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I've recently finished “Investment Gurus” by Peter Tanous, where he interviews various money managers who had long-term hot hands as of about 1996. One of the interviews was with David Shaw, the legendary quant and founder of D. E. Shaw & Co. As far as investing insights, it was one of the least informative interviews because everything Shaw does is proprietary and he wouldn't even give annual performance numbers.

But he seemed to let something slip during the interview when he was explaining how his firm spends enormous money to recruit only the brightest people. He threw out an example of finding the world's top expert in Bayesian statistics. “What is Bayesian statistics?” Tanous asked. Shaw gives an answer, but it seems as if he's trying to get off the subject as smoothly as he can. And my ears perked way up.

In a nutshell, Bayesian statistics involves using prior information to help make better predictive models. According to efficient market theory, right now there should be an equal chance of the market going up versus the market going down, because the market price is determined where sellers' pessimism equals buyers' optimism (greatly simplified, I know). But a Bayesian might say, “Well, the market certainly could go up or down from here, but 5 out of 5 times in the last 5 years when the VIX has been above 40 the market has had a tradeable 10% rally in the next 1-3 months, so I think the market now has a > 80% likelihood of going up.” So the Bayesian would buy, based on information available from the prior sample. And then, based on the outcome of his trade, he would subtlety alter his probabilities prior to his next > 40 VIX trade.

http://bigcharts.marketwatch.com/quickchart/quickchart.asp?symb=vix&sid=0&o_symb=vix&freq=2&time=12

A common dilemma for folks not buying into the “all equities, all the time” mantra is deciding on an appropriate asset allocation, and whether that allocation is going to be fixed (e.g. 70% stocks, 30% bonds) or mutable (e.g. 30-70% stocks, 70-30% bonds, depending on price/value considerations). If you're going to go the tactical route, you need to have a mental model of how and when to alter your allocation.

A simple example would be to use the Fed model (i.e., earnings yield of the S&P divided by interest yield on a 10-yr treasury). Ed Yardeni is back online with his version, which uses consensus forward predictions of SPX earnings. I prefer trailing earnings myself. And if I had access to historical data on investment grade corporate debt, I'd rather use that as a hurdle, but you can simply add 100 or 150 bp to T-bonds as an approximation of that. But regardless, some variant of the Fed model could provide you with your priors.

Yardeni (p. 6): http://205.232.165.149/public/val.pdf
Valuation Model  Asset Allocation (see also page 5 of Yardeni link)
Stocks + 2 SD = 30% stocks, 70% bonds
Stocks + 1 SD = 40/60
Stocks at par = 50/50
Stocks – 1 SD = 60/40
Stocks – 2 SD = 70/30

One problem with this approach is that during volatile times you'd be rebalancing way too often. But if you were working with Vanguard's S&P 500 Index and Total Bond Index inside a 401(k), you might content yourself with annual, or perhaps semiannual rebalancing. And you could adopt an additional decision rule to help minimize whipsaws: following a rebalancing there will be no additional rebalancing for at least 6 or 12 months.

In a margin account, I'd be tempted to add volatility (VIX) as an additional parameter. The current combination of falling prices and high VIX would favor rebalancing to stocks, and the medium of rebalancing could be SPX options. If you're sitting at 60/40 right now by the above model, you could sell enough Sept 800 puts for $27 to take you to 70/30 if and only if the market drops below 800 by Sept OE. If the threshold to take you to 50/50 stocks is SPX = 950, then you could also sell the 950 calls for $7.50 (it's not much, but it's “free money” and it forces you to make your rebalancing decision). If nothing happens by Sept OE, you could recalculate the up and down benchmarks for Dec OE and sell the appropriate puts and calls outright. Or you could sell the puts or calls only if they provided a threshold level of return (i.e., you wouldn't sell a 10% stake in your portfolio for a $7.50 premium as above, but your minimum option price might be $20 and that could be a limit order).

What I'm looking for is a mechanical, but statistically justified, method for reallocating capital at times when turmoil makes it difficult to make the right decisions. In Jimi's case, this might be a means that would get him to take the plunge with equities right now. In my case, it's a method that might keep me from going 150% in equities right now (i.e. buying the farm, and buying 50% more of it on margin too).

This example is a bit simplistic, but I think it has to be simple to work. A two, or at most 3 factor model is probably as much as Occam's razor is going to allow here. The Fed Model is 2 factor (P/E of the SPX, 10-yr bond yield) and throwing in option premiums (i.e. VIX) takes it to a 3 parameter model. Any more parameters than that greatly increases the risk of overfitting to historical data.

I'm thinking of doing something like this with my yet to be launched 401(k). And I've still got plenty of time to work out the kinks. I'd be interested in what anybody else thinks about tactical asset allocation.

Todd
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