Daily price data underestimates stock beta

Those who manage market neutral equity portfolios spend a great deal of time estimating betas (see definition) of individual holdings. The goal is to measure the amount of index-equivalent exposure needed to offset the "market-sensitive" component of each stock's volatility. This often becomes more of an art than a science, with dozens of different (and often proprietary) approaches. These include splitting the measure into the "up-side" and the "down-side" beta based on observations that some companies' share price responds differently to rising vs. falling markets. Another approach used by some risk managers is to look at "stress beta" - a measure of how a stock responds to extreme movements in the market.

There is however one overriding mistake that many portfolio managers make in their estimates of beta. For those who have holding periods of longer than a day, it probably does not make sense to use daily movements in stock prices to estimate beta. Daily data contains a significant amount of noise that tends to dampen the relationship between a stock and the overall market. Daily responses to news about a particular company are sometimes exaggerated, and adjust within the next few days to trade more in tandem with the overall market. On days when the overall market has little direction, stocks of some companies temporarily decouple from the market. All this could lead to erroneous results in measuring beta.

Let's look at an example. In the chart below, the y-axis represents the daily returns for Alcoa Inc., a large US firm focused on aluminum products (website). The x-axis shows the daily returns for the S&P500 index (here we are using SPY because many managers trade this ETF as a liquid proxy for the S&P500). The red line is the regression fit to this scatter plot. The classical way of estimating beta is simply using the slope of this red line, resulting in a measure of 1.63. This means that on average Alcoa shares will move 1.63 times as much as the S&P500. The company by its nature is cyclical and carries a significant amount of leverage, resulting in share price movements that are higher than the index (sometimes referred to as a "high-beta" stock).

In theory if someone is long $10 million worth Alcoa shares and decides to short $16.3 (10 x 1.63) million worth of S&P500 against it, the market exposure should be "hedged". That means the long/short position should exhibit the lowest possible volatility one could achieve by hedging with S&P500.

But most portfolio managers don't hold stocks for just a day. Using weekly as opposed to daily price data results in a beta of 2.05, a materially different outcome (see chart below). It means that in order to minimize the volatility over several days, one needs to short $20.5 million worth of S&P500 against $10 million worth of Alcoa - not $16.3 . The "daily beta", represented by the red line below would have resulted in higher losses during large market corrections than the weekly measure (green line).

Weekly data is based on each Thursday's close

Portfolio managers have numerous options for beta calculations. But one key factor for those who do not turn over their holdings daily is making sure to avoid using daily returns data for these measurements. Betas derived from daily stock prices could significantly underestimate the overall market exposure of a stock portfolio.

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Fed's securities purchases blunt the impact of convexity hedging

Mortgage backed securities (MBS) have sold off sharply over the past month as fixed income markets face the new reality of rising rates.

Source: Mortgage News Daily

But unlike most other fixed income securities, MBS duration tends to increase with yield. That's because higher MBS yields typically mean higher mortgage rates and lower mortgage refinancing activity (which we have already seen). Pools of mortgages backing many MBS, particularly loans with lower coupon, will experience slower prepayment speeds going forward. Slower refinancing extends the effective duration of the bonds (illustration below).

If you have a 30-year mortgage at 3.6%, it is now less likely you will refinance any time soon (mortgage rates today are above 4%). One reason your mortgage is not treated as a full-term 30-year note is the probability that you will sell your house, thus terminating the note. There is also some probability that in the future, mortgage rates will drop below 3.6% again, providing you another opportunity to refinance. The expected average life of your 3.6% mortgage and the security that is backed by your loan has therefore been extended (from you potentially refinancing in the next six months to you selling your house in say 5 years). And if rates rise further, prepayments will slow even more. The chart below shows the prepayment speed (PSA) for just such a security over the past month as well as the expected prepayment speeds going forward. It also shows what happens if rates increase by another half a percent.

Source: CS

What does this mean for investors who hold MBS or actual pools of mortgage loans? They own securities that become riskier (more sensitive to rates) as rates rise. These portfolios have what's often called a "negative convexity" risk profile. To combat rising durations of their portfolios and therefore higher exposure to rates, many investors now have to short longer dated treasuries or rate swaps. And until recently many MBS investors haven't been doing much hedging because the hedge (the treasury short positions) has consistently lost them money. Now many are jumping in - all at the same time - to put the hedges on. And that hedging is putting downward pressure on treasuries (upward pressure on yields).

Bloomberg: - As rates increase, the expected average lives of mortgage bonds and loan-servicing contracts extend as potential refinancing drops, leaving holders more vulnerable to losses from rising rates. Investors then may seek to pare the duration risk or rebalance existing hedges by selling longer-dated Treasury securities, mortgage bonds or transacting in interest-rate swaps or options on those contracts, sending yields even higher and spreads wider.
...
One measure of duration of agency mortgage bonds rose to 4.8 years last week from 3.7 years in April, Barclays index data show. The duration of Fannie Mae (FNMA)’s 3.5 percent debt, which is now 6.2 years, would rise to 7.8 years if rates rise 1 percentage point, according to Bloomberg’s prepayment model.

This mortgage-driven rise in rates happened before - in 1994 and again in 2003. The act of shorting (selling) treasuries increased yields, raising MBS durations and forcing more treasury selling. Some have referred to this market dynamic as the "convexity hedging spiral".

The 1994 convexity hedging impact

Of course this is not 1994 (or 2003 for that matter.) At least for the time being, the Fed is still buying massive amounts of both MBS and treasuries. And all that buying limits the impact of convexity hedging. Treasury sellers that want to hedge portfolios always find one large buyer with "deep pockets". Furthermore, all the MBS held by the Fed is not getting hedged. With no requirement to mark the book to markets, the Fed is fine taking losses on that portfolio.

Bloomberg: - “The actual convexity hedging flows will be less when rates rise this time than it was in the past,” Dominic Konstam, the global head of interest-rates research at Deutsche Bank ... The hedging “was massive in 2003, and we won’t see a repeat of that. With the Fed holding so much of the mortgage paper, it really knocks down the amount of mortgage hedging needed when yields rise.”

What will happen once the Fed ends its program however is anyone's guess.

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Treasuries reduce volatility better than munis, corporate bonds

Some readers have asked if other fixed income asset classes could be just as effective as long term treasuries for an equities portfolio in hedging an equities book (discussed here). Here the comparison is made to municipal bonds, investment grade corporate bonds, and HY corporate bonds. Long term treasuries are still superior in reducing the portfolio volatility - at least based on the last couple of years. That's because muni and corporate spreads tend to be inversely correlated to equities, reducing the hedge effectiveness of these instruments.

Again, the x-axis is the percent of the portfolio invested in the S&P500, with the rest of the portfolio being in one of the fixed income asset classes. The y-axis is the combined portfolio daily volatility over the past two years.

That is the reason investors are willing to take asymmetric risk and dismal current yield to hold long term treasuries. Whether this relationship holds going forward remains unclear. A scenario in which both treasuries and equities sell off some time in the future is not unrealistic.

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Market Neutral Anti-Beta Index: an alternative portfolio hedging tool

Implied volatility based products have not provided the hedge effectiveness many managers were looking for in 2011. In some instances, particularly as implied volatility came off sharply, index options simply did not perform as expected for many portfolios.  

The chart below shows VIX futures versus the HY CDX total return index as an example of someone trying to hedge a credit portfolio with a VIX product. Having worked reasonably well through August-October, the hedge behaved poorly for the rest of the year.

HY CDX vs. VIX Futures

There are alternatives to using equity volatility products to hedge a portfolio.  One of those is the Dow Jones Market Neutral Anti-Beta Index.  It represents a market neutral basket of stocks which is long low beta stocks and short high beta stocks.  The idea is that during market uncertainty and risk aversion, high beta stocks will under-perform low beta stocks. The chart below shows that when properly scaled, a hedge using this index would be fairly effective.

HY CDX vs. Dow Jones Market Neutral Anti-Beta Index

There is in fact an ETF that seeks to replicate this index called QuantShares US Market Neutral Anti-Beta Fund (ticker symbol BTAL). It will work for a small investor but may be too illiquid for a larger institutional manager.  But the underlying stocks in the index a fairly liquid and the basket can be easily replicated.  It has to be adjusted on a monthly basis because betas for the constituent stocks change over time.  The index methodology is included below.


Dow Jones Market Neutral Anti-Beta Index

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Index option hedges have not been effective: poor "option responsiveness"

As one trader said - "the freakin option hedges are just killing me!" The frustration in the market place has been that being long index options to hedge portfolios hasn't produced the results people were looking for. Typically as stocks sell off, implied volatility jumps. In the recent years for the S&P500 the relationship has on average been roughly -5.5 to 1. That is for a 1% move in the S&P500, the implied volatility should move 5.5% (of vol - not vol points) in the opposite direction (again, on average).  The chart below shows the daily regression between the two.

What market participants who use index options to hedge have been looking for is sometimes called "option responsiveness".  If you are long some SPY puts and the market drops, you would expect not only to get a kick from the underlying decreasing, but also from the implied volatility jumping based on the above ratio.  But that strategy hasn't been very successful lately.  In fact VIX (implied volatility index) to S&P move ratio has been on the decline. The chart below takes the monthly average of the ratio, using only the days when the S&P moves have been over 25bp (up or down).

There are numerous explanations for this recent trend, none of them very satisfactory.  The most popular one has been that portfolio managers had overloaded on put protection during the "dark days" of the crisis and with put positions "decaying" against them, used any market sell-off as an opportunity to lighten up.  That means that the ratio may hold when the market is up, but be below expectations when the market drops - working against those who are long puts.  This dampened the implied volatility increases during sell-offs, reducing "responsiveness".  Given the premiums people had to for the puts with recent elevated levels of implied volatility, it's no wonder portfolio managers are frustrated.  One trader called it "option fatigue".

Fundamentally, the 60-day historical volatility in the S&P500 is about 29% and VIX is roughly at that level as well.  Some may argue that implied vol should trade at a slight premium to historical, but the market is obviously pricing in some reduction in volatility going into the holidays.

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Harvard's big swap unwind

As we discussed a few months back, Harvard's lesson in Asset/Liability management had indeed been costly. What has come to light recently is the pain Harvard took on their interest rate hedges. As the school went on their construction spree and undertook a variety of capital projects in the last few years, they were running exposure to short-term rates. This was due to the way the university was financing these capital projects (which is typical for such financing).

In order to lock in their short-term rates on the capital projects' debt, they swapped floating for fixed (agreeing to pay fixed rate and receive floating). Simple enough. But as the rates collapsed late last year, Harvard got a massive margin call on the swaps. Again, this is standard - the value of the swaps went against them (they continued to pay the same fixed rate but were expected to receive floating rate that's significantly lower) and banks called for margin. In principal, that should be OK as well, because the swap losses should be offset by Harvard's lower financing costs.





But a couple things went wrong. Some of their capital projects were put on hold, so they couldn't take advantage of cheap financing. At the same time their liquidity in the endowment became significantly constrained because of the nature of their illiquid investments. And with the economy collapsing, unencumbered donations nearly dried up. The margin call was much more than they could handle and Harvard ended up issuing bonds to cover losses. They ultimately decided to get out of their exposure (possibly at the worst time.) They unwound some $1.1 billion of swaps. However, rather than unwinding the remainder of the hedges (and paying the losses upfront), they simply locked in the losses with offsetting swaps, creating a long-term liability stream. Here is the statement on the offsetting trades:

Harvard (see attached): ... in fiscal 2009, the University entered into additional interest rate exchange agreements with a notional value of $764.0 million, under which the University receives a fixed rate and pays a variable rate. These new interest rate exchange agreements, or ‘offsetting’ agreements, were intended to reduce the risk of further losses in value (with associated collateral posting requirements) within the portfolio of interest rate exchange agreements.

In fact this unwind and others like it at the time caused the 30-year swap spreads to go negative. The overall impact on Harvard's financials was severe:

Bloomberg: Harvard paid $497.6 million during the fiscal year ended June 30 to get out of $1.1 billion of interest-rate swaps intended to hedge variable-rate debt for capital projects, the report said. The university in Cambridge, Massachusetts, said it also agreed to pay $425 million over 30 to 40 years to offset an additional $764 million in swaps.

So how can a bunch of really smart people run into so much trouble with a hedging program. The consultants out there are shouting - you should have hired us to do this. This is too complex for you Harvard guys.

Bloomberg: “It says that people don’t understand the complexity of the products they are buying and selling that doesn’t begin and end with mortgage securities,” said Robert Doty, a municipal finance adviser at American Governmental Services in Sacramento, California. ... “It shows that with these products that are so highly complex, people are a long way from knowing as much about these products as they think they do,” he said.

"so highly complex"? This is how this particular consultant gets paid, by making sure that everything in finance is "too complex" to do without his guidance. In fact this is not about complexity, it's about the practicalities and appropriateness of financial products. And this is when academia often fails - the rule of "we must hedge everything with swaps" was put in place by someone who is not only clueless about the simple mechanics of margin, but also doesn't understand the purpose of hedging.

What is the purpose of hedging here? For Harvard it was to avoid paying really high rates on their financing. But what is high? If LIBOR was at 4.5% when they started on their projects, would it be that difficult for them to pay 5% or 6%? Probably not. The real pain would kick in above say 8%. Hedging for this type of situation should be viewed as a form of insurance. And as we all know, when you buy insurance, the cost depends on your deductible. So Harvard instead of entering into swaps, could have easily bought some interest rate caps struck at say 8%, making sure they never have to pay above that level. It's a high deductible, making these caps reasonably inexpensive. In retrospect it would have been money wasted, but as with any insurance, you buy it hoping it will be wasted.

Alternatively, if they didn't want to pay upfront premium for caps, they could have put on cancellable swaps. The right to cancel would have made their fixed payments higher (depending on maturity, maybe a percent more). But they could have simply cancelled them last year with no breakup costs or margin call. It's a standard and fairly liquid product (in the category of "swaptions"). Of course some would say - oooo, this is too exotic. This concept is actually commonplace, as the "option to cancel" is built into most people's mortgage. When mortgage rates drop, most can refinance with no penalty of unwinding the old mortgage (something borrowers generally can't do in the UK for example). If you refinanced your mortgage before, you've exercised your "option to cancel".

The media is making this sound as though it's a "bad investment" gone wrong - mostly because they don't understand the situation, and it creates good hype. In reality it's simply an issue of sound asset/liability management, proper usage of financial tools, and a bit of common sense. Makes for a good Harvard Business Case study.


Harvard- Financial Report

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Inherent dangers in hedging with Index CDS

Credit Default Swaps are often thought of in terms of providing protection against credit events. However in many instances CDS are used to simply hedge against mark to market losses even if there is no default. Some use Index CDS to reduce volatility of portfolios due to spread fluctuations. The concept is that if the underlying portfolio spread widens, the CDS premium should increase as well, providing some cushion against losses.

However the basis spread between cash securities and CDS can widen dramatically, making the hedge fairly ineffective on a mark to market basis. In 2008 some investors wanted to take advantage of that spread, hoping for convergence. The idea is that if a bond yield, less the financing cost (to leverage the bond), is higher than the CDS protection, one can make a "riskless" return by owning the bond and the CDS.

The assumption however is that one has the ability to hold these bonds and the CDS to maturity. But in 08 that assumption went out the window, as banks asked for additional margin to leverage bonds even if they were hedged with CDS. In addition to that, hedge fund redemptions forced managers to raise liquidity. These two events combined to force the unwind of the basis trade, making the bond-CDS spread widen even more. The wider spread created mark-to-market losses for other basis trade holders, forcing them to unwind as well. It was a punishing cycle.

Those who hedged their portfolios with Index CDS saw their hedges fail, as the CDS premiums did not rise nearly as much as the portfolios got marked down. It was particularly painful for those who had to unwind the portfolios, crystallizing the mismatch.

The chart below tracks the value of the Credit Suisse High Yield (a diversified basket of cash bonds) index vs. HY CDX (index CDS on a basket of HY names). CDX here is shown in terms of price equivalent rather than spread (if premiums increase, the effective "price" drops). End of 08 spelled disaster for many who had these types of hedges on, particularly if they beleived their portolios were neutral. The hedge stopped tracking the portfolio completely.



A similar scenario occured with leveraged loan portfolios. The hedge (LCDX) broke down. In addition, during that period the loans and the LCDX became illiquid, making it even harder to unwind. LCDX performed so poorely as a hedge, it never really recovered from the "ineffective" image and continues to be illiquid.



"Neutralizing" credit portfolios with Index CDS hedges is no longer viewed as reliable strategy. Managers still use these products, but it's no longer considered a dependable hedging program on it's own.

For those who are interested in learning more about Index CDS, please see the Credit Indices primer from Markit (below):

Divergent views on CDS

Here is a great excerpt Michael Johnson's (M.S.Howells & Co) write-up on CDS. It addresses the fact that many equity and credit investors have highly divergent views of credit default swaps. He points out that a heavily restricted CDS market will make the equity market tank.

The equity market's perception of CDS and its importance to the credit markets is materially different than the opinion of many fixed income professionals. Many equity based investors consider CDS to be destructive while fixed income investors consider it to be one of the most important tools available to manage credit risk. The difference is larger than many fixed income professionals might wish to acknowledge.

Fixed income professionals might not wish to acknowledge the difference because the elimination of CDS - besides likely restarting the credit crisis – would essentially force credit providers to "marry" credit risk rather than date credit risk. For example, equity and fixed income investment committees often require PMs and analysts to specify loss limits on positions that force the firm to reduce their exposure by selling the risk or hedging the position.

Hedging an equity position by using puts or selling short equity in liquid names is a relatively straight forward process. However, without CDS a credit investor can be stuck holding a position for an extended period of time (maturity or death) even as its borrower increases the credit providers risk (drawing down a revolver) without an effective hedging tool.

This is a bigger deal than many might wish to consider. The underwriting process of even the most basic loan agreements are likely to become more restrictive and a larger portion of the economic value that has historically flowed to the equity markets will be captured by credit providers. Zero loss underwriting standards will be rolled out at some firms and that will reduce credit availability. (Zero loss underwriting will become more necessary due to the inability to hedge credit deterioration and potential losses associated with LGD.)

Although many investment professionals will argue that CDS provided banks with a tool that allowed them to become reckless and extend too much credit, it is also critically important to remember that bank losses during the 2008 could have been materially worse if the banks did not have CDS hedges in place.

CDS also provides broker dealers with the ability to hedge large fixed income trading books. The elimination of CDS would require them to reduce their portfolios and could jump start another round of deleveraging... remember how that felt?

Credit markets need CDS to function properly....and the equity markets need the credit markets to function properly... so......CDS is here to stay….