Risk Theory, from Jim Sogi

March 18, 2009 |

 Here's an investment theory. Rather than buy when the expectation is greatest, buy when the risk is the least. The question is whether or not they are the same times. I define risk as the lowest probability of account drawdown from entry, rather than common definitions of volatility. A corollary of this is that buying at what appears to the public as the greatest risk is actually the time of least risk. A recent discussion here looked at expectation of range vs expectation of change. The theory of the least risk would be to buy at the expected maximum extension of range, at the time of greatest expectation. The other issue is the holding period and expectation of gain. Some argue that the maximum expectation period over time will reap the highest returns. The problem is that the deviation goes up as fast if not faster, increasing risk. The second problem is the issue of changing cycles and prior history may not match future performance. Dr. Phil has pointed out that profit stops reduce deviation but not necessarily rate of return. Yet account deviation is the bottom line. He has proposed formulas to optimize risk/loss vs return. But realtime trading demands some sort of realtime system. This is hard to implement. The underlying idea is that management of risk is more important than maximizing return. This has been the basic systemic flaw in the recent boom and bust. The idea is distinct from the idea of leverage as risk. The answer will differ from individuals to institutions and funds with differing goals.

Martin Lindkvist comments:

Try creeping commitment, that is, start with a small line and increase if market goes in one's favour. But this has a built in assumption of some kind of trending behavior of prices, which might or might not be true depending on other circumstances.

A twist to the creeping commitment of a single position is to start out a period (year, or other of your choice) and increase risk taking after profits have been made, and decrease if losses are incurred to the capital at beginning of time period; that is play harder with "market money". I believe that both this method and the first one might have some psychological benefits if nothing else.

Risk in the usual deviation sense has sometimes been disguised, through e.g asymmetrical strategies ("picking up nickels in front of a bulldozer") where the risk might seem far away only come back hard when least expected. Moral - one should always be suspect when one thinks one have found a good way of managing risk - "what am I missing". Liquidity issues comes to mind too.

Using leverage as the risk manager, still seems to me the most clean way to manage risk. Cutting off risk with stops or options also is a way but run of the mill costs for these should be higher over time. That doesn't matter though if you meet black swan on day one….

Phil McDonnell writes:

A knotty part of this question is to define risk. To academics it is probably something like standard deviation of returns. To traders it may be only the losing trades, in other words only the downside deviations need to be considered. Another metric might be draw down or maximum loss.

The risk measure one chooses makes a big difference. For example suppose we look at the standard deviation of the market after it has been rising for a while. Assume our criteria of rising is that the market is above its 200 day moving average. We would find that the risk measured by the standard deviation is less for all such periods than it would be for those periods which are below the 200d moving average.

When markets approach major bottoms they are often quite volatile. Currently we often have daily moves of 3 to 5%. If one were to study the subsequent behavior the probability of large down moves the next day are quite high as are the chances of large up moves at such times. This is true even though one can often argue that after such large declines the market is close to good value levels and has not much more to fall.

Note that one can get two different answers to the question depending on time frame. At a low area such as now, the long term risk outlook might be that it cannot go much lower. But because of volatility the short term outlook is for continued riskiness.

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

Legacy Daily replies:

As for this statement, "Rather than buy when the expectation is greatest, buy when the risk is the least," the risk of not being in the market is the least (assuming cash is constant). Perhaps you mean "buy the highest expected return for the lowest risk." Theoretically, "maximize return but minimize risk" may be suitable for a linear programming model where one would need to define the various constraints and let the machine solve for the best alternative to maximize return given the constraints. The challenge: the right definition of the constraints. Also, the optimal solution may change tick by tick.

And as for this statement, "a corollary of this is that buying at what appears to the public as the greatest risk is actually the time of least risk," I think many market participants buy and hold. Therefore, the main reason a market appears a great risk to them is because their money disappears. The more money disappears, the greater the fear (hence perception of risk). It also seems that these "emotions" are only visible during intermediate-term/long-term market turning points which may not be suitable for a day trader.Furthermore, "time in the market" and "percent invested" are also ways to increase/decrease risk when account balance rather than security price volatility is the key criteria. Account balance is an extremely useful risk manager. AUM does not have the same effect.I cannot remember where but I came across the concept of a very successful trader at one point or another getting completely wiped out and some being so good that they could build a fortune multiple times and get wiped out more than once in a lifetime. If true, is that possibly a manifestation of "buy when the expectation is greatest" with not enough focus on "when the risk is the least?"


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