Position Size Calculator - Instructions

Before choosing and entering probabilities into appropriate boxes please take into consideration the fact that often perceived probability differs from the real value. That is the case, since every action a person takes has to be first filtered by various psychological mechanisms. This applies to every human being, as everyone has emotions, thoughts, memories and various experiences. Both probability and psychology are complicated parts of science and describing all existing correlations between them is needless for this part of our website. Here, we will focus on how people psychologically adjust probabilities and what can you do to minimize this mistake.

For more details please take a look at the following chart:

Naturally some people adjust probability more than others but the general tendency is to transform it in the way shown above. For small probabilities (let’s say under 10-20% ) it is common to perceive probability as higher than in really is. This means that when you think that the probability of a given outcome is about 7%, the odds are that it’s really 4%-5% or so. Probability around the 50% level is fairly better reflected by estimations; still please note that the steepness of the slope is quite low, meaning that smaller changes in perceived probability may mean bigger changes in actual probability. For example let’s say that real 30% is perceived as 40%, while real 70% is perceived as 60%.

The problem arises again at high probabilities over 80-90% level. This time the case is that people usually perceive the probability as lower than it really is. The other thing important here is that the slope is very steep, meaning that it is very difficult do differentiate between high probabilities. Since it makes a huge difference in the model whether you enter 95% and 99% (after all, in the first case, the chance of losing is 5 times bigger!) you must give special attention to these probabilities especially given the difficulties from the psychological point of view. Remember that it is always better to enter too conservative value than over-optimistic.

This model is designed to perfectly suit the type of transaction that is described in the Likely Scenario block; in our opinion it is prudent not to put all one’s money into option transactions. That would imply that the results of calculations do not apply to your whole capital, but only to the part dedicated to speculating on options. For example you decide you want to put 20% of your money into physical silver and gold, 50% into gold and silver stocks and 30% you decide to use for speculation using options. If our model says you should put 10% into short-term options, 60% into medium-term options and left rest in cash, that means putting 3% and 18% of your total capital for these options.

If you are using this model for a single transaction, you should interpret results (percentage of your capital you are to invest) as a part of the total amount of capital you would draw from in order to cover losses on such transactions. In other words – the part of your capital dedicated to such single transactions. If you make only such single transactions, you may use results directly. However if you plan to limit your exposure and want to be sure not to lose more than – let’s say $15,000 of your $100,000 portfolio, than you should apply results to these $15,000, not the whole $100,000.

In this model you profit on rising prices by buying call options and you profit on falling prices by buying put options. All types of options are used to profit on the same price move in the underlying security/securities. By "the same" we mean a move of the same direction, range and time frame.

Naturally the probability of realizing gains is bigger for options that have more time until expiry. On the other hand the more time option has until expiry date, the less leverage it offers. Therefore short-term options are more profitable than medium-term options, which are more profitable than the long-term ones.

Options you use should be on the same security. It is allowed to use different securities if they are highly correlated (such as stocks from the same sector – gold stocks for example), but it is not advisable, as it reduces the accuracy of calculations. You can also use this tool on groups of stocks as long as you are able to calculate probability that the whole group of stocks will achieve particular gains and what exactly these gains would be. In that case you would expect the top / the moment you wish to close your positions to occur simultaneously for the whole group. Again, that might be the case for stocks from a particular sector of the economy, for example for gold stocks.

Please note that we never ask you about exact time, which would be needed to calculate options' value in the Black-Scholes model. The reason is that the time should be already taken into account in both probabilities and profits. In terms of probabilities the more time you allow for your predictions to materialize, the more probability of achieving them you get. On the other hand as the time goes by, your' options will lose their time value (so called time decay), resulting in lower profits.

The positive outcome – for which you are required to enter certain probability is realizing predicted gains on short, medium or long-term options.

The negative outcome – the option expires worthless – the probability of such event is of course the difference between 100% and the chance for the positive outcome.

You decide what short, medium and long term means. This tool will make accurate calculations as long as short-term options expire earlier than medium-term options, which expire earlier than long term ones. It’s up to you to choose how long "short", "medium" and "long term" really is.

Like most models that try to calculate the sizes of particular positions in hope of maximizing the gains of models’ users, the Position Size Calculator is also equipped with mechanisms that help you manage the level of risk you take. Without controlling risk, this model would suit only the most fearless and profit-oriented speculators. These individuals are willing to accept losses as long as particular strategy makes their long-term returns superior to profits, they might achieve by using any other strategy. Make no mistake about it – even without any risk control this model would not risk your capital if it would not mean greater returns IN THE LONG TERM. Although we are pretty comfortable with accepting risk if it does mean biggest gains in the long run, we do realize that this approach may not fit all investors and speculators using this model.

Our goal was to figure out how one can evaluate risk without using arbitrary values and any widely used statistical measures. By the former we mean choosing your risk preferences from a list (averse, neutral or risk lover) or putting a number on your preferences toward risk (0 – risk averse, 10 – risk lover). We always had mixed feelings about this type of selection. Just how one is supposed to know put a number on his/her preferences? “Is it already eight or only six?...” Naturally, there may be psychological tests that are supposed to help you evaluate your risk preferences but we still find it rather unclear. How can you be sure that after answering various questions regarding risky situations in many aspects of your life, you will know exactly how will you feel with a particular loss of money? Isn’t that possible that you would assess risk differently in different aspects of your life? In our opinion this is at least probable.

We stated earlier that we would prefer not to use any popular statistical measures to evaluate risk in this model. We don’t want to get into details here, but in our view the key assumption (normal distribution of returns) made in these measures, such as variance and standard deviation simply does not apply to capital markets.

Because of these two reasons it seemed prudent to develop a new way of assessing risk. Fortunately, the mechanism we built perfectly fits the Position Size Calculator. We decided to make your selection as close to the financial risk itself as possible. Probably your biggest concern when it comes to risking capital, is how much money you could lose. Well, some might say – if you don’t want to lose any money, don’t invest at all. That’s not far from the truth, however if you are still reading this, we assume that you do want to invest. So let’s change the original concern to “how big loss are you willing to accept temporarily”. This simple alteration gives us room for further analysis. First – how much of a loss is a real concern to you? For the purpose of this instruction we will assume that that would be half of the capital dedicated to this strategy. The next question is “how willing” or more likely “how unwilling” you are to take that kind of loss. By this question we mean the probability that this loss would temporarily occur. Deciding what that probability would be, is the only thing that you need to enter in the basic version of our risk control mechanism. The advanced version gives you the ability to choose other levels of losses. For example you might better measure your ability to accept losing 30% of your capital than the default value of 50%.

Please note that temporary losses are unavoidable, the only question is when exactly they will take place. For example if you were right about the probability of success and it equaled 80%, most likely when you will win on this particular transaction the first time you enter it. However if this situation repeats let’s say 10 times, you will most likely win 8 times and lose 2 times. Please think about it -losing two times in ten is not only probable, but it’s likely. What if these two times would be the first two times you invested? Actually the probability of that happening is quite low here (4%), however please note, that you may be right (in that case thinking that the underlying security would move in a given direction) and still lose money. Having invested 30% of your capital into this transaction, you would be left with about half of your money. How would you cope with that loss? Would your next investment decision be affected by it? If you’ve invested the amount of money that the Position Size Calculator suggested, you can be sure that as the time goes by and you continue investing, your capital will increase. The point is not to panic when the inevitable (the loss) happens. Only you know how much money can you lose temporarily, so that the fact of loss does not affect you too much. Too big influence on you and therefore on your investment decisions usually leads to further losses or to missing opportunities.

Remember that if the loss is let’s say 25% and you enter probability of this loss occurring let’s say 10% that does not mean that bigger loss is not possible. Bigger loss is possible, but the probability of such event taking place is definitely lower than entered 10%. The loss for which you choose the probability should be the level that you can most comfortably decide what probability suits you best. It does not mean that this is the maximum loss you are willing to take. Again, if you want to be sure that you will not lose certain part of your capital – don’t use it for speculation.

Entering 0% and 100% - these values have exceptional meaning. Being sure (100%) that a particular loss will not take place is simply impossible. If you decide to speculate you have to be ready to accept at least some risk. There is no such thing as a risk free investment. Even inflation-protected bonds really do carry some risks. What about a situation when inflation is really higher than reported? You might be losing money and not even realize that you do! How about the collapse of current monetary system? Unlikely? Yes. Impossible? No.

Putting 0% in the risk box means that you don’t care how low your holdings may temporary go as long as it means more profits in the long run. If you do select this value and decide not to use our risk-control mechanisms please be sure that you are not overstating entered chances for profiting on particular options and the gains that are to be made.