Thursday, October 29, 2009

What are the dangers of using a short-term, downside measure for a fund with a long-term investment horizon?

We received a comment on my VaR vs. Tracking Error: The flawed debate post that is worth its own post as an answer.

Reader "P" asked:

"What do you consider to be the most significant dangers of using a short-term, downside measure (e.g., VaR) for a fund with a long term investment horizon? Is there much literature on this? Presumably much of it is behavioural?"

P, thank you for your question. It sparked a spirited debate internally amongst our blog contributors. Collectively, this is our answer to your question.

First, we believe there are two questions implicit in the one you asked:

1. Why would a long horizon manager need to look at short-term risk?

Long horizon models have long half-life by definition. As a result, when a market reversal occurs after a period of low or moderate volatility, long-term models become wildly out of sync with a market for at least 3-4 months. In this case, the only model that can give reasonable risk readings is a short-term model. This has nothing to do with a provider, but is inherent in a long horizon model's construction. If one could afford to be without any risk readings in times of turbulent market reversals, then one could stick with only a long-term model.

2. Is there a danger of whip-sawing?

We tend to agree with you that this problem is behavioral. If the portfolio has a long-term horizon and is down significantly in the short-term, it is reasonable to wonder whether the portfolio manager, senior management, and/or the client will remain committed to its long-term horizon. If not, then the short-term downside risk can’t be ignored.

So, if the danger of whip-sawing is real, this turns into a question of how a long horizon manager uses the short-term model. Obviously, short-horizon managers will use a model in a different way, because their bets are on the same horizon with risk, so they can weigh risk-return tradeoffs on the same frequency. For a long horizon manager, a short-term model is not a day-by-day investment tool, but rather yet another reading on a dashboard of relevant market indicators. It is an FYI when markets are tranquil. It becomes crucial and a source of actionable intelligence in turbulent times.

We welcome your questions! Please leave comments on any post and we will respond here or to you directly.

Thursday, October 22, 2009

Flushing returns down the volatility drain with Leveraged and Inverse ETFs: part 2

This week, I will follow up on a blog from several months ago in which I discussed how volatility can destroy returns in leveraged ETFs. I received several comments on that blog and continue to see articles written about leveraged ETFs in various publications so I thought the time was right for a continuation. The crux of the original blog was that compounding kills performance, particularly in times of high volatility, such that the long-term returns of leveraged ETFs are actually quite unpredictable. They meet their objective over the short horizon, like intra-day or one day, but multiplying the long-, mid-, or even near-term performance of the index by 2 or 3 (or -1, -2, or -3 for inverse ETFs) does not produce an accurate estimate of the performance of the leveraged ETFs over that same time period.

This week I will add some empirical data to the analysis. But first a pop quiz.

Listed below are the names and one-year returns of the Russell 2000 along with the ProShares 2x, inverse 1x, and inverse 2x Russell 2000 ETFs. Can you match each security to its return?

Read on for the answers.

1) ProShares UltraShort Russell 2000 ETF (Inverse 2x)
2) ProShares Ultra Russell 2000 ETF (2x)
3) Russell 2000 Index
4) ProShares Short Russell 2000 ETF (Inverse 1x)

a) -62.3%
b) -31.4%
c) 1.9%
d) 14.1%

The Russell 2000 is up 14.1% over the past one year (#3 goes with d). Does it surprise you that the 2x ETF is up only 1.9% over the same period? That 2x ETF returned about 1/7 of the performance of the underlying index! The inverse 1x returned -31.4% while the inverse 2x returned -62.3% which equates to over four times the inverse return of the index! Were these ETFs managed poorly?

To test, we need to look at the daily returns of the Russell 2000 and multiply each day’s return by the leverage factor of each ETF. Then, we can compound the adjusted daily returns. The Russell 2000 index itself is up 14.1% over the last year. Assuming perfect daily replication of 2x the index, the return would be 3.7% over the same period compared to the 1.9% returned by the 2x ETF. Perfectly replicating the -1x inverse index and -2x inverse index each day would return -29.9% and -60.8% respectively, approximately 1.5% higher than the equivalent ETF. It is much more the case that compounding in a very volatile market led to the seemingly poor performance rather than poor management of the funds.

In fact, that period was one of the most volatile periods in the last 20 years, with a 2.98% daily standard deviation of the Russell 2000. How big an effect can volatility have on leveraged and inverse ETF performance? Let’s take a look at another period.

1995 was a year of particularly low volatility. The daily standard deviation of the Russell 2000 that year was only 0.51%. Of course there were no leveraged or inverse ETFs back then, but we can approximate by multiplying each days return by the leverage ratios and compounding. The Russell 2000 returned 28.45% in 1995. The returns of the hypothetical ETFs from that time are shown below. In all five cases, the returns of the leveraged ETFs are higher than expected by multiplying the full year Russell 2000 return by the leverage ratio.


The tests run for the S&P 500 ETFs returned very similar results. The one year performance data for all ETFs tested are below.


Not surprisingly, the 1x ETFs performed almost exactly as expected over the year since daily volatility has no affect on long term replication in this case. These are the only ETFs that should be considered for long-term inclusion in one's portfolio. Leveraged and inverse ETFs do have their place for short-term hedging and other very short-term strategies, but not for the long-term investor.

You should consider your rationale and time frame for investing in these assets. Investors do seem to understand this point, as trading activity (average daily volume divided by shares outstanding) is considerably higher for the more highly levered ETFs.

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Wednesday, October 14, 2009

The reports of my death are greatly exaggerated

Hardly a day goes by without seeing a headline in a financial publication about the decline of the U.S. Dollar. Making the case for a weaker dollar and How to avoid greenback grief are two articles that appeared on the same page of the commentary section of the Financial Times on the same day this week. Last week, The Independent published a story titled The demise of the dollar. There are a variety of reasons for this which have been discussed at length in these and other articles (for example, OPEC countries threatening to price oil in a currency other than USD, low interest rates in the U.S. vs. other countries, low expected growth rates in the U.S. vs. the rest of the world, etc).

In recent posts, Sean Carr spoke about the rise of currency risk in portfolios and what would happen if the dollar strengthened. Oh, how times change. After a bit of resurgence from the end of July to middle of August, the greenback looks to be in a downward spiral. Public opinion (or at least many of those expressing their opinion in the press) seems to expect this to continue.
A weaker dollar will no doubt help many American exporters and foreign tourists who wish to visit the U.S. But how will it affect the equity markets? Using FactSet’s stress testing tools, I’ll examine the effects of a 30% decline in the $, from the perspective of a U.S. investor. I’m using a dollar index against a handful of currencies, as published by the Fed Reserve. I’ll use the R-Squared Global Equity model, using Northfield and Barra will produce similar results.

This stress test shows the S&P 500 increasing almost 27% in this scenario. The Materials and Financials sectors are the big beneficiaries. Materials companies benefit from higher commodity prices due to a weaker dollar. Defensive sectors such as Health Care and Consumer Staples are poor performers on a relative basis.
Moving to the MSCI World ex U.S. index, the stress test predicts an increase of about 50%, significantly more than the U.S. market. The sector story is similar to the S&P. Materials and Financials benefit, Health Care and Consumer Staples underperform.

On a country basis, Hong Kong and Japan underperform, while Europe outperforms. The strengthening Euro helps many European stocks. A weakened dollar will hurt Japanese exporters, as the U.S. consumer accounts for a quarter of exports from Japan. Many Hong Kong stocks have significant operations in China, and the Chinese Renminbi is of course currently pegged to the dollar.
Now that we have a general sense of what will happen in the event of a large decrease in the dollar, how are portfolio managers positioning themselves in case of a dollar decline? Using the Lipper Active Indices, we can get an idea of how the average active fund manager in a given strategy is positioning their portfolios. Let’s use the Lipper International Active index against the MSCI World ex US benchmark. Here, in the $ decline scenario, the active index would underperform its benchmark by about 4 percentage points. On a sector basis, significant underweights in Materials and Financials contribute to the underperformance. On a country basis, overweights in underperforming USD stocks, cash, and Hong Kong stocks and underweights in outperforming Canadian and European stocks are major contributors to this underperformance.

Many in the financial press believe that the dollar is on its last legs and expect a continued decline in the greenback. From this analysis, I draw two conclusions. One, the average fund manager may not be adequately positioned for large decline in the dollar. Or two, he/she may think all the reports of the dollar’s death are "greatly exaggerated,” stealing a line from Mark Twain when he heard about his obituary in the paper.

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Monday, October 12, 2009

Taking Risk welcomes new global contributors

We're expanding our horizons! Since starting in January, Taking Risk has featured one UK-based and three U.S.-based bloggers. Now we're adding three more to represent Europe, Asia, and Australia. Watch for entries from these new contributors in the coming weeks.

Willett Bird, Hong Kong
Willett is the head of FactSet's portfolio and quantitative efforts in Asia, covering Japan, Korea, and Southeast Asia. He joined FactSet's Connecticut headquarters in 1997 as a Consultant before moving to Hong Kong in 2000 and assuming his current position in 2003. Willett graduated from Georgetown University and will be finishing a joint degree MBA from the Northwestern Kellogg School and the Hong Kong University of Science and Technology in June 2010. He holds the CFA designation.

Bryan Hoefs, London
Bryan is the UK Manager of FactSet's Portfolio Analytics group, where he manages and develops portfolio and quantitative applications. He joined FactSet in 2001 as a Consultant and has been part of the Portfolio Analytics team since 2003. In his position, he works with portfolio managers, hedge funds, and risk and performance teams in a variety of areas, including risk analysis, long/short analysis, multi-manager and fund of fund analysis. He graduated from the University of Wisconsin - Madison and holds the CFA designation.

Andrew Kovacs, Sydney
Andrew heads FactSet’s portfolio and quantitative efforts in Australia. He joined FactSet in 2000 after working at the Bank of New York for two years. Andrew held portfolio and risk roles in New York and Tokyo before assuming his position in Australia in 2008. He graduated from Boston College and is also a CFA charter holder.

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Thursday, October 1, 2009

Black Swans and Money Helicopters: Staying Ahead in a Nonlinear World

In the spirit of the previous post by Sean Carr, we'd like to begin with an excerpt from Charles MacKay’s Memoirs of Extraordinary Public Delusions and the Madness of Crowds. In the chapter dealing with John Law’s Banque Royale we find the following reasoning emanating from the mind of France’s then Regent Duc D’Orleans:
“If 500 million of paper (money) had been of such advantage, 500 million additional would be of still greater advantage.”
It is a curious fact that almost 300 years after that statement was made, we can all sort of sense what the Duc must have been thinking, even if we don’t know much about John Law and his exploits. But curiosity is not the reason we started with this quote. The real reason is in that it illustrates one of the most vicious fallacies in our thinking about the world around us: linear extrapolation. Some quantity appears to have done some good; twice as much should be twice better. Whether it is fortunate or not, the world is not the linear place. Double the quantity of a good thing, and the results may not be what you expect. This goes for exercise, food, alcohol, medicine, and even leisure (though the last one is debatable).

So, today we are wondering: are the central banks around the world going to overdo it? Are we going to get inflation in place of the credit crunch? We don’t know, but in the world of risk it pays to think about the possibilities. Before we offer our analysis, let us be clear about what we are not intending to do. We are not going to argue whether it was worth to take the stimulative steps that have been taken. If anything, we tend to agree that the prospect of financial meltdown was so real that some drastic measures were necessary. Our purpose is to merely examine where we are, where we are likely headed, and how to prepare for it.

Where We Are
Some of us may have thought that the stabilizing actions of the Fed were of the improvised fire fighting variety. In fact, Ben Bernanke has outlined many of the measures currently taken as early as 2002 in a speech before the National Economists Club in Washington, D.C. In it he described the steps that would be taken in a zero Fed Funds Rate scenario (we bring our apologies for the extensive quotation, but after all if you want to know where you are it is worth asking the driver):
“Because central banks conventionally conduct monetary policy by manipulating the short-term nominal interest rate, some observers have concluded that when that key rate stands at or near zero, the central bank has "run out of ammunition"--that is, it no longer has the power to expand aggregate demand and hence economic activity…

However, a principal message of my talk today is that a central bank whose accustomed policy rate has been forced down to zero has most definitely not run out of ammunition…

Indeed, under a fiat (that is, paper) money system, a government (in practice, the central bank in cooperation with other agencies) should always be able to generate increased nominal spending and inflation, even when the short-term nominal interest rate is at zero.

The conclusion that deflation is always reversible under a fiat money system follows from basic economic reasoning. A little parable may prove useful: Today an ounce of gold sells for $300 (remember, this is 2002), more or less. Now suppose that a modern alchemist solves his subject's oldest problem by finding a way to produce unlimited amounts of new gold at essentially no cost. Moreover, his invention is widely publicized and scientifically verified, and he announces his intention to begin massive production of gold within days. What would happen to the price of gold? Presumably, the potentially unlimited supply of cheap gold would cause the market price of gold to plummet. Indeed, if the market for gold is to any degree efficient, the price of gold would collapse immediately after the announcement of the invention, before the alchemist had produced and marketed a single ounce of yellow metal.

What has this got to do with monetary policy? Like gold, U.S. dollars have value only to the extent that they are strictly limited in supply. But the U.S. government has a technology, called a printing press (or, today, its electronic equivalent), that allows it to produce as many U.S. dollars as it wishes at essentially no cost. By increasing the number of U.S. dollars in circulation, or even by credibly threatening to do so, the U.S. government can also reduce the value of a dollar in terms of goods and services, which is equivalent to raising the prices in dollars of those goods and services. We conclude that, under a paper-money system, a determined government can always generate higher spending and hence positive inflation.

Of course, the U.S. government is not going to print money and distribute it willy-nilly (although as we will see later, there are practical policies that approximate this behavior). Normally, money is injected into the economy through asset purchases by the Federal Reserve. To stimulate aggregate spending when short-term interest rates have reached zero, the Fed must expand the scale of its asset purchases or, possibly, expand the menu of assets that it buys. Alternatively, the Fed could find other ways of injecting money into the system--for example, by making low-interest-rate loans to banks or cooperating with the fiscal authorities…

If we do fall into deflation, however, we can take comfort that the logic of the printing press example must assert itself, and sufficient injections of money will ultimately always reverse a deflation…

The Fed can inject money into the economy in still other ways. For example, the Fed has the authority to buy foreign government debt, as well as domestic government debt. Potentially, this class of assets offers huge scope for Fed operations, as the quantity of foreign assets eligible for purchase by the Fed is several times the stock of U.S. government debt.
Alas, the alchemists never found the philosopher’s stone and gold is still in limited supply. Today’s financial alchemy of central banking does not even require a printing press; the money is created electronically. Credit markets now appear to have stabilized, and economic data in many parts of the world shows signs of increasing output, so what is next?

Where We Are Headed
One of the best books on inflation is Milton Friedman’s Monetary Mischief. In it he attempted to answer many of the questions that we are asking. What would happen, he asked, if a helicopter were to simply fly over and drop the money from the sky? (Ben Bernarke also used the helicopter metaphor.) The precise sequence of events is impossible to predict, but there are some generalizations that can be made from empirical evidence.

In the short run, according to Friedman, the increase in money supply will show up in an increased output without affecting the price level. Interest rates also decrease in the short run. This short run has usually lasted 6-9 months. The effect, however, shows up in the rising prices in the longer run, usually 12-18 months after the short run effects have commenced. Therefore, it is reasonable to expect inflation to pick up within the next year or two. It is impossible to suggest the level of inflation, because the adjustment may be drawn out with ups and downs along the way. The matter is complicated by the Fed’s decision to stop reporting M3 figures, which would help in gauging the level of the brewing inflation.

How Long Will The Inflation Last (Or Will The Real Paul Volcker Please Stand Up)
Just as there is a lag between the increase in money supply and the effect on prices, so there is a lag between the implementation of the inflation fighting program and reduced inflation. In other words, once started, inflation cannot be stopped quickly. It took Paul Volcker at least two years to stop the inflation in the early 80s at the cost of raising the short term interest rates as high as 18% at one point.

However, in our present situation, it will take considerably longer. The reason is that unlike the early 80s, both the U.S. Government and U.S. Consumer are heavily indebted. The net savings rate is around zer0, and U.S. debt is close to $10 trillion not counting the implied guarantees. In such a scenario, significant increase in the interest rates would be difficult to say the least. Continued increase in the money supply on the other hand reduces the real debt load. To summarize, inflation will likely go on for a while.

Stress Testing The Inflation
If the risk model we are using (FactSet offers models from Barra, Northfield, R-Squared, and APT) had history back to the early 70s when high inflation was last observed, this stress test would be as easy to set up as any factor test (for example a 30% decline in S&P financials). To set up the inflation stress test we would simply find the data series for CPI and use Stress Testing horizon feature to specify something like a 10% increase over 12 months. However, the only model with that much history is Barra’s U.S. Long-Term Model (USE3L). Here is the result:
As we can see, the nominal return to S&P 500 is almost exactly flat in our test. The four worst losers are Automobiles and Components, Banks, Consumer Durables and Apparel, and Diversified Financials. The biggest winner is Energy, followed by Pharmaceuticals, Food, Beverage and Tobacco, and Health Care Equipment and Services. It is important to remember that these are statistical predictions, the order and magnitude matter, while precision does not. -14% and -17% are likely to be statistically equivalent.

But most risk models do not go back before the 1980s. How could we possibly use stress testing to ascertain the effect of inflation on a given portfolio when nothing in the recent history of the risk models gives us any idea of what a high inflation environment looks like? In general, stress testing the relationships that have not been observed or have been significantly altered in the recent history is difficult. However, it is certainly possible. As we were doing empirical research in the Fall '07-Spring '08 on our stress testing engine, we asked the following hypothetical question: How would we stress test the effect of a nationwide decline in housing prices on a stock market portfolio? Our situation at that point with respect to declining housing prices was similar to our situation today with respect to rising inflation. Both did not yet take place and were not observable in the recent model history. We had to make an expert judgment on finding the market metric that was both observed and highly related to the object of our study. As a result, we chose to stress test the S&P Financials decline in place of the housing decline judging that the latter if it occurs is bound to be shortly followed or preceded by the former. We did have significant financial declines in our available sample, particularly the LTCM related mini credit crunch in 1998. Subsequent events of Fall 2008 showed that our conjecture was valid and was giving valuable results approximating well the effects of declining housing market (see Portfolio Crash Testing).

Applying this logic to the stress testing of inflation, we designed the following test which uses the multiple shock functionality of our system: Gold up 40% and simultaneously Case-Schiller Real Estate Index flat 0%. We believe that such a test will approximate the conditions likely to be observed if inflation picks up significantly. The Inflation-Gold relationship is obvious, but what about flat Real Estate prices? Why are they necessary? The reason is that we want to separate two types of inflations: broad Consumer Price Inflation from the Asset Inflation. The money supply started growing before 2008. In fact, the last reported growth rate for M3 was around 18% in 2006. Throughout the early 2000s, money supply growth was mostly pushed out of consumer prices and into commodity and asset (financial and real estate markets) by the consumer price deflation exported from China and other low-cost producers. The environment that we want to test is the broad consumer inflation and that is why we explicitly add the zero real estate growth parameter. The result using Northfield Global Model is shown below:
The best performer again is Energy, just as expected. The next best is Utilities, followed by Pharmaceuticals, which paints a slightly different picture. The worst performers are again Automobiles and Components and Consumer Durables along with Retailing. The Real Estate stocks are down slightly likely because flat nominal Case-Schiller Index actually means some loss in real terms for the housing market. It could be argued that an alternative specification could be that the real estate prices could go up in nominal terms staying flat in real terms.

The next step after examining the portfolio level impacts of the stress test should be to go into one of the asset level reports in the Portfolio Analysis, for example, the Weights report. This would allow for the decomposition of portfolio impacts within the portfolio subsectors and industries and down to security level.

As we have seen, it is possible to go beyond traditional factors test to approximate factor shocks that have not been observed in our sample. We close with the observation that many of the events considered to be Black Swans (completely unpredictable in substance or timing) are really more of Grey Birds (anticipated by some experts in substance, but unpredictable with respect to timing or specific sequence). The fact that the timing or sequence of shocks is not known should not deter us from having them on our Stress Testing radar.

Additional contributions by Chris Carpentier, FactSet Portfolio Product Developer

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