Conventional risk measurement metrics fail to tell us anything about the probability of loss. Most departments will say that’s not their job but if it could be measured it would add an element to that analysis that would be invaluable to senior management. To do this, we need to have confidence in a method that accounts for all the possible forces involved. This may be ambitious but let me show you how I can do it for the S&P 500.

The S&P in the short term is not really driven by supply and demand conditions since those change only slowly as a function of earnings, long term investor preferences, global political and economic conditions, commodity price behavior etc. In the short term, we have fewer variables and number one among them is sentiment. Allow me to quote an old (2002) study: “Excess returns are contemporaneously positively correlated with shifts in sentiment. Moreover, the magnitude of bullish (bearish) changes in sentiment leads to downward (upward) revisions in volatility and higher (lower) future excess returns.”

If fear of loss is high, then prospective returns are high. Risk measurement will fail to distinguish between the “risk” in a long position of S&P 500 futures on December 24 and that same position on January 20 but the price was 10% lower and Vix had spiked up, from 15.74 to 27.59. Every hedge fund manager should look more favorably on that position in January than they did in December.

Calculating Energy Under Normal Conditions

What we need is a variable or index that tells us something about the risk of loss. To work, it must take into account all the key factors that drive the S&P in a one- to four-week horizon. They are:

1. The level of fear;

2. The time since we last suffered through trauma;

3. Bond momentum.

To put it simply, if we have just undergone market trauma so fear is high and bonds have been rallying, then the risk of loss is very low. The further we get away from “the episode” and the lower fear (Vix) is, the worse our prospects are for making money in a long ES position. At that point, all we can hope for is a bond rally. I honestly don’t think there is another important factor. (Please call me if you think of one.) There is virtually no such thing as a fearless non-interest rate driven S&P rally of consequence. On the other hand, we should be very nervous if Vix is low and bonds are lifeless.

The Bear Market Case

Fear as indicated by Vix can spike to unpredictable levels and can stay high thereby defeating our efforts to fade it. The problem stems from the distribution and boundaries of Vix. The solution is to replicate it with a better function (“SynVix”) that gives us more signals and where constrained boundaries are harder to break. This helps us differentiate between a pullback and a bear market (See Managing and Trading Risk). We certainly may end up with a low risk reading that arrives too early or gets changed the next day as this figure comes undone. Similarly, our bear market indicator will, at some point, clear a hurdle and we will be in bull market mode so again, the indicator will swing somewhat violently. These swings are rare, necessary and unavoidable.

Look-backs and Durability

To be confident that the approach is durable we must have internal variables that are not too back-fitted to suit the last (say) 10 years. Here are some of those settings:

1. My synthetic version of Vix (“SynVix”) uses the same look back period as Vix (20 days).

2. My bond momentum length is set at 10 days and does not vary.

3. My bear market test is based on a 10-day average of SynVix.

The only art to this is the use of normalization exponents to match up the volatility of the different components so that the weights are balanced. None of those meaningfully change the nature of the calculation. In the end, if you follow the (S&P 500) market, you will already have a feel for these inputs and you will frequently be able to anticipate the level of the index.

When Will This Fail?

The worst case for this approach is a huge bear market rally. Let’s say it is October 2008 and the market is a mess or it’s 9/11 and the markets are closed. They continue to descend and you are comfortably situated (since my index has told you to stay away — buy signals are very limited). At some point, bearish sentiment will peak and this method will not pick the bottom. It’s not that clever. If a manager argues that the low has been set and he wants to buy everything in sight, then I cannot assert that he will be wrong. Market bottoms occur at all levels of Vix and waiting for a reversal in its trend is a dubious approach.

I made a decision to be cautious rather than aggressive when it came to handling meltdowns. If this index keeps you out of a meltdown, then your ability to outperform everyone will be guaranteed. Similarly, there will be times when the S&P will rally even though sentiment is bullish and bonds are dead. All my data shows that you don’t need to be in those rallies to make money or beat the market. I will help you time your next vacation. Getting in a little late will do.

The other risk here is that the index may get what it wants after a “significant” correction but that weakness continues for several more days after the first buy indication. I can’t guarantee a buy signal on the low day. I am simply trying to show you when your risk has fallen so you should continue to hold or accumulate more, until or unless the bear market trigger goes off.

The Index

I end up with two components that matter:

1. The level of volatility adjusted Fear;

2. Vol. adjusted (Bond + Stock Momentum) * the inverse of the number of days since the last bout of trauma.

Both contribute something different but we can easily imagine when they will not be truly independent. When fear rises, bonds rally, but when they diverge that is information that can make a huge difference to our prospective gains.

Time Frame Use

This is not an effort to provide you with a long term indicator particularly suited to measure the probability of a severe crash. The fact is, I don’t know when a correction will be 3%, 10% or 30%. I have to be prepared for any of them and I have to take advantage of all of them to make money. If I wait for a huge pullback to get long, I may/will miss a significant rally since many long and large rallies happen without any major correction. I have tried to look at correction size and length as a variable for the scale of the ensuing rally but the relationship is too unstable (variable). This solution allows me to participate in most rallies and miss (most) meltdowns.

Other Uses

If you have this index, then it would be logical to consider it when you put on S&P 500 correlated positions. Similarly, it should lead you away from bonds since a buy level in equities usually means bonds will struggle, at least in the short term. It should also tell you when to reduce exposure to markets where (S&P) beta tends to rise during stressful periods, such as Emerging Market equities. In fact, I could construct the entire structure of a hedge fund portfolio by looking at this index along with some relative value analysis.

I have done this strategy work and am happy to share its properties and manage assets on this basis.

Quantitative Evidence

I have another essay that goes through these time series and examines their nature and the return outcomes of S&P futures as a function of various threshold settings. You can see the volatility of the indices and judge whether it is too high or too low for your use. Understanding the sub-components and agreeing with the methodology is critical.

I shall be as transparent as I can be.