Jun

15

 I found myself lying awake in my bed last night thinking about the Nobel Prize Winner. No! Not like that….but about what he said in Stockholm last week. Expected Utility Optimization. What he said is that the goal of asset allocation should be optimizing the expected utility for the actual investor in question, and that the mean variance model should just be looked upon as a special case. And of course he is right. I mean, by the way he sets it up, he is right by definition. But….I am thinking how it would play out in the real world. In my fantasy, a consultant would sit down with an investor, asking questions to find out his preferences. Of course this is already happening in a general sense but here it would end in a very specific investor utility function). Then the asset allocation would be done based on the utility function.

I am thinking that what will be overlayed on the usual return/risk models, are constraints (e.g cutting off tail risk, smoothing out fluctuations and what have you) and while the model presumably maximises return given a risk level and those added constraints; if we add constraints there must be risk premia transferred to someone else? By definition, since the investor specified his utility function (and given that the formulas and models held up and he got "what he wanted") he is better off than before, but so must someone else be?

I am not sure this new allocation model will start a revolution in the way asset allocation is done. I think however that finding situations where other investors are up against constraints, could help open up possibilities and profits. In the micro realm, many traders prefer to cut off the risk of gaps against them, by not holding overnight. This might open up possibilities for traders well capitalised and with good stomach, to do just that (this must be tested). Other suggestions are welcome.

Adi Schnytzer critiques:

AdiIt never ceases to amaze me that people who know markets and work in them don't realise that we don't know the probability that anything will happen tomorrow unless we are in a fair casino. So the idea that anyone can maximize expected utility is nonesense since you don't know the probabilities. I am currently working on developing a risk index as a follow-up to such an index developed recently by Aumann. He cutely argues that even though we don't often know the probabilities to assign to events, it's important that, in principle at least, we have an index. Well, I've been looking for real life examples of his index (and my follow-up) in stock and derivative markets, and simply cannot find one. As a top bookie once said to me: "If I only knew the winning probabilities of the horses, I wouldn't need to know winners; I'd be making a fortune anyway." Spot on.

Jim Sogi adds:

Martin talked about "…cutting off tail risk".

The thesis that outliers shape the future is intriguing, but also that the risk cannot be eliminated. The idea that one can cut left tail risk is an illusion that in itself creates a greater risk. As Phil says, it also cuts right tail return.

Jeff Watson concurs:

Risk can be quantified, assumed, bought, sold, transferred, created, subordinated, reassigned, split, delayed, diluted,  fragmented, hedged against, and layed off……. Risk can respond to some methods, but it is still risk, and is near impossible to eliminate.

Speaking of planning in general, Stefan Jovanovich adds:

I have quoted this before, but it seems worth repeating, if only to add a mite to Adi's wisdom. Planning in business is all very well, but the trouble is that your plan's assumptions always turn out to be works of fiction. As John Wannamaker said, "I know half the money I spend on advertising is wasted. If someone would tell me which half, I would very much appreciate it."

Vince Fulco concurs:

This quote has always seemed appropriate… 

Moltke's famous statement that "No campaign plan survives first contact with the enemy" is a classic reflection of Clausewitz's insistence on the roles of chance, friction, "fog," and uncertainty in war. The idea that actual war includes "friction" which deranges, to a greater or lesser degree, all prior arrangements, has become common currency in other fields as well (e.g., business strategy, sports). [Wikipedia].

Russ Humbert warns:

One of the hardest things to get people to see is that most people/businesses have a long term utility function but operate as if all risk is short term volatility.  For example, I work for a company that has a niche market and is privately held. The owner wants to pass this business on to his great-grand kids so each will be as well off as he is now.  He has only teen kids now. This niche has very little volatility of earnings and good ROEs. But this just encourages piling on the same long term risk, to minimize the short term risk.  That is: grow the core business, not diversify. We already have the leading player in this niche.  Barriers of entry: a learning curve, requires some marketing  nimbleness, and need for stable size and reputation.   However, long term this has  no good ending. Best case we double our market share and flatline growth. But many worse cases.  Bigger, deeper pocket competitor or many, learns our niche attracted by the ROE and stable vol. We are regulated out of the market. Products slowly go obsolete, replaced by Government safety net. We lose our reputation, etc.  See this in spades throughout the fallen out of favor or failed businesses, due to subprime mess.  Low vol high ROE business, until….  For the speculator this would be like choosing a strategy that 95% time gives "Alpha" in a beta model based on quarterly results of recent history.  But all the "alpha" is hidden because, 5% time it causes you to go broke or close to it.  It just hasn't happen yet, or recently.   Basically volatility as a risk measure can hide long term complacency defeating most utility functions.

Going back to the military aspect Bill Egan adds:

An interesting aspect of the fog of war is the common mistake of not reevaluating the plan often. A major cause of this error is that people confuse perseverence towards a goal (a good thing) with sticking to the particular plan they are using at the moment to achieve that goal. Criticism of the plan and proposing actual changes to deal with new information or uncertainty are considered as defeatism or disloyalty and the operationally fluid are smacked down. The no longer relevant plan is then ridden on to failure to a loud chorus of "yes, sir! yes, sir! three bags full, sir!" A pleasant sight if it is your opponent doing this but awful if it is your leadership. I have fond memories of serving as a company commander under a battalion commander who always asked us to tell him if he wasn't making sense and meant it. Good man. 

Phil McDonnell  enlightens:

PhilThere are many deep questions in Mr. Lindkvist's ruminations on Expected Utility Optimization.

My first comment would be that there are at least two distinct classes of utility function. The first class might be what can be called the Ad Hoc Class. This would include the questionnaire method of approximating one's utility function.

Other methods might be classified as normative, as in what one should ideally want to use for a utility function. As a well known example we have the Sharpe Ratio. This is based upon the normative idea that one should maximize expected return but with a quadratic penalty for increased volatility which is treated as a surrogate for risk.

The idea of using a square root function as a weighting for betting returns actually goes back several centuries to Cramer, a mathematician. His friend and frequent correspondent Daniel Bernoulli countered with the idea of a logarithmic weighting function, which is also what I espouse with extensions. Bernoulli's ideas were not translated into English until the 1950s and thus were lost to Western thinking until very recently.

Dr. McDonnell is the author of Optimal Portfolio Modeling, Wiley, 2008


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9 Comments so far

  1. David Whitesel on June 15, 2008 3:43 pm

    First Happy Fathers Day to all dads hereabout.

    Mr Lindkvist says; In my fantasy, a consultant would sit down with an investor, asking questions to find out his preferences. Of course this is already happening in a general sense but here it would end in a very specific investor utility function). Then the asset allocation would be done based on the utility function.

    In some sense, throughout the entire post your apparently mixing traders with investors, with consultants, all with different needs.

    This left me wondering if the post wasnt seeking some form of plausible deniability?

    After all, tail risks are not random, and thus the risk associated with them, requires a different kind of complex identification, especially as it relates to investors and thier consultant advisors, where tail risks are the constraints sought by systemic interest standing in opposition to investor interest.

    Traders hope to optimize tails while investors necessarily use them in far different ways. If an investor is thinking outside the single reference of todays price, the investor has assigned investment utility to the object, and considers price risk and equity status as transitional over time.

    Not having heard the presentation, or read any transcripts;
    The question of utility is therefor reversed to “whose” Utility is your nobel winner, or you in your interpretation, concerned with?

    Just some thoughts, against which i am certainly missing too much information. my reply reflects my confusion im sure.

  2. Bob Johnson on June 15, 2008 4:11 pm

    When maintaining a proper asset allocation portfolio, to one whom subscribes to a reversion to the mean methodology, individual asset left-tail risk becomes opportunity. The true risk is at the mean of curve, a low volatility regime; when rebalancing is infrequent and asset-classes without drift offer little chance of capturing gains.

  3. George Parkanyi on June 16, 2008 12:05 am

    Well Mr. Lindqvist,

    I am not only doing what you suggest in your last sentence with real trading accounts, but documenting the results ad nauseum in my blog (just click on my name above to get to it, and then read the (concise) details of the REAP (Relational Equity Allocation Program) methodology).

    I have created 6 groups of 5 stocks and ETFs (a variant of the basic strategy). The names are the same in each group. From the initial start of the group, and at every trade thereafter, I set the current price as the reference price from which to calculate % movement going forward. As soon as any two securities in a group diverge relative to each other by 30% (in any combination of up or down as long as the highest has done 30% better than the lowest), I sell 30% of the higher and move the cash into the lower. Then a I reset the reference prices on the trade date and wait for the next 30% divergence.

    Sounds simplistic, but there is measurable compounding effect (that can be statistically projected as a direct function of the average volatility of the component securities) in doing this over a long period. Mechanically, I am interested more in compounding share count (which this does) rather than dollars - the dollars come later by virtue of the increase in share ownership and valuation (at some point).

    You are in effect averaging down, but not in absolute terms. Outliers are managed by not moving money from one group to another, and by matching securities for non-correlation. The portfolio overall is down in these markets, but ahead of the S&P500 since the market peak in October and this year, but most of the loss is concentrated on one group that suffered a major outlier (Thornburg Mortgage) on top of a few other normal-course hits in the past year’s market weakness. The rest of the groups are actually holding up well.

    If you follow this strategy with just long stocks, you will still take drawdowns in bear markets even though your share compounding is independent of overall market direction. What helps very well to stabilize the overall portfolio are short equity ETFs, and you don’t need many. 10% weighting of 2X NASDAQ, DOW and S&P500 ETFs (e.g. ProShares) seems adequate. (The stability comes from the opposite correlation).

    Even with the recent integration of highly volatile long and short ETFs into the portfolio (to take advantage of exactly that volatility), the recent action has been very stable, and, the crude guage with which I use to measure compounding effectiveness - total portfolio share count - has risen steadily in 2008.

    So bring on the gaps - I actually use them for the price divergences they provide, both positive and negative.

    Alternative energy researchers are trying to harness the random wave motion of the oceans. I’m basically trying to do the same thing with financial markets by channeling some of that random short-term price movement into a steadily growing stream of share ownership via the compounding inherent in the process.

    As long as you diversify well, single-security outliers won’t have much impact. There’s always systemic risk - but that’s what bullion under the mattress is for. :)

    The method is fully documented, with a performance update and comments on every trading date - I’m open to comments and suggestions on the concept and on flaws or possible improvements, should anyone care.

    Cheers,
    George

  4. David Whitesel on June 16, 2008 9:38 am

    Just an addendum; i visited Dr Sharpes web site and reviewed once again his many contributions. frankly, i would recommend that everyone re read the piece entitled a Parable of ????.

    It captures the essence of the problem of elevating terms like utility onto client relationships as modus for social engineering.

    the lions share of the utility function, as it emerges from the various papers, isnt particularly flattering to those who might practice it.

    market macrosystems are non equalibrium states, the influx of derivatives tied to an underlying utility framework is but an attempt to arrange expectations to fit the measurement solution imposed by the self referencing system.

    this divides interest in “private property”, and accords privilidges to counterparties, in a slight of hand/mind sort of way.

    As long as this dialog is installed to this framework…….the Parable becomes the solution, again, not flattering to those whose practice is based on partial disclosure, to facilitate extrapolated self interest.

    over and out.

  5. Rocky on June 16, 2008 12:37 pm

    George:
    Forgive my naivety about your approach — but aren’t you essentially selling a continuous series of straddles? We know apriori that in a sideways market, your sort of price-anchoring approach is the most profitable. However, will it beat the S&P during presistently trending periods of subsectors? And how do you deal with the gambler’s ruin problem (theoretically your porfolio will eventually own a portfolio of the stocks that are approaching zero price).

    Additionally, I’d guess that if you have compared your returns versus the cap-weighted S&P500 … viz a viz the RSP (equal weighted S&P) versus the cap-weighted S&P, you’ll discover that your approach is rather closely correlated with the RSP.

    Bottom line: I’d argue that the results of averaging down and re-allocating capital has very different result when you are operating at the ASSET CLASS (S&P vs. Bonds etc) level then when you are operating at the stock level. Your experience with Thornburg Mortgage emphasizes the flaw. Stocks really do go to zero. The S&P500 does not.

    Please explain what I’m missing in your approach… thank you.

  6. reid wientge on June 17, 2008 4:25 pm

    At the OTB parlor I have found small success betting the favored horse, as measured by odds on the tote board prior to the race, to place and show. I dont know the horses - I am betting the probability that those who bet and create the odds are operating in their own self interest and that they possess sufficient knowledge to be accurate within the parameters chosen. Success is achieved when collective knowledge/betting pool outweighs random events.

  7. George Parkanyi on June 17, 2008 8:07 pm

    Hello Rocky,

    Your response is repeated here with my answers in bold

    Forgive my naivety about your approach — but aren’t you essentially selling a continuous series of straddles? NO, I’M FULLY INVESTED IN STOCKS AND ETFS, SOME OF WHICH ARE SHORT EQUITY AND COMMIDITY ETFS. THE ACTION IS NON-LINEAR. WITHIN A GROUP, AND TWO STOCKS/ETF OUT OF 5 CAN COMBINE FOR A RE-ALLOCATION WHEN THEY REACH THE SPECIFIED DIVERGENCE. I’M NOT SPREADING THE SAME SECURITIES AGAINST EACH OTHER IN ANY GIVEN MATCHING OR RATIO, AND THERE IS NO TIME DECAY INVOLVED. We know apriori that in a sideways market, your sort of price-anchoring approach is the most profitable. CORRECT - BUT YOU GET A LOT NEAR-TERM PRICE MOVEMENT (E.G. WITHIN 3-6 MONTHS, SOMETIMES LESS) TO CREATE SIGNALS REGARDLESS OF BROAD TREND - THEREFORE THIS WORKS IN ANY MARKET AS LONG AS YOU DIVERSIFY FOR NON-CORRELATION AS MUCH AS POSSIBLE.

    However, will it beat the S&P during presistently trending periods of subsectors? YES - IN A STRONG TREND THE SUBSECTOR WILL UNDERPERFORM FOR A WHILE AS YOU GRADUALLY SELL OUT, BUT BY SELECTING DIFFERENT SECTORS, LONG AND SHORT COMMODITY ETFS, AND SOME SHORT EQUITY ETFS, YOU HAVE PLENTY OF NON-CORRELATION TO ALWAYS HAVE SOME SECTORS PERFORMING VERY WELL WITH FREQUENT ADVANCES AND PULLBACKS. THE COMPOUNDING EVENTUALLY TRUMPS THE BROAD TREND. THIS HAPPENED WITH A SHORT GOLD STOCKS 2X ETF I HOLD - I WAS EFFECTIVELY SHORT GOLD FROM $800 OR SO UP TO ITS PEAK AND UNDER WATER FOR A LONG TIME, BUT THAT ETF DELIVERED BOTH BUYS AND SELLS ALONG THE WAY - 5 EACH, AND IT’S CURRENT COST BASE IS MODESTLY PROFITABLE AT THE MOMENT.

    YOU ALSO TEND TO UNDERPERFORM INITIALLY, BECAUSE YOU ARE ALWAYS SELLING RELATIVE STRENGTH AND BUYING RELATIVE WEAKNESS, BUT WHEN THIS REVERSES AND THE SECTORS ROTATE, THE ACCUMULATED “WEAK” STOCK BECOMES STRONG AGAIN AND VERY PROFITABLE. IN 2005 AND 2006, I RODE MERCK FROM $42 THROUGH THE VIOXX THING DOWN TO $26 AND BACK UP TO OVER $40. IT WAS QUITE PROFITABLE IN THE END. RECENTLY BUFFALO WILD WINGS, BROADCOM, GENESEE AND WYOMING, SUN HYDRAULICS AND TRINA SOLAR HAD BIG DECLINES, BUT ALL RECOVERED QUITE SMARTLY. CURRENTLY I HAVE SHORT OIL AND NATURAL GAS ETFS IN SIGNIFICANT DRAWDOWN, BUT THESE SHOULD CONTRIBUTE EFFECTIVELY WHEN ENERGY PRICES CORRECT.

    YOUR AVERAGE COST BASE IS ALSO ALWAYS TRENDING DOWNWARD - I STARTED TRINA SOLAR AT $52 - IT’S AVERAGE COST IS NOW DOWN TO $39 AFTER 5 BUYS AND 5 SELLS.

    And how do you deal with the gambler’s ruin problem (theoretically your porfolio will eventually own a portfolio of the stocks that are approaching zero price). NO - LOOK AT ANY CHART. STOCKS ARE CYCLICAL AND VERY FEW GO TO 0, ESPECIALLY ESTABLISHED ONES. THE ODDS OF A LARGE NUMBER OF STOCKS GOING TO 0 OR NEAR-0 IS VERY LOW. AND BECAUSE YOU TRADE ON RELATIVE PRICE MOVEMENT, NO STOCK OTHER THAN A DELISTING IS DEAD MONEY. A $30 STOCK COULD GO TO $10, BUT THEN IN RECOVERING TO $15 MAKES A 50% MOVE. THAT MOVE CAN CONTRIBUTE TO THE OVERALL PORTFOLIO. EVEN IF THE STOCK TRADES IN A PERMANENTLY LOWER RANGE FOR MANY YEARS, ITS COMPOUNDING AT THE LOWER LEVEL EVENTUALLY OVERCOMES THE INITIAL DECLINE TO THE LOWER RANGE.

    I ALSO COMPARTMENTALIZE THE PORTFOLIO - IT IS THE SUM OF MANY MINI-PORTFOLIOS (I CALL THEM SIX-PACKS BECAUSE MY MAIN RESEARCH WAS DONE USING GROUPS OF SIX. IN MY PORTFOLIO THE GROUP WITH THORNBURG IS THE ONE WITH MOST LOSSES BUT THE OTHER GROUPS ARE ACTUALLY QUITE ROBUST. AND EVEN THORNBURG I CLEARED OUT OF BEFORE IT BECAME A PENNY STOCK. YOU USE RESEARCH AND JUDGEMENT TO ESTABLISH THE NAMES. ONCE YOU GET A GOOD MIX, YOU SHOULDN’T HAVE TO CHANGE THEM FOR YEARS UNLESS A COMPANY GOES INTO SERIOUS DISTRESS OR IS TAKEN OVER AND NEEDS TO BE REPLACED.

    Additionally, I’d guess that if you have compared your returns versus the cap-weighted S&P500 … viz a viz the RSP (equal weighted S&P) versus the cap-weighted S&P, you’ll discover that your approach is rather closely correlated with the RSP. NOT SURE WHAT YOU MEAN, AND WHY YOU WOULD THINK THAT. I’M NOT BUYING AND HOLDING (I AM PARTIALLY) - I’M CONSTANTLY RE-ALLOCATING BETWEEN THE SAME STOCKS WITH A PERSISTENT BIAS FROM HIGHER RELATIVE PRICE TO LOWER RELATIVE PRICE - AN AGGRESSIVE FORM OF AVERAGING.

    Bottom line: I’d argue that the results of averaging down and re-allocating capital has very different result when you are operating at the ASSET CLASS (S&P vs. Bonds etc) level (WORSE) then when you are operating at the stock level (FAR SUPERIOR). Your experience with Thornburg Mortgage emphasizes the flaw. I HAVE RISK MANAGEMENT TO ADDRESS THIS TYPE OF OUTLIER. Stocks really do go to zero. NOT OFTEN The S&P500 does not. AND IT DOESN’T MOVE VERY FAR EITHER IN A YEAR. YOU SHOULD SEE THE ACTION IN 2X COMMODITY ETFS! I SEEK OUT VOLATILITY - BUT WITH A VERY STRONG EMPHASIS ON SCREENING FOR LONG-TERM DURABILITY. I DON’T MIND WHERE A VOLATILE STOCK/ETF GOES, AS LONG AS IT IS NOT TO 0.

    Please explain what I’m missing in your approach… THE PHENOMENAL COMPOUNDING POWER OF USING VOLATILE STOCKS AND RELATIVE PRICE MOVEMENT AS THE TRADING BASIS (STOCKS DIVERGE AGAINST EACH OTHER IN ANY KIND OF MARKET), AND THE MONEY MANAGEMENT TECHNIQUE OF COMPARTMENTALIZATION.

    I RESEARCHED THIS ALGORITHM WITH SIMULATED RANDOMIZED DATA AND ISOLATED THE COMPOUNDING EFFECT AS FUNCTION OF VOLATILITY (AS MEASURED BY THE RANGE WITHIN WHICH PRICES WERE ALLOWED TO SWING). THEN I BACK-TESTED WITH REAL DATA AND THE RESULTS FROM THE SIMULATED AND ACTUAL RUNS CONFIRMED EACH OTHER.

    BOTTOM LINE, I DON’T WORRY ABOUT COMPOUNDING DOLLARS, I FOCUS ON COMPOUNDING SHARE COUNT, THE DOLLARS ARE A NATURAL CONSEQUENCE OF THAT.

    HOPE THE EXPLANATIONS HELP.

    thank you.

    YOU’RE WELCOME

    CHEERS,
    GEORGE

  8. George Parkanyi on June 19, 2008 11:57 am

    Martin,

    That was thought-provoking and it raises a good point.

    Has anyone done a calendar of naked Nobel prize-winners yet? :)

    Cheers,
    George

  9. kasbe pradnya on September 18, 2008 5:02 am

    very bad article

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