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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