July 18, 2005
Skews and Smiles
Suppose that you had good evidence that there was a 70% chance that the market will be higher, say, 5 weeks from today. Would that evidence be sufficient to warrant an exposure to stock market risk?
The answer is that you need more information. If, for example, the average potential gain is 3%, but the average potential loss (with just a 30% probability) is -8%, then the expected return is actually negative (.7 x 3% + .3 x -8% = -0.3%). A risk-averse investor would walk away.
Still, many investors would be uncomfortable in a defensive position. Even though their overall expected return from market risk is negative, there's only a 30% chance they'll be disappointed if they take that market risk, but a 70% chance they'll be disappointed if they don't. So investors might take the risk anyway. For those investors, comfort and avoidance of short-term frustration may be more important than expected returns or risk management.
In statistics, the returns above would be described as a “skewed distribution.” If a normal distribution looks like a symmetrical bell, a skewed distribution looks lopsided, with one tail longer than the other. A bell can also have fat tails on both sides and a thinner middle, which is called “kurtosis.”
Sure, investors might say, but that's just theory. In most cases the distribution of stock returns is very symmetrical, right? Wrong. The further the market gets away from normal valuations – especially when it's overbought, the more the distribution of future expected returns tends to skew. You get a high probability of small further gains, coupled with a small but above “normal” probability of damaging losses.
You can actually observe this in the way that options are priced. Most option pricing models, such as Black Scholes, assume that the probability distribution of stock returns is a nice, symmetrical bell. The width or “standard deviation” of the bell is determined by expected market volatility. For S&P 500 options you can currently look up the volatility that's priced into the options using the ticker symbol VIX (it's currently 10.33%, which is an extremely depressed level indicating that investors have little concern about market fluctuations here).
In theory, you should be able to pop 10.33% into an option price formula today, and be able to accurately price S&P 500 options regardless of their strike prices. Problem is, if you actually try, you'll find that 10.33% only works well for at-the-money options. Actual option prices for below-the-market strike prices are much higher than what the formula suggests, and actual option prices for above-the-market strike prices are much lower than what the formula suggests.
Stated another way, implied volatilities are unusually high for low-strike options, and very low for high-strike options. Normally, the pattern of implied volatilities is shaped like a “U,” which option traders know as a “volatility smile.” It's presently a steep diagonal line, and none too happy about it.
Does that mean that S&P 500 options are mispriced here? No, it just means that investors, as a whole, don't believe that the future distribution of stock returns is nice and symmetrical. If you do the math (which is so tedious that I wish it on nobody), you'll find that market participants expect a very high probability of relatively small gains, a far below “normal” probability of large gains, and a small but above “normal” probability of very negative returns.
[Geeks note: In a fat-tailed or kurtotic distribution, you get a big, happy looking volatility smile because you've put value into extreme strikes both above and below the market. In a skewed distribution, you're putting probability into the negative tail but not the positive one, which forces the market to load a whole lot of the weight on relatively small gains in order to preserve arbitrage relationships. A hard skew shows up clearly in the graph above.]
Hot Potato and Musical Chairs
The skew implied by options prices suggests the sort of considerations that investors should have at present. With valuations very rich, bullish sentiment high, and stocks generally overbought, there's a certain momentum to the market that makes it likely – in terms of probability – that stocks will be higher in the weeks ahead. Unfortunately, there's a small probability of some real damage, and that's what keeps us defensive.
Being defensive isn't the most comfortable position, of course, because most probably we'll be disappointed to miss some amount of gains in the market. But that small probability of a large loss matters here, particularly because as I've noted in numerous weekly comments, whatever gains that the market generates at this point are unlikely to be durable. A moderate market decline without much internal damage might make it reasonable to accept a limited amount of market risk, but given the market's present overbought condition, it makes sense to tread lightly here.
If you listen to the tenor of investment strategists here, the basic message sounds a lot like what we heard in the late 1990's: stocks may not be priced to deliver strong returns on a sustained basis, and there are substantial risks in the longer-term picture, but for now, things seem to be going well and so there's no need to be defensive just yet.
Famous last words: The light's still yellow. Punch it.
Essentially, investors are playing hot potato and musical chairs here. Smelling smoke in the crowded theatre, but with the aisles still fairly empty, not willing to miss any of the show until somebody yells fire. It's a dangerous game.
But again, there's a pretty good probability that they'll be right for a while. For our part, it's that smaller probability that matters here.
As of last week, the Market Climate for stocks remained characterized by unusually unfavorable valuations, but market action has improved to a nearly neutral condition. There isn't substantial evidence that investors are skittish here, or that there are meaningful upward pressures on risk premiums. For that reason, as noted above, a moderate market decline would present some opportunity to establish a limited exposure to market risk, provided that internals such as breadth, leadership, credit spreads, and so forth didn't materially deteriorate.
At present, the tradeoff between expected return and risk continues to be unsatisfactory. It is, however, skewed, so it's not possible to say that a market decline is the most “probable” outcome. My hope is that the distinction between probabilities on one hand, and expected returns on the other, are relatively clear from the discussion above. The most probable outcome can be a small gain, even if the expected return is negative.
Even though the S&P 500 is less than 3 points above its March peak, and the index remains lower than its level of 5 years ago, and has underperformed T-bills for the past 7 years, I realize that the chatter about “4 year highs” can make it seem frustrating that the Strategic Growth Fund is well hedged here. That's especially true if investors choose unrepresentative trough-to-peak periods on which to evaluate investment performance, rather than the peak-to-peak comparisons which are relevant to long-term investors.
Since my impression is that the Fund continues to nicely achieve its objectives, it's important that shareholders remember that those objectives focus on achieving strong absolute and risk-adjusted returns over the complete market cycle (i.e. peak-to-peak, bull markets and bear markets combined). I recognize that marginal new highs have a feel of excitement to them that beckons investors to “come and play.” But I really do believe that investors ought to buy low and sell high, on average, and that discipline in that attempt is worthwhile in the long run.
In bonds, the Market Climate remains characterized by moderately unfavorable valuations and nearly neutral market action. The jump in bond yields last week provided a small opportunity to increase the duration of the Strategic Total Return Fund, which is now at about 2.4 years – still low, but nibbling slightly on bond price weakness. The Fund continues to hold about 20% of assets in precious metals shares, which remain the dominant source of day-to-day fluctuation in the Fund.
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