Divestor

A concept that is important to people that are considering the purchase of stock options (I will strictly deal with “call” options for the purposes of this discussion) is the concept of delta.

Delta is the change in price of the option over the change in price of the underlying. For those that are calculus-minded, it is the instantaneous change, given that all other variables are constant (parameters such as strike price, time to expiry, implied volatility, etc.)

As an example, if you owned an option contract (100 shares) to buy stock XYZ at $50/share, and if XYZ was trading at $50, with an implied volatility of 50%, expiring on the 3rd week of Friday January 2011, would have a delta of 0.537, according to the Black-Scholes Model. This effectively means that the current price you have exposure to the equivalent of 53.7 common shares at the current price and time. This increases as the stock price increases – a $55 share price translates into a delta of 0.729, and a $45 share price results in a delta of 0.318.

Intuitively, this makes sense – as your option goes deeper “into the money”, you start to have more real equity in the underlying stock.

This is in response to an article published by Sivaram Velauthapillai who was citing a Globe and Mail article on the art of calculating returns.

The calculation and interpretation of “return on investment” is not as easy as one might think. The two most important and basic formulas in calculating return I will illustrate. They do not factor in the removal or addition of cash in an account.

The simple method of calculating the return, in very non-technical terminology, the following:

(simple return) = [(value today) – (value invested)] / (value invested)

To convert this into a percentage return, multiply by 100 and append a “%” to it.

You can see by this formula that if the “value today” is less than the “value invested”, you will have a negative return.

This formula should be in the arsenal of everybody investing. If you cannot calculate it on your own, there is really no point in investing in the markets at all since you will have no idea how to measure your own performance. Online sites have tools to measure performance, but without understanding the underlying formulas, the numbers will be meaningless.

The next parameter to get thrown into the equation is “return over time” – for example, making a simple return of 40% over one year is different than making a simple return of 40% over four years. Most people take 40% and divide by 4 and say they made “10% per year”, which is an incorrect calculation since it ignores the effects of compounding.

If you make 10% a year, your actual return would be 1.1^4-1 = 46.4%, not 40%.

To factor in compounding when calculating an annual return, you must engage in some mathematical finagling, which is a test of how much you remembered in high school math:

(annual compounded return) = exp[ln[1+(simple return)] / (time in years)]-1

For those not mathematically oriented, exp[…] and ln[…] refer to the exponential function.

When plugging in a 40% simple return over 4 years, you end up with an annual compounded return of 8.78% a year, which is the correct answer – verify by doing (1.0878^4)-1 = 40%.

The calculations become more complicated when you try to measure them for cash, time, and simple return. This will wait for a future post.

What happens in the month of December?

The answer is best described as “Christmas motivations”. You see it in the marketing, you get a sense in offices that things will be winding down soon, and you get a huge anticipation of the one or two week break at the end of the year where people can finally relax for a little bit before starting the new year.

In terms of market movement, I cannot think of a December that involved significant movement. Perhaps some market historians out there can put some numbers to this statement.

One movement, however, that is caused by the December year-end is typical “window dressing” (i.e. fund managers that want to make their holdings make them look like geniuses) and tax loss selling. Stocks that are below their average trading prices throughout the year should have somewhat more supply pressure, so this is always something to look out for – especially in less liquid issues.

I have been continually doing some research on candidates, but am not finding too much and find the allure of cash to be high. It is difficult having such a high cash position and watching a day like today when the major indexes go up over 2%, but I will not be lured into deploying my reserves when I am already 75% invested. In any respect, my portfolio has such little correlation to the major indexes that it becomes a non-factor.

Being patient is boring, but boring allows me to sleep at night and gives me the luxury of stalking other investment opportunities, as sparse as they may be.