Sunday, March 20, 2016

Historical Statistical Handicapping

Any financial market can be approached similar to how an insurance company might approach their payouts. Each trend has a particularly amount of days you expect it to last, and aside from general statistical baselines, there are other risk factors that determine the health of the market that may indicate whether it is likely to outlast the historical norm or not.

Say for example, an average price move in the month of April over the past 20 years is 2.1%. If the markets have already gained 2.1%, you may have approximately 50% of outcomes that outperform this and you'd expect to continue higher, and 50% of outcomes that you expect would continue lower. While you might account for the risk that the downside is worse than has occurred historically, as well as the statistical expected value, and weigh many other factors, you can start with 50% chance as a baseline and adjust from there.

If you establish maximum bullishness and minimum bullishness, you might weight the odds according to the data. For example, if on a risk adjusted basis you suspected about a 45% chance of an equal move upwards as downwards, and your maximum risk was 100% and minimum was 0%, you might position in 45% stocks, and 55% cash. Of the stocks you deploy, you would focus on groups you expect to outperform.

By using historical handicapping, and a disciplined approach, you more often than not will avoid being very long near highs like most people do.

There are many metrics to historically measure a move vs other outcomes.
1)Monthly seasonal data
2)Election cycle annual data
3)10 year cycle data (the years 1966,1976,1986,1996,2006,2016 would compare to each other as the 6th year of a 10 year cycle for example)
4)Peak to trough duration and magnitude statistical analysis.
5)1-2-3 Trend reversal vs markets

Once you can assess the probability that the move continues higher and use that data in concert with your targets and stops, you can define the risk and reward of the move and estimate probability. This will give you an edge which can be measured through the use of a "Kelly criterion calculator" to assess the edge on a risk adjusted basis to other markets at the time.

Although the Kelly Criterion advocates risking way too much for normal individuals, it can still be useful on a comparative basis to other decisions. For those that understand how to fractionally adjust from that risk (depending on certainty of data and individual risk factors), you can use it to maximize your gains at a defined risk, or weight your total risk allocation according to your defined edge.

Since options market has a time duration, a clearly defined cost, and an upside defined by price movement, if you had all of the available data on market movement, knew the cost, and could calculate the intrinsic value gain, this sort of analysis would be extremely helpful for trading options on the broad market index funds. You could use those same kelly criterion calculators to calculate the long term expected growth at one full Kelly bet at each strike price. You could then choose the strike price that represents the best return with an equal amount of long term risk.

Unfortunately, some of this could be skewed by the extremes. For example, with 100 data points, the top performance represents a 1% of a happening. If that performance was high enough, betting on strike prices very far out of the money may be most profitable. However, that single data point could easily be much more likely or much less likely than 1% to occur, and the average top 1% of performances in the future could be much better or much worse than that single data point.

So if you use options, you probably should stick to the strike prices nearest to the money, or at least bet with the understanding that the farther out of the money you go, the less reliable historical data is.

While the baseline data is very useful, you have to put it in context with a variety of factors. If the average lifespan of a US male is 80 and a person is 40, you may expect them to live 40 years +/- the margin of error. However, if the person is 80, he's already proven he's not one of the individuals to die from 0-80, so the odds of him being an outlier may go up slightly. The expectation for someone who is 80 with a clean bill of health might be 85 or 90.

Unfortunately with the market, the greater the upside move without a pullback, traditionally the more steep the decline has the potential to be. Take 1920-1929 for example and 1929-1932 that followed. Unlike an insurance company, the payout to the individual that dies is fixed, while the risk if a decline begins is somewhat undefined.

You would have to instead measure the birth of a bear market, and the duration and magnitude. If the bear market starts here, how long does it last, and what is the loss if you are long until your exit conditions are met? If the bull continues, what is the gain? And what is the probability of each outcome?

This gives you the ability to handicap the move, apply an upside, and a downside and the probability of each and use the Kelly criterion to provide an allocation. You can use sites like multpl.com to look at historical prices by month or year dating back to the 1800s.

http://www.multpl.com/s-p-500-historical-prices/table/by-year

You can then use tools like Microsoft excel or open office. You can measure highs and lows over specific holding periods or from lows to highs and so on. You can also use charting software like thinkorswim's platform (TD ameritrade) and measure peak to trough or trends following a particular signal. Each measurement can be given a weighting.

----------------------------------
Of course up until now we have only discussed handicapping a market as a whole such as stocks. We haven't uncovered measuring ratios from one market to another, valuation metrics, valuation metrics from one market to another, and submarkets (sectors), or subsectors (industries) or even individual stocks. But you certainly can try to handicap these as well and make individual stock bets. That can be done as well.

Wednesday, March 9, 2016

The Allocation System

This portfolio aims to be very flexible, but as a baseline, fit theoretically equilibrium/optimal conditions according to game theory or "game theory optimal". When you are more bullish, you can shift to greater than 50% "risk on" assets, when you are more bearish you can shift to a greater than 50% "risk off" assets. When your trading edge is superior, you can increase the short and long term trade allocations.

Additionally, it also should provide the flexibility to integrate your skill and handicapping abilities to at times deviate from the baseline substantially in order to game" the market or "exploit" conditions that will provide you with an edge.

10% income is the only permanently fixed asset allocation with few exceptions. They will be mentioned later. The idea is that it's unlikely that you will need access to all of your cash and eventually as you need more, the income will convert into cash to grow the cash position as you need it. That should reduce the number of trades for rebalancing that needs to be done and makes maintaining your intended allocation a little bit more, and also gets a little value out of the cash by putting it to work for you.

10% cash minimum will allow you to mitigate risks and provide emergency capital in the event that a once in a lifetime deal is available while you may sell something else and wait for the funds to clear or whatever.

0-50% XIV allocation with SPY LEAP put pairing. The potential for a really aggressive allocation is made possible by buying SPY LEAP puts when volatility is cheap to mitigate the unlikely disaster as well as hedging capital also used on hedges.

The XIV is used for several reasons. It's structural edge (drifts higher for opposite reasons that VXX drifts lower), it's correlation to the market, and more importantly when volatility is high there are few individual trades for your cash to go to, so to maintain "risk on" targets, you have to add something and XIV is the perfect purchase when the VIX spikes. In rare circumstances, TNA may be substituted for XIV.

SBCC allocation -stocks, bonds, commodities, currency will make up somewhere between 20-40% of allocation generally. Baseline of 5% of each asset when XIV allocation is high and/or uncertainty is low to 10% when uncertainty is high and/or XIV position is high. 15% is possible when trading conditions are tough at the expense of the intended balance between stock allocation, hedging capital, short term and long term trading.

SBCC allocation may shift between various stock related instruments such as using birkshire hathaway as stock allocation or focusing on a sector specific SPDR ETF like XLK. Bonds can be composed of US treasuries, municipals, corporate, emerging market bonds, etc. Commodities can be composed of base metals, agricultural commodities, energy commodities and softs, or can get more specific such as Silver (SLV), gold (GLD) or oil (USO) or natural gas (UNG) or coffee (JO). But general aim is this portion of portfolio on it's own matches equilibrium condition and gains from volatility rather than ability to pick stocks so when you're off you're game it still produces wins.

Long term trade, short term trade, and hedges/hedging capital should all roughly match each other in 'normal' conditions as well as the stock allocation at the time. I tend to believe market is neither in equilibrium, nor random, so I tend to aim for slightly higher allocations towards short and long term trades than in allocation, and hedges tend to be conditionally dependent. Whether or not hedging capital ends up in hedging or remains in cash is up to individual discretion. If individual trading edge is higher than usual, the individual trades can be larger. If the current trading edge is lower than usual, individual trades can be smaller than broad allocation. Also, if individual positions have risen, you can reduce the stock allocation to hold the individual positions until the target and maintain risk parity.

Income should be held at a consistent 10%, mostly in instruments with low or negative correlation to the XIV. This way, rebalancing to add income can be done after selling XIV high and the capital can seemlessly be used to buy the income when the yield is high and the price is low relative to recent price action more often than not due to the inverse correlation. If there is a slight correlation at least the buys and sells of XIV won't heavily interfere with ability to buy and sell income to produce the 10% balance.

Cash should under almost no scenario decline to under 10% in addition to the hedging capital that may or may not be used for hedges at the time.
---------------------------------
Correlation:
I may begin making exception for income due to certain instrument's inverse correlation to XIV. LWC for income meets bonds providing additional income than 10% and can be placed in addition to the bond allocation or instead of. IN either case the bond+income should be consistent with the total of the bond range (normally 5-10%) plus the income (~10%). You can see when you needed to sell the XIV, usually LWC was a decent buy. When you needed to buy XIV LWC was usually a decent sell.  So maybe a 5-15% income range will be alright, but that should be more of an effect of growth of your portfolio relative to LWC or LWC relative to portfolio over time.

The real problem is the slow movement of income related funds don't support a lot of transactions. Nevertheless, more often than not, there's going to be capital available from one sale to fund the purchase of another if/when necessary. TLT works as well, however, the yield is low and I suspect at some point there will be a shift away from government debt into corporate debt.



Correlation Matrix


You can see that there's a mixture of low correlation, negative correlation and positive, and understanding what works at a given phase can better help you understand how you might shift the composition of the portfolio. Negative correlated items will have you add one while selling another. Positively correlated items are usually "either or" and you may swap out of one in favor of another in some situations, and low or no correlation are mostly bought or sold independent of each other .

In the very long term, technological growth has prevented commodities from growing in price. This and the risks vs the potential reward is a good argument for lower allocation to commodities. However, you can see the correlation of one commodity to another is not very high which supports treating each one as it's own asset class. Rather than seeing it as 10% commodities, you could treat it as 2.5% base metals, 2.5% precious metals, 2.5% energy commodities, 2.5% agriculture. Shifting to and from these asset classes or even shorting one or another occasionally makes a portfolio with equal commodity balance to stocks, options, commodities, etc perfectly acceptable. A similar approach can be taken with currencies due to the diversity of correlations among many currencies.

Design of portfolio: Flexibility to maintain approximately 50% risk on/ 50% risk off or intended risk on/off targets even after substantial changes in the market such as doubling of short and/or long term trades or halving of those trades.
Substantial gains in market can be sold to offset the growth of ST and long term trades. Hedges can go from cash to actual hedges, and profit of hedges can be used to fund the expansion of stocks or more ST trades to restore balance.


Extreme ranges of allocation examples:


One condition I didn't include is the extreme uncertain market, where there's no deflationary risk, and the stocks/bonds/currency/commodities allocation (SBCC) is larger. I also didn't cover variations where you actually handicap the SBCC to weight larger amounts towards the markets you expect to outperform on risk adjusted basis.

Nevertheless, there's a really wide range of potential allocations. But there's still intended limits to create enough structure, and shifts need to make sense with the conditions at hand.

The majority of the portfolio will be governed by the XIV/SPY put pairing and that will be governed by the VIX. Another large part of portfolio will be governed by the standard limits such as income of 10% cash no less than 10%, and most other positions should at least be 5% weighting. The remainder will be approximately timed as you go through the risk cycle to maintain the appropriate balance as well as target the right stock picks.

For example, when the vix spikes, you begin to remove hedges and possibly sell some income in some circumstances and add XIV and stock allocation and maybe some long term picks and rotate into overweight risk over time. Then as market stablizes you rotate from sort of a general broad allocation of stock index and XIV to individual trades while balancing out the SBBC allocation more neutral over time. You continue to rotate out of the VIX and maybe buy income again and you consider hedging and selling some long term picks, and reduce the risk allocation to be neutral and then even slightly more risk off. Possibly shifting to cash during uncertain times, or even aggressively bearish in some conditions. You begin rotating into alternative markets for your risk on like commodities and income and high yield corporate bonds or preferred shares for income or hedges, currency, cash and government bonds for more "risk off" or even betting on downside. If/when the VIX spikes you then begin the process again. Meanwhile your individual stock trades might capitalize off of specific rotation from lower risk to higher risk back to defensive, and possibly using long term sector rotation over many cycles to adjust the weightings of the long term allocations.