The quick drop in silver last week seemed to have caught a few off guard, to the extent that talk of manipulation pervaded the air. However, I had already suggested a sell off in silver last weekend and was not take by surprise by current events. However, in the light of that weekend comment about a silver price correction, I was asked a question about whether to sell silver stocks. That is a natural enough question which I answered, but which I want to expand on here. If you, like me, believe we are still in a primary bull market for silver, then you may want to consider one or two matters before churning a stock or bullion position.

Let us suppose you somehow knew your favorite silver stock was about to correct by 20% but you were not sure of the exact day, only that it would do so in the next week or so. Should you sell looking to buy in at a lower price? The obvious answer seems to be yes, but look at what you have to contend against.

• You will not bail out at the exact top unless you are lucky.

• You will not re-enter at the exact bottom unless you are lucky.

• The bid-ask spread on a stock guarantees a loss even if you sold and bought in the same minute.

• The broker fees ensure further erosion of a re-entry profit.

So let us suppose your stock is going to lose 20% and will drop from $20 to $16. Let us further suppose that you get the exit and re-entry correct to within 5%. Furthermore, let us assign a bid-ask spread of 2% either way on this stock. This is not an easy number to fix; a recent check of 20 silver stocks gave spreads between 1% and 8%. But in plain English, for a $20 price, you get $19.60 when you sell the stock but it costs you $20.40 to buy it back.

Let us finally assume that your broker fees plus any taxes will be $10 to sell your stock and another $10 to buy them back. That is not so bad.

We will now assume you have 500 shares notionally valued at $10,000 (based on a $20 quote) that you wish to sell. The stock hits a price of $20 and you exit at 5% below this at $19. The bid on this is $19 - 2% or $18.62 and your broker charges $10 for the privilege. You are left holding $9300.

The price drops to $16 and you get back in at $16.80 and the ask price is 2% higher at $17.14 plus another $10 fee means that you can afford to buy 542 shares i.e. ($9300 - $10)/$17.14. So your net gain for the whole exercise is 42 extra shares. That seems worth the effort, you may reply. Now suppose you are only 10% accurate in your exit and re-entry. Now you will end up with 490 shares or 10 less than you started with and the whole exercise has been a waste of time. Evidently timing is a prime factor here.

If you can time your exits and entries to a high degree and the share price drops more than 20%, it could be well worth it - but that is a big if. You can repeat the exercise for bullion but the rewards could be less as bullion can drop less than stocks in a correction and the bid-ask spreads are higher.

I sent the gist of the above to subscribers early this week but after that I decided to put some science back into silver, rather than the speculation we so often see about trading the gray metal. I applied what I knew about mathematics and came up with a formula whereby silver stock and bullion investor can risk assess whether to churn their positions or sit still. The formula is as follows:

**N**e = **N**b x (**P**b/**P**e) x **A**2 x **S**2

So we have **N**e, which is the number of shares one will have at the end of the exercise, and **N**b is the number of shares held at the beginning. The aim is obviously to have **N**e greater than **N**b. Continuing, **P**b is the price of the stock at its peak prior to the downturn and **P**e is the price when the correction ends and the stock bottoms out.

Our variable **A** is the accuracy of one’s ability to predict an exit and re-entry point. So, in our first example above, we assumed the investor was within 5% of the top and bottom. That is a 95% accuracy and this would mean **A** would equal 0.95. The formula then squares that number.

Finally, **S** is the bid ask spread on each side. In our example, we took a 2% spread either side of the quoted price. Therefore, **S** would equal 0.98 (100% - 2%). Again we square that number.

One thing we have omitted from this equation is the brokerage fees. Including these complicated the formula too much and so long as we used a large value for the shares such as $10,000, it had little impact on the final result. So, if we feed the numbers from our original example we get the following formula:

**N**e = **500** x (**20/16**) x **0.952** x **0.982**

Giving us an answer of **N**e = 541.7 which agrees well with our manually calculated 542 shares. I encourage anyone thinking about selling to do the sums first based on their own expectations and costs and experiment with this formula in their portfolio risk assessment.