes occurs without the realization of tail risk.  A breakdown in the correlation matrix can be viewed as a necessary-but-not-sufficient condition for tail risk.

This last definition based upon the stability of the correlation matrix has the advantage that it provides room for recognition of the fat tail of the distribution of  returns and it defines “the event with huge consequences” in terms of financial market performance.  More importantly, tail risk usually proceeds quickly.  By contrast, deterioration of the correlation matrix can be seen before it completely breaks down.  Thus, one can view the deterioration in the correlation matrix as a continuous variable that will change going into a tail risk event as defined in the first two definitions.

The previous posting, “Markets in Motion,” talked about the market volatility in oil prices and foreign exchange rates.  Both phenomena raise the probability of tail risk by all three definitions discussed above.  Historically, extreme foreign exchange rate fluctuations have been associated with equally extreme economic and financial events.  The reason for the extreme importance of foreign exchange rates is simple.  Foreign exchange rates feed through both to the stability of the financial system and the performance of the underlying economies.

Many financial advisors recommend rebalancing a portfolio regularly.  The end of the year or the beginning of the new year is a convenient time for financial advisors to include a reminder about rebalancing.  There is no magic associated with annual rebalancing, but the change in the calendar does provide a convenient marker for financial advisors or investors who need a reminder. 

Rebalancing a portfolio is often presented as a way for an investor to reduce risk that may have developed as a result of differences in performance of different assets.  However, in fact,rebalancing does not necessarily reduce or increase the risk in a portfolio.  Whether it increases or decreases the risk depends upon what assets are being sold and what are being bought.  (Technically it depends upon the volatility of the assets being bought and being sold).  The real reason for rebalancing is to keep the risk-return profile stable at some level initially set to represent the investor’s risk tolerance. 

A previous posting entitled “Does AlgorithmicTrading Make Sense for Small Investors?” discussed the limitations on some of the assumptions associated with the approach when applied across asset classes.  Instability in the correlation matrix was one of the limitations mentioned.  So far, the phenomena discussed in “Markets in Motion” have not resulted in tail risk in this sense, at least not for US investors.  Consequently, for a US investor, rebalancing seems to have achieved the desired results so far in 2015.  For example, as stock prices declined, bond prices increased. (It is worth noting, however, that when one takes a global perspective, rebalancing has not worked for investors in every country). 

However, when examined closely, it can be seen that rebalancing appears to have achieved the desired objective, but that appearance is due to returns.  The point of "Markets in Motion" was that the phenomena being discussed, oil prices and exchange rates, have increased volatility of all assets.  The portfolio’s overall risk has changed if the change in the volatility of different asset classes is not uniform.  It seems naive to assume that the volatility of all asset classes is changed in the same way. 

In order to achieve a rebalancing that maintains the risk-return profile, one has to forecast not just how returns vary with fluctuations in oil prices and exchange rates, but also how volatilities of each individual asset class is changed.  In and of itself, the fluctuations in volatility may make any portfolio of financial assets more risky.  That is true if the fluctuations in oil prices and exchange rates increase the volatility of all asset classes.  It is also conceivable that it would reduce the risk. 

To illustrate using just using US stocks and bonds, in 2014 the returns on stocks and bonds can be represented as follows: the S&P (NYSEARCA:SPY) delivered 13.5%, a broad-based bond index (NYSEARCA:AGG) delivered 6%, long-term Treasuries (NYSEARCA:TLT) delivered 27.3%.  Thus, a portfolio of stocks, bonds and Treasuries would be rebalanced at the end of 2014 by selling Treasuries and increasing stocks and non-Treasury bond holdings.

One way to view that rebalancing is to believe that during 2014 the increase in the value of Treasuries reduced the risk in the portfolio to the point where rebalancing into stocks and bonds was needed in order to restore it to a given risk-return profile.  In other words, the rebalancing is needed to restore the risk that was eliminated in the portfolio by the increase in the weight of the Treasury component.  The alternative is to view the volatility associated with a higher returns to Treasuries as implying that they are more risky than they were going into 2014.  In this view, Treasuries are now viewed as an asset with greater risk than they had at the beginning of 2014.  Selling the Treasury reduces the risk because Treasuries have become more risky assets. 

One could argue that because an investor must anticipating the impact of oil and exchange rates on two variables (the level of asset prices and their volatility) it has introduced additional uncertainty.  That is a real source of increase in risk, but it is not potential of tail risk.  The important change in the risk associated with any portfolio becomes apparent when one adopts a definition of tail risk that involves only financial assets.  For the US, it is reasonable to assume that the increase in the price of Treasuries has increased their potential volatility.  It is easy to dismiss that as just true of any asset that gains significantly in price.

However, one should keep in mind that a significant portion of the increase in the price of Treasuries is a response to foreign exchange fluctuations.  In short, foreign exchange rates have made Treasuries more risky by increasing their price.  But again, that is just normal portfolio adjustment.  Once one starts to think in terms of global investors, one has to realize that each investor has an investment option that is analogous to Treasuries for US investor.  That option is their home country’s sovereign debt.  Some of the investments moving into Treasuries last year, and especially so far this year, moved from foreign countries’ sovereign debt.  However, those flows come from both equity and bond holdings in those foreign countries.  The correlation between stocks and bonds has broken down for those foreigners if funds flow out of all asset classes.

For the US investor, the potential for tail risk is currently concentrated in the international portion of their portfolio.  A previous posting entitled “Funds for AssetClass Diversification” discussed two mutual funds used to achieve international diversification.  The posting also discussed the philosophy behind holding those two funds.  They are treated similarly to any other position.  Thus, mutual funds are not the only way international diversification is achieved.  In addition to the funds there are individual stocks in non-US companies.  The potential of tail risk impacts each fund and individual stock holding differently.  Since this posting has so far discussed rebalancing in terms of asset classes, the balance of this posting will focus on the funds.  Individual stocks will be the subject of future posting.

The two funds in question are Spartan International Index Investor Class and the Lazard Emerging Market Equity Blend Portfolio.  The reader should keep in mind that it is not these particular funds that are at issue.  They were just chosen as representative of an asset class.  That is the role they played in the portfolio, and it is their role in this posting.  So, the issue becomes whether just having a representative of the asset class continues to make sense.

If the hypothesis that volatile foreign exchange rates and oil prices have increased the tail risk associated with foreign assets is correct, neither fund continues to provide the benefits that justifies including it in the portfolio.  In addition to the diversification benefits, the funds also embody a new higher probability of tail risk. An alternative strategy is to focus on specific stocks in non-US companies as a way to avoid the tail risk.  It should be possible to pick countries and companies that are less exposed to the potential of a collapse of the financial system of the country.

Since both funds include equities denominated in a variety of currencies, shifting to individual holdings could increase the currency risk as well as the company specific risk.  However, the tail risk seems to justify accepting the need to bear the foreign currency risk.  The currency risk was always there; picking individual holdings just makes it apparent.  The decision regarding how many non-US stocks and how many currencies have to be represented then becomes an issue of how confident the investor is in their ability to trade off tail risk against more concentrated currency and stock specific risk. 

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