“Market Mis-timing”: a study of the distribution of returns from the S&P 500 1950-2012

March 26th, 2012

Nick Hays

Dhaka, Bandladesh

No prizes here for “most catchy blog title”. However I hope this short article does exactly what it says on the tin.

This topic is an area of some interest to me because although I remain fascinated by the daily movements of markets and short-term trading, I am also an advocate of a conservative, long-term approach to investing.

While both strategies have their merits, my research has led me to conclude that for the average retail investor, the long-term ‘buy-and-forget’, index investment approach is by far the preferred approach.

This assertion will be the subject of an upcoming series which I am in the process of writing. In the meantime, this article examines one variable of the ‘buy-and-hold’ investment strategy: time horizon. In other words, how long the investor commits to locking up his funds.

A common fear amongst retail investors is buying at the ‘wrong’ time, or as I am calling it ‘market mis-timing’. Simply put, we are afraid that we may buy at the top of the market and just as the bull is running out of steam.

This fear is entirely rational when you consider recent history. For example, a buy-and-hold investor who bought the S&P 500 index at the peak of the dotcom bubble in March 2000 would have been sitting on paper loss for the next 7 years, and would still be nursing a negative return even today, 12 years later. That is a compounded annual return of -1.4% (including dividends, but before adjusting for inflation).

However, looked at from a longer-term perspective and the picture appears very different. From 1965-2011 the S&P 500 gave a buy-and-hold investor a compounded annual return of +9.2% (including dividends, before inflation).

The fact is that over the very long term, stocks have historically been a reliable source of positive returns for patient investors who were willing to accept a level of volatility and periods of negative returns.

While past performance is no indicator of future returns, I am a firm believer in the power of mean reversion in data sets that are sufficiently large and long-term in nature.

If we believe that the stock market’s positive trend remains intact over the very long-term, then intuitively we understand that the longer the period we are willing to lock our money up in the market, the less we need to worry about the risk of buying at the ‘wrong’ or ‘right’ time. The logical conclusion of this is that a theoretical ‘infinite’ time period would reduce the risk to the absolute minimum. (In fact it’s an oft-quoted fact that Warren Buffett’s preferred stock holding period is “forever”). Obviously in the real world we cannot entertain an ‘infinite’ holding period - eventually investors want the money back so that they can consume, hence a practical time horizon must be selected.

Put another way, there is a trade-off between, on the one hand, the risk of “market mis-timing” and on the other the time value of money – the opportunity cost of locking up our money for extended periods of time.

In summary, my aim is to quantify and estimate the appropriate minimum holding period for a buy-and-hold index investor. Note the “appropriate minimum holding period” is defined here as the period which adequately reduces the spread of the investor’s expected returns, as measured by the standard deviation. I have used the S&P 500 as an illustrative example, examining holding periods of 1 through 10 years commencing on every trading day within the period 3^rd January 1950 - 5^th March 2012.

The result is in line with what we intuitively know to be true. The below chart shows that the longer the holding period, the less extreme the distribution in potential returns:

As you can see, the standard deviation of returns declines quite gradually between the 4-10 year holding periods. However below 4 years, the volatility increases significantly, at which point the relationship starts to take on an exponential characteristic.

I am quite confident that if I were to examine other broad stock indices, or if I expanded the number of holding periods examined, e.g. between 1 month and 20 years, the pattern would look the same as above.

Using this as a guide, a minimum holding period of 4 years appears to offer a reasonable level of protection from volatility of returns while still being a ‘realistic’ time horizon for the average investor. 4 years is the point on the chart where the curve begins to flatten – that is to say that 4 years is the point of diminishing incremental benefit from longer holding periods.

Longer holding periods obviously offer greater protection, and investors must weight this benefit against the opportunity cost of locking up the money for a longer period.

Expressing the same data another way, the below chart shows the maximum, minimum and average (arithmetic mean) of returns for the same holding periods:

 

The idea for this chart I borrowed from Michael Keppler’s “Risk is not the same as Volatilty”. It neatly illustrates the relative risk/reward profiles of various holding periods.

As you can see, an investor with a time horizon of 1 year could have earned returns of anywhere between -49% and +69%. An investor with a 10 year horizon would have reduced the spread, with the minimum being at -6.5% and the maximum being +18%.

Note however that regardless of the holding period, over the 1950-2012 period the average return is quite consistent, fluctuating only between 8.5% (1 year) and 7.1% (years 4 and 6-10)

The Long and the Short?

Almost by definition, the average retail investor cannot consistently time the market to avoid buying at the ‘wrong time’. If this is accepted, then the average retail investor must accept the unknown risk of whether they are buying at the top of the cycle, the bottom, or somewhere in between.

S&P data from 1950-2012 suggest that an investor with a time horizon of only 1 or 2 years must accept a wide range of potential returns.

To reduce the uncertainty of future returns, the retail investor must extend his minimum holding period, weighing this against the opportunity cost / time value of money. The data indicate a holding period of 4 years as a potentially optimum point in this trade-off, though pin-pointing the actual optimum level would require an assumption to be made on the time value of money.

(Reduced time value of money due to unusually low interest rates - such as those seen today - would push the optimum period further out, as an investor would gladly 'pay' the extra required to reduce the potential return spread).

Riding the rally

March 17th, 2012

Nick Hays

Dhaka, Bangladesh

Today - on The Long and the Short:

* Right on the money?

* Sideline money - returning to the risk game

* Riding the rally

In last week's post I concluded with some words of caution about making any short bets on the S&P 500 index. The price action since then has shown that I was right on the money. Perhaps this was a case of being right for the wrong reasons or perhaps there is something to this technical analysis lark. Either way let's review which of my calls worked and which didn't.

On the short-side, last week I identified a pattern of negative RSI divergence which had been in place since mid-January, and a clear break below the index’s rising channel.  Last week’s chart below:

However I also cautioned that the short-term signals were bullish, in particular when looking at the key Fibonacci levels since the index made an intra-day bottom at around 1340 on Tuesday 6^th March. The chart I showed indicated that the index had quite easily broken through all the key Fibonacci levels:

I pointed out that the next important resistance levels to watch for on the S&P would be at the 100% retrace level (1378) and following that at the rising green trend line.

One week later, and it appears that the levels I identified did indeed prove to be significant.

The short-term chart below shows that 1378 on the S&P provided some initial resistance in early trading on Tuesday 11^th March, with the market ‘gapping up’ on opening and meeting that level almost exactly. After briefly falling back, the market had pushed through this level of resistance by mid-morning.

  

The next target for resistance which I identified, the lower band of the rising channel, also appears to have held some significance for the market, being approximately the level at which the strong rally of Tuesday 13^th was stopped out. This is highlighted in the chart below by the black circle.

Importantly, the lower channel actually provided support to the index on Wednesday 14^th and since then has closed above the lower channel for two days (Thursday 15^th and Friday 16^th). It could be that the index is now re-entering the original trading channel, or a new trend may be forming. Either way what is clear is that the market has shrugged off the recent correction and is looking to push higher.

Another reason to expect further gains in the short-term is that the RSI has bottomed and is now indicating bullish momentum, as highlighted in the chart above.

One call I got completely wrong was on the VIX ‘fear index’. Since last week’s post where I made a case for a spike in volatility on the basis of RSI divergence, the index has fallen 15% and is now trading below the trading channel I originally identified. The VIX is now 16% lower than when I first wrote about it, and 30% below its 1990-2012 average:

The current VIX levels indicate an element of market complacency which gives me some cause for concern. In the medium term, significant economic and political headwinds exist (some of which I identified here and here) and I maintain a bearish outlook within this time horizon.

However, in the short-term I am bullish due to a combination of the S&P technical indicators discussed above and my expectation that risk assets will continue to benefit from the current climate of easy monetary policy and massive liquidity injections by central banks.

"Sideline money"

In addition I anticipate institutional ‘sideline money’ re-entering the market during March and April, providing significant support to the current momentum in equity markets.

The reason I say this is that elevated Eurogeddon tail risk during the past few months has caused many asset managers to shield their client portfolios by going underweight equities and increasing allocations to cash. Their resulting benchmark underperformance means a great deal of pressure for these managers to boost returns during Q2.

With the risk of a ‘disorderly’ Greek default now off the table (at least for the time being), I expect this sideline money to flood back into the market as asset managers seek to get back in the game by loading up on risk. This wave of buying should provide support to the rally and should counter-act any end-of-quarter profit-taking and portfolio re-balancing by the large institutional players.

Riding the rally

There is undeniably a great deal of risk out there, however this is the case for every bull market. Rather than shy away from risk, a successful investor must accept the fact that uncertainty and the unknown are inescapable – they are fundamental characteristics of investing.

In the short-term we should look to ride the rally, remain flexible and be ready to adjust portfolios according to the changing technical and macro picture.

Looking for the downside

March 11th, 2012

Nick Hays

Dhaka, Bangladesh

Today - on The Long and the Short:

* Shot of adrenaline for the markets

* Trading the VIX: approach with extreme caution

* S&P 500 breaking down?

* Monetary freight train

After a couple of weeks of fairly docile trading the market was given a shot of adrenaline this week, once again demonstrating the market’s ability to turn on a dime and catch out all but the most nimble of traders.

Tuesday’s sharp sell-off in equities (driven by a combination of ‘fear-factors’ which I wrote about here) reversed on Wednesday and Thursday, with the S&P 500 up 1.6% and recovering all of Tuesday’s losses as markets priced in the expectation of a positive outcome from the largest sovereign default in history. Friday’s trading saw the index up a further 0.4% up on Friday.

Additionally, the VIX ‘fear index’ has taken a beating, giving up all its Tuesday gains and suggesting that I may have been too soon in identifying a possible breakout here.

Last week is a perfect example of how dangerous it can be trading for the short-term if you don’t adequately manage your risk. This is even more to important to remember in the case of the VIX, as it essentially acts like a leveraged inverse bet on the S&P 500 – hence it can be useful as a hedge but timing it wrong will not look pretty. Case in point, during the past 5 trading days the VIX spiked 21% and then swiftly tanked 19%. Get caught on the wrong side of that trade and you are liable to have “your face ripped off” as the saying goes. (The VIX is now about 1% lower than when I first wrote about it in on February 24th)

The possible VIX breakout I identified was premature, and turns out to have been a so-called ‘head fake’. This is a good lesson – with hindsight I underestimated the significance of the 20.5-21 level on the VIX, which has been an area of significant support and resistance during the past 3 months. Had the index broken through this range then a break-out could have had legs. Chart below:

Despite last week’s trading, I am still watching for a concerted move higher by the VIX. One reason for this is something called ‘negative divergence’ and I’ve highlighted this in the lower section of the chart above. The RSI (or Relative Strength Index) is a measure of momentum, comparing the number and strength of ‘up days’ against the number and strength of ‘down days’ for any given stock or index during the previous ‘X’ number of days. It’s not rocket science.

Traders often watch for ‘divergence’ between the stock’s pricing movements and the RSI – that is to say if the stock is moving in one direction but the RSI is moving in the other. Some take this as an indicator that the market may be about to turn. If a stock or index is moving up but the RSI is moving down, this can be seen as evidence that the rally is running out of steam - this is called ‘negative divergence’. Conversely, if a stock is trending down but the RSI is heading up, it can be an indicator that the sell off may be overdone and is approaching a turning point. This is called – can you guess – ‘positive divergence’.

The VIX has been showing fairly strong positive divergence since December 2011, indicating that we could be reaching an inflection point at which the VIX makes a sustained move higher. (Note: the RSI is just one indicator - it’s very important not to rely on any single indicator, but to use multiple indicators to help you trade. I’ll be writing about other indicators as I come to them in later posts.)

While on the topic of the RSI, the S&P 500 is also showing a good example of divergence and this is one reason I’ll be watching this chart closely in the coming weeks, and keeping an eye out for possible pull-backs. Chart below:

  

As you can see from the above chart, since late December the S&P 500 has been trading upwards in a fairly obvious channel, as shown by the green lines. This channel has provided strong support and resistance at various points which I’ve indicated on the chart with the green and red arrows. (The non-filled arrows I’ve indicated are less convincing as support and resistance, because they do not quite touch the trend lines).

Two observations on the S&P: firstly, recent trading has seen the S&P break down below the support level of the trend line, eventually finding support at the 1340 level, a price which also held up the S&P on two earlier occasions in mid-February (shown by the thick red line).

Secondly, since the back end of January the RSI (bottom part of chart) has been trending downwards- this is an example of negative divergence and suggests the S&P rally may be getting old.

However as mentioned it's vital to use multiple indicators against which to test your theory. Another indicator I'm watching suggests some caution before betting on a decline in the S&P. Below is a chart of minute-by-minute S&P 500 data during the past 10 trading days, showing the correction from the intra-day high on Wednesday 29^th February to the low on Tuesday 6^th March:

The dotted red lines overlayed on the chart show the key Fibonacci retracement levels of 23.6%, 38.2%, 50.0% and 61.8%. More on Fibonacci in a later post but suffice to say many traders view these levels to be highly significant and closely watch how the market responds at these potential resistance and support lines.

As you can see in the above chart, the index encountered some resistance at Fibonacci retracement levels 38.2% and 61.8% (shown in the arrows above) but has since cleared these key levels with some ease. To me this suggests we should be very cautious before entering into any aggressive ‘short’ positions at this stage.

Monetary Freight Train

There's plenty of risk out there - as highlighted here and here - and signs that we could be overdue a more protracted correction.  I’ll be watching the S&P 500 for resistance at the 100% Fibonacci level of 1378. Above that, the lower band of the green trading channel I identified could become the next significant point of resistance.

However it pays to remain flexible and never become fixated on one point of view. This market continues to surprise on the upside and betting against the trend is dangerous. It’s become fashionable of late to question the current rally, and much of the financial media is calling for a correction – this in itself makes the contrarian in me cautious about betting on a sell-off.

It's important to understand that in large part the current rally is a product of the huge amounts of liquidity and ‘free money’ that is being injected into the banking system by the Fed, ECB, BoE et al. The scale of what is going on right now in central banks around the western world is absolutely unprecedented and getting on the wrong side of this monetary freight train could be extremely hazardous to your health.

“Eurogeddon” averted or just more can-kicking?

March 9th, 2012

Nick Hays

Dhaka, Bangladesh

Today - on The Long and the Short:

* Largest sovereign default in history confirmed: "Uncharted territory"

* “Eurogeddon” averted? Or just more can-kicking?

* The law of unintended consequences

* “No way out”

Tuesday’s sharp sell-off in equities, driven by a combination of ‘fear-factors’ which I wrote about here, reversed on Wednesday and Thursday, with the S&P 500 up 1.6% during those two trading sessions, recovering all of Tuesday’s losses in the process. 

In the same time frame the VIX ‘fear index’ has taken a solid beating, giving up all its Tuesday gains and suggesting that I may have been too soon in identifying a possible breakout. (I will be writing more about the VIX and S&P 500 in my next post.)

News flow out of Europe has been the dominant driver behind the price movements during the last couple of days, with fears of a disorderly default in Greece receding as negotiations for the PSI (Private Sector Involvement) reach a  conclusion. The PSI involves holders of E206bn in Greek government debt agreeing to trade in their existing bonds for newly issued ones of lower value. This write-down, or “hair cut”, equates to a loss of over 70% in Net Present Value terms for the bond holders.

Today it was confirmed that investors holding 83% of holders of Greek government debt have accepted the proposed bond swap. This beats the 75% below which the deal would have failed, triggering a disorderly default and likely financial chaos across the Eurozone.

The largest ever sovereign debt default, and the first for a Western European country in 50 years, this is huge news and analyst commentary on the deal is pouring in. The short-term market reaction is likely to be one of mild relief. However the longer-term picture remains far from certain and I expect it will not be long before doubts begin to resurface – to be sure, this has been the cycle for at least the past 12 months.

What comes next is very much up for debate as, in the words of Berenberg Bank’s Chief Economist, “We are in uncharted territory”.

Eurogeddon averted? Or just more can-kicking?

The aim of the debt deal is to reduce Greece’s sovereign debt burden from more than 165% of GDP to a more manageable level. Best-case scenarios project this deal will set Greece on track to reduce its debt levels to 120.5% of GDP, just above the maximum threshold of 120% considered sustainable by the IMF.

Longer term, however, considerable risk remains that this deal is little more than the latest in a series of can-kicking exercises, simply buying more time before the next crisis inevitably rears its ugly head. In fact the IMF itself sees Greece’s debt to GDP ratio on an “ever-increasing trajectory” and much doubt remains as to whether the debt burden can be reduced in the long-term. In fact, the new bonds are already trading at steep discounts to face value, indicating that the market still does not expect Greece to be able to pay back in full. 

The severe austerity measures ongoing in Greece are a painful but necessary step towards debt reduction for the country; but most economists agree that these measures must be accompanied by much-needed market reforms to improve its trade competitiveness. Deprived of the option to de-value its currency (aside from the ‘nuclear’ Euro-exit option) Greek competitiveness will have to be restored through a combination of a painful reduction in wages (making Greek exports more attractive) and removing the market-unfriendly policies and red-tape which currently throttle the private sector.

The scale of the reform required and the difficulty to implement it should not be underestimated. In this respect, Greece is like a patient requiring double heart bypass surgery, a lung and kidney transplant and chemotherapy all at once. Carrying out the necessary treatment to get Greece back on its feet undoubtedly means a lot more pain ahead for the country and its people: expect to see more urban violence, tyre-burning and pitched battles with riot police in the months ahead.

Street thuggery aside, the upcoming elections in May will provide a more constructive outlet for the Greek electorate to voice its frustration - and perhaps to vote in a new government on the back of promises to 'ease the pain'. This could mean scaling back on austerity measures, further debt default, a Eurozone exit or all three.

The road ahead for Greece will not be free of challenges, that much is clear, and the market’s relief resulting from the debt resolution will probably not last long. In fact I believe the deal itself sets a dangerous precedent and may result in a number of unintended consequences.

Unintended Consequences

Risk 1: Greek debt deal may encourage other sovereigns to follow the same path.

If Greece can reduce its debt burden by imposing a 'voluntary' default on its creditors, what is to say other nations won't also look to this approach? The other PIIGS nations - Portugal, Italy, Ireland and Spain - may well calculate default to be a more politically acceptable route to debt reduction than the programme of grinding austerity measures to which they have currently subscribed.

Anticipating this, credit markets would demand higher yields to compensate for the additional risk of default. Higher yields make the governments’ debt harder to service, with more and more output being consumed by interest payments. Hence their fiscal position becomes less sustainable and this in turn makes default all the more likely - a downwards spiral ensues.

Risk 2: Greek deal undermines the value of CDSs (Credit Default Swaps)

CDSs are essentially insurance premiums which investors and speculators can purchase to profit from a default on the debt obligations of a corporation or a government. One key difference between a CDS and an ordinary insurance premium is that you don’t have to own the underlying asset in order to buy the CDS – an analogy would be insuring a house against fire damage when you don’t actually own the house.

CDSs are economically useful because they enable bond investors to hedge their exposure, with the aim of reducing their overall risk. This ability to hedge their position and reduce risk makes investors more willing to invest in the bonds in the first place – all else equal, this increases demand, raising the bond prices and reducing the yield (yields go down as bond prices go up). The corollary of this is obvious: undercut the value of sovereign CDS and you raise the yields on government debt. When this happens, governments find it more expensive to raise capital or to roll-over maturing debt.

This is exactly the risk facing us today. Let me explain.

For all the talk of this being a "voluntary" write-down, the reality is that the private sector has been strong-armed into the deal, and was left with little choice but to take it. The message from the Greek Finance Ministry essentially boiled down to, "it's this or nothing": in other words, either everyone takes the "voluntary" PSI deal now or we proceed with an outright default and you get nothing.

The short-term consequences of an outright disorderly default would have been nothing short of catastrophic, certainly dwarfing any hedging gains from CDS payouts. Hence it should probably come as no surprise that today’s debt deal demonstrates the fact that Greek bondholders (on aggregate) have calculated that a 70% "voluntary" haircut and no CDS pay-out is preferable to a 100%  disorderly cut with a CDS payout.

But to call this "voluntary" is stretching the definition. The decision facing bondholders was like a man being given a choice between being hit by a car or by a freight train. Pausing for just a moment, the man responds, “Neither option sounds good to me, but on balance I'll take my chances and go with the first one...”

Essentially bondholders have not been given a choice at all. And what is more, in the process of accepting the "voluntary" default, bondholders may have surrendered their rights to any CDS payouts.

Whether to pay out on CDSs or not is the subject of discussion at an ISDA meeting (International Swaps and Derivatives Association) this afternoon. The committee (made up entirely of investment banks  and asset managers) requires a super majority (12 out of 15) to make a ruling. However regardless of the outcome of that meeting, the mere existence of doubt as to whether CDS payouts should or should not  be made in itself trashes the value of that instrument as a future hedge. To re-use the analogy, why waste your money insuring your house against fire when you expect the insurance firm will wriggle out of its obligation?

By undermining the value of default insurance (and all else remaining equal) bond yields will rise as traders price in the higher risk associated with holding a position which cannot be directly hedged. This has the potential to lead us to the same downwards spiral which I highlighted in Risk 1.

The long and the short of it?

Any relief rally associated with the Greek deal will be short-lived as questions of the country’s fiscal position resurface and investors begin to get to grips with the longer-term implications of today’s events.

Odds-on bet: we have not seen the last of easy monetary policy from central banks worldwide and we are likely to see a lot more of this in future. Governments and investors alike have become addicted to liquidity courtesy of the Fed, ECB, BoE and BoJ and, like an addiction, each time a bigger ‘hit’ is needed to have the same effect. As the Wall Street Journal wrote on 27^th February:

“All of the available signals point to the likelihood that the Fed will have to turn to more vigorous creation of new money (inflation) at some point—or face the possibility of rising market rates on government securities that sharply raise the Treasury's borrowing costs and devalue the Fed's enormous balance sheet.

No way out. No way out.”

EDIT:
Related Bloomberg article:
 “The rules have been changed here,” Gross, co-chief investment officer at Pimco, said in a radio interview on “Bloomberg Surveillance” with Tom Keen and Ken Prewitt. “The sanctity of their contracts is certainly lessened. Bondholders have that to look forward to going into the future.”

 

Fear Returns

March 7th, 2012

Nick Hays

Dhaka, Bangladesh

Today - on The Long and the Short:

* Fear returns

* VIX break-out?

Major stock indices took a nose dive yesterday while the VIX “fear index” spiked over 15% during the biggest one day equities sell off of 2012 to date.

After two weeks of relatively calm and flat trading, some of the risks I identified in my earlier post here appear to have bubbled to the surface. Amongst them are renewed doubts regarding the finalization of the Greek debt deal, the increased probability of slower Chinese economic growth in future, and signs that the Fed will press "pause" on any further monetary easing for the time being.

Whether this is the start of a larger correction or not remains to be seen. What is clear to me is that risk had been significantly under priced and yesterday was a much needed splash of cold water on the markets.

What is more, one chart that I'm watching closely is indicating that things could be about to get worse:

As you can see in the above chart, since late December the VIX has been trading in a downwards sloping channel, indicated by the red lines. Technical analysts use charts to work out possible areas of ‘resistance’ and ‘support’ for prices. The trading channel I’ve identified is not perfect but yesterday’s price action on the VIX may suggest that it has broken out of this channel and is poised to go higher. Given the negative correlation between the VIX and risky assets such as stocks, a spike in the VIX would point to lower prices for the major indices.

Much will depend on the outcome of this week’s Greek PSI (Private Sector Involvement) negotiation. The Iran situation also remains very much a wildcard event with the ability to send major shockwaves through the markets. Recent Obama rhetoric in my view has increased the probability of an escalation in the Middle East. (Interestingly from a local perspective here in Dhaka, a Saudi diplomat was shot dead at close range yesterday in my neighbourhood - perhaps inevitably, media speculation of an "Iran connection" is rife.)

Very interesting times indeed, let’s keep watching…