Calculating returns is not simple

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.

The December Stretch

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.

US Thanksgiving Shopping – Amazon vs. Walmart

The USA celebrated their Thanksgiving weekend last Friday, and one tradition they have is buying new stuff. Reading all the stories about the crowds and such always makes for media amusement in what is otherwise a very slow news day.

Some more sober statistics is that retail sales apparently were up 0.3%, while online sales were up a whopping 16% by comparison with respect to last year’s thanksgiving to this one.

One can easily see why people buy stuff online – it is so much easier to compare prices, shipping costs are now baked into the retail price, and you avoid crowds. I think shopping in crowds is a cultural event for a lot of people, in the quest for finding that elusive “great deal” that you can brag to all your friends about after.

This brings me to the subject of the valuation of Amazon (Nasdaq: AMZN), the largest online retailer. They are trading at $177/share, which gives them a market cap of about $80 billion. Amazon’s sales for the past 12 months were $31 billion, and income was $1.12 billion. So on a past 12 months basis, Amazon is trading at a P/E of 71x, or a yield of 1.4%.

Quite obviously, the market expects Amazon to grow a lot to fit into its present valuation. If the analysts are correct, Amazon priced in 2011 projected earnings will have an earnings yield of 1.96%, or 51 times earnings. You have to assume that Amazon will be able to grow their income considerably within a short period of time to begin to match some other firms with comparative valuations. For example, Walmart (NYSE: WMT)’s 2011 valuation has it at 12.1 times earnings, or an 8.3% earnings yield.

For Amazon to fit into this valuation, they will need to increase their bottom line profits by a factor of 5.9 times from what they have currently made over the past 12 months. This is a huge leap and there is obviously growth in the marketplace that can be better purchased elsewhere.

However, in terms of providing retail customers with a venue to shop in, they do an absolutely fantastic job. This is another classic case of a great company having a stock that you would not want to invest in at current valuations.

A minor follow-up on BP

I note that BP (NYSE: BP) traded as high as 44.37/share – I had projected during the brunt of the Gulf of Mexico oil spill that BP would likely rise to about $42-$47/share by the end of the year. It’s pretty close to the end of the year, so I would consider this to be a successful prediction.

There are so many other factors affecting BP’s valuation that there is no longer any “political edge” to the stock valuation, beyond the usual political considerations that go around with oil companies. All of the transient effects of the oil spill have been well priced into the stock – notably the implied $50 billion cost of clean-up, which has been cleanly lopped off BP’s market capitalization.

The company took a massive charge-out, so it will be showing negative net income for the next 9 months, but after this they will be showing their usual large profits – around $18 billion or so. This gives them a valuation of about 6-7 times projected earnings, or about a 15% earnings yield. Assuming the market mania for yield continues to maintain itself, whenever BP gets around to re-instating its dividend (which was historically 84 cents per share per quarter), this will give it an 8.1% dividend yield, and then the lemmings will buy into the company, raising its valuation.

First Uranium – valuation

I don’t know why I find the trading of First Uranium (TSX: FIU) to be this exciting, but it is fairly obvious the market is pricing in a turnaround in its operations. Considering that it couldn’t have been managed worse in the year 2009, this is not entirely surprising. FIU shares are up about 60% over the past month. A share price of $1.25 gives it a capitalization of $220 million. The shares will start to face resistance as it cuts into the overhang caused by the secured note issue (which is a $150M issue with a $1.30/share conversion price). Conversion of the notes will result in about 115M shares issued, or about 40% of the company.

Valuing the notes, subordinated debentures and equity is not a trivial process.

The notes currently are not the most liquid product on the planet, with a closing bid/ask of 105/124 cents on the dollar. These notes are also secured by assets and in the event of a default would likely have some sort of recovery. Using the flawed Black-Scholes model, and using a 50% implied volatility (which is an incorrect estimate) gives a 36.5 cent per share value per call option at $1.30, expiring in March 2013. At 105, ignoring the conversion feature of the note, represents a 6.7% current yield and a -2.0% capital loss for the remainder of the 2.4 year term. The actual return realized by noteholders will depend on FIU’s trading price.

Using the 50% implied volatility figure, the option embedded within the notes have a “delta” of about 65%, which means that for every 1% that the equity changes, the underlying value in the conversion feature will change 0.65%. If FIU trades significantly above $1.30/share, the equity portion will dominate the value of the note, while if FIU trades under $1.30, other considerations such as ability to liquidate the assets become more of a consideration. There is no “clean” way of valuing these notes, as you have to separately calculate the fixed income and equity components, despite the fact that both of them are linked!

The unsecured debentures, maturing on June 30, 2012 are trading bid/ask 75/77, and using the midpoint as a reference, the yield to maturity is a whopping 23.0%; or the current yield is 5.6% and capital gain on maturity at par is 18.7%, for a joint yield of about 24.3%. It is likely that if FIU is trading significantly above $1.30 around the maturity date of the debentures that they will be able to refinance them. If FIU is trading under this, then it becomes increasingly likely that the debentures will receiving significantly less – the people holding the debentures can force a bankruptcy, but given their low seniority they will likely not be in much of a position to doing so.

The equity has traded historically as high as $8/share in May of 2009, and the company was very smart to pull off an equity offering near this price (before the shares tanked). Indeed, if this valuation was at all correct, even when you factor in the subsequent dilution, there is the potential to see the operation go for $3-$4/share if everything goes to “plan”. Of course, it has not in the past, and will likely have issues in the future!

FIU’s capital structure is a very strange one to analyze, especially with respect to the profitability of its operations. As I stated before, this is a classic high risk, high reward situation. In no way would anybody be sane to “bet the farm” on it, but a small allocation is in order – which is what I have at present in both the notes and debentures but not the equity. The notes already have enough equity value in them that can take direct advantage of a price rise in equity.