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Minyan Mailbag: The Speculation Game and Risk Control


As far as how much capital to use, it is an art more than science.


Dear Prof. Succo,

Thank you for warning readers of what to expect if the Dow dropped 200 points and for all your great posts. I have learned a great deal from reading your insights.

I have a quick question. I noticed in your comments about Harley-Davidson (HDI) that it appeared that you were speculating on the direction of HDI stock. If so, may I ask what % of your portfolio bets on the direction of a stock?

Minyan Dennis


We "speculate" on the volatility of a stock, not its direction. We do "lean" a certain way from time to time, but that is a function of the price movement of the stock. Of course, the nature of upside volatility is normally different than downside volatility, so in essence, we do structure volatility trades in an expectation of directional movement. But we are often pleasantly surprised by unexpected upside volatility: heavy short interest, although in the long run often correct, can have the tendency to drive stocks up violently when the shorts do not get the news they have been waiting for. This has happened to us in HDI a few times even though we are negative on the company and its stock.

I also want to comment on the word speculation. If you use too much capital in an isolated speculation (guess), it is often an avenue to ruin. If you apply an appropriate amount of capital to each speculation so that some work out and some don't, but the overall payoff profile is positive, we can then use the term "gaming theory," which is what we try to do.

I have commented on this in depth. This is risk control. As far as how much capital to use, it is an art more than science. But a paradigm to think about when allocating capital is called "optimal F."

Optimal F is a method of managing a portfolio by maintaining a constant proportion called "F" in risky assets. This requires a constant rebalancing between risk less and risky assets to keep a proportion of risky asset the same.

Suppose a player is given $1000 (or any finite amount) and can risk any amount repeatedly in a game where a player has an edge. If he bets $1 he wins W dollars with probability P or loses L dollars with probability (1-P) (the total probability is 1).

The best strategy for the player to maximize his "expected winnings" is to risk in each game a fixed fraction F of his total capital such that::

F= ((W X P) – (L X (1-P))) / W

For example, if the game is such that the player betting $1 wins W=2 dollars with probability P=0.4 or 40% or loses L=1 dollar with probability 1-P = 0.6 or 60%. His Optimal F is: F = ((2 * 0.4) – (1 * 0.6)) / 2 = 10%. The player should always risk 10% of his current capital per game.

If the probabilities are not known for sure, it is possible to prove that for a player it is better to under-risk than over-risk: under-risking will result in the less then maximal winning amount, but over-risking can result in the loss of the whole capital before the probabilities are allowed to work.

In portfolio trading practice this rule translates into a multiple simulation of the portfolio looking at each trade as a probabilistic bet. The simulation involves trying different maximum % allocations per trade and maximum % per total risk until optimization goals are satisfied.

The rule of thumb is that when probabilities are not certain, it is better to be more conservative. This will result in a less than optimal return; a too aggressive approach with the wrong probabilities may lead to unexpected and unacceptable losses.


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