investment

The issue of percentages comes up almost every time we talk about any kind of numerical data. This is especially true in the investment world where people generally tend to talk in terms of percentage gains and losses - rather than the absolute values. That’s simply because it’s easier to interpret financial changes on a common scale of 100. However, there are certain pitfalls that one should be aware of when dealing with percentage values. Here’s a quick (and elementary) look at some of these traps.

Absence of a time frame

When it comes to investments, simply stating percentage gain/loss is not nearly enough. There is something else that MUST go along with the percentage data: it is the duration or time frame. Without the time frame, most financial percentage figures are effectively meaningless. For example, simply saying “Get a 100% return on your investment” doesn’t make any sense -100% return in how much time? 69 years 8 months (corresponding to 1% annual return)? or 3 years 10 months (corresponding to 20% annual return)?

So, whenever you judge the performance of a stock (or compare two stocks), make sure that you are aware of the time frame before you start comprehending numbers like “300% increase”! *cough* penny stocks emails *cough*

Arithmetic mean against geometric mean

Let’s consider this statement “Our picks have yielded 25% average annual returns over the past two years“. Sounds genuine - after all it mentions the time frame clearly. But let’s run through an example and see how this can be pretty deceptive.

• Initial investment: $100

• Value of investment after one year: $200 (100% return this year)

• Value of investment after second year: $100 (50% loss this year)

• Net gain/loss amount over the two years: $0

Now, when you calculate “average annual return” using arithmetic mean, you are basically taking the average of 100% and -50%, giving you a 25% average annual return. But obviously, since your net gain amount is $0 (or 0% over two years), the simple arithmetic mean is not really telling you the entire story in this case.

This is where geometric mean comes into picture. Click here to learn how to calculate geometric mean of a given set of percentage values (including negative percentages). If you apply the geometric mean for the above example, you will end up with 0% average rate of return - which is correct. This rate of return - calculated using geometric mean - is known as “annualized return“.

Another way to look at it is that geometric mean takes into account the effect of compounding, whereas arithmetic mean does not.

I won’t be surprised to find a lot of proponents of volatile stocks using arithmetic mean to make their case of higher returns. So make sure you are aware about the difference between “average return” or arithmetic mean and “annualized return” or geometric mean.

Irrelevant time frames

Sometimes, data is presented with reference to a time frame (perhaps with careful consideration to the geometric mean) but this time frame may be largely misleading. In fact, I still don’t have a good explanation of what makes an “appropriate” time frame, but I am working on it.

For example, let us consider the share price of the S&P 500 exchange traded fund (SPY) over various time spans, going backwards from yesterday:

• 1 year return: 10.99%

• 5 year return: 69.69% [11.16% annualized (geometric) return; average (arithmetic) annual return of 13.94%]

• 10 year return: 62.83% [5% annualized (geometric) return, average (arithmetic) return of 6.28%]

Now, it is obvious that the annualized return differs if you choose different time windows over the history of the share. Depending on how you want to make your case, you could choose one of these time windows and go crazy with it. For example, you could pick the 5% annualized return for the last 10 years and blast the ETF’s performance, or you could pick the 11.16% return for the last 5 years and try to make a generalized statement like “… gives almost a 12% return on an average“.

Additionally, in all probability, people who want to downplay the 10 year performance will use geometric mean to make their case (geometric mean is always lower than the arithmetic mean), and people who want to glorify the 5-year performance, will use the arithmetic mean.

Readers should be wary of such pick-and-choose explanations. Try to find data that is most relevant to your investment time frame.

The disconnect between percentages and amounts

These types of examples are rarely seen in the investment world (I haven’t seen any), but are often observed in blog monetization circles. Here is an example:

My advertising income increased by 300%

Yeah right! It was 5 cents yesterday and today it’s 20 cents.

Obviously, in this case, the percentage value creates a greater boasting impact than the actual dollar value - so it might be used as a good marketing ploy to sell ideas/products.

It helps to have this scaling effect in your mind when you compare your income/net worth with others. For someone with $1,000,000 in hand, 10% means $100,000; whereas, for someone with $1,000 in hand, it’s just $100 (think in terms of buying power).

This becomes very obvious when you think in terms of percentage discounts on clearance products. What’s more attractive, a “50% off” sale on a $2 item you need or a “5% off” sale on a $100 item you need?

So, there you have it. Pay more attention to percentages in future.

More than a month ago, I discussed certain features of my slow but steady investing progress, and expressed concerns over owning two different ETFs that essentially track the same markets (EEM - iShares Emerging Markets ETF and VWO - Vanguard Emerging Markets ETF).

At that time, a few readers suggested that I should choose VWO over EEM because the former offers a lower expense ratio (0.3%) than the latter (0.76%).

In the process of educating myself on this subject, I came across an interesting article comparing the two ETFs in question.

Here is an excerpt from the article on Seeking Alpha:

Another thing in the article that I thought was strange was the author’s implication the VWO is a better choice, if you have to have emerging market exposure, than EEM because the expense ratio is a lot less. For the record VWO’s expense ratio is 0.30% (according to the article) and EEM’s expense ratio is 0.76% (according to Yahoo Finance). I think of this as forest for the trees analysis. At this point I will note that VWO has an OEF equivalent (VEIEX). Since VWO’s inception in March it has lagged EEM by at least 200 basis points (I am eyeballing the chart). For one year EEM looks to have outperformed the OEF equivalent by about 300 basis points. And for two years EEM seems to be ahead by about 1000 basis points. Even if the numbers are off, EEM has clearly outperformed by more than the expense ratio at every normal time interval since its inception.

The author seems to imply that EEM is a better performing ETF in spite of it’s higher expense ratio. I am still trying to find more information on this issue before I decide to go with one or the other ETF.

Meanwhile, I tried to check up the constituents of each ETF and found this article. Looks like there are differences in the weights these ETFs assign to different markets - although they may be tracking the same markets. That’s probably one of the reasons why there is a difference in their performance.

Any insights into this?

A few days ago, this news on BBC just wouldn’t let me concentrate elsewhere (source):

Zimbabwe’s annual inflation rate slowed in August to 6,592.8% from July’s record of 7,634.8%, according to the Central Statistical Office (CSO).
…
At the end of August, President Mugabe introduced jail terms of up to six months for anyone caught trying to raise prices or wages.

What? 6592.8% inflation! That’s crazy. I think you can actually feel the money becoming lighter and less valuable with the minute. To keep up with this rate of inflation, a person earning $10,000 now, would have to earn $659,280 a year from now in order to maintain his/her lifestyle!

Everything becomes 65.92 times more expensive within a year. If your salary doesn’t increase for whatever reason, you stand become 65.92 times poorer than the previous year without spending a dime!

Man, that just doesn’t sound quite right.

We are so used to a relatively *stable* economy, that we have come to accept certain ideas by default (sort of, “taken for granted” - although we pretend that we look at the historical data and try to predict the future) - for example, inflation rate around 2~4%, interest rates between 0~6%, stock market returns between 8% and 12%, etc. - it almost gives a feeling of complacency at times.

I wonder how our investing minds would react to a Zimbabwe-like economy. If, by some misfortune, we are ever caught in this type of an economic atmosphere, I wonder if we will have the ability to think outside the box.

Anyways, to see how other characteristics of this 6000% inflation economy look like, I checked up some data on the Reserve Bank of Zimbabwe. Here is what I got:

• Exchange rate: 30,000 Zimbabwe Dollars (ZWD) = 1 US Dollar (can currencies fall any lower?)

• Interest rate: Overnight Rate (analogous to Federal Funds Rate in US) = 600% (at this interest rate you will arithmetically “double” your initial investment in about 4 months! - although that doubled amount will only be a fraction of it’s original *value* in the same amount of time.)

It’s obvious that the inflation will override the growth of funds in a savings account by about 10 times (assuming if you get a full 600% on the savings account) - makes a simple savings account an invalid option to park your money, even at that interest rate.

Next, I tried to look for some data on the Zimbabwe stock market. I recently explained how the interest rate cycle and market sentiments go hand-in-hand. With that picture in mind, the 600% interest rate in the background, and with the knowledge that the economy was falling apart, I was expecting terrible scene at the stock market.

However, I was in for a big surprise here. This is what I found about the Zimbabwean stock market (source):

Zimbabwe is in the middle of an economic disintegration, with GDP declining for the seventh consecutive year, half what it was in 2000. Ever since President Mugabe’s disastrous land-reform campaign, the country’s farming, tourism, and gold sectors have collapsed. Unemployment is said to be near 80%.Yet something odd is happening.

The Zimbabwe Stock Exchange (the ZSE) is the best performing stock exchange in the world, the key Zimbabwe Industrials Index up some 595% since the beginning of the year and 12,000% over twelve months. This jump in share prices is far in excess of increases in consumer prices. While the country is crumbling, the Zimbabwean share speculator is keeping up much better than the typical Zimbabwean on the street.

This is probably going to cause a paradigm shift in my thinking about how stock markets react to economic conditions - I was expecting the graph to be exactly opposite! On the basis of conventional investing knowledge in US, there is no way anyone could have predicted that kind of stock market performance - in an economy that’s just out of control, and with lending rates that should be absolutely out of whack with that kind of inflation.

Perhaps, more than the money equations, it’s the geo-political situations that affect the market sentiments. Perhaps, there is more to stock markets than what my tiny brain can comprehend at the moment. Perhaps, it’s just the randomness that people talk about. Whatever.

Yeah.. whatever … I am just glad not to be in Zimbabwe .. I think I would have resorted to gold smuggling by now.

Stuff like this keeps reminding me of Warren Buffet’s ovarian lottery concept.

Presenting the Hemline Theory of stock market performance.

According to Reuters:

Lower hemlines are coming back in fashion for spring and that could spell bad news for the U.S. stock market.

The higher the hemlines, the better the outlook for stocks, according to a popular, but frequently disputed, theory. When hemlines drop, watch out — the Dow Jones Industrial Average is likely to fall, the theory goes.

Bolstering the hemline theory, miniskirts were in vogue and stocks rose in the 1960s.

By the early 1970s, the Arab oil embargo forced Americans to endure gas pump lines, the economy suffered and the popular style was the ankle-length maxiskirt.

I guess someday we can relate stock market performance to the phases of the moon, or to the appearance of some random comet in the sky, or to the height of women’s shoe heels, or perhaps to the number of men getting haircuts in a given month.

Won’t blame you if you want to see more miniskirts.

Nearly four months ago, I mentioned that my portfolio contained about 98% of cash and that I intended to make some efforts towards changing the situation. Now, after some agonizingly slow progress, I have managed to take some concrete steps towards that.

Things started to take shape after I finally (successfully) opened a brokerage account at Zecco. In the three months that followed, my portfolio underwent the following transformation:

[I call it "stocks" as a general term - but they are, in fact, ETFs]

The current portfolio is built entirely of various ETFs (Exchange Traded Funds), which I put together after reading several pieces of articles on several websites and forums. Here is how the different ETFs contribute towards the portfolio:

[To learn more about the symbols, hover or click on these links: SPY, EEM, EWZ, VTI, VWO, IXG, FNI, EFA, ADRE]

I played around with MorningStar’s Instant X-ray tool to understand how this portfolio looks like, in terms of asset allocation, and here is what I got (unfortunately, I did this AFTER I bought all those ETFs) :

MorningStar called this distribution as “conservative” and described it as:

Your portfolio is conservative. An asset mix such as yours normally generates low returns but experiences very little volatility. Financial planners typically recommend these types of mixes for investors who have investment horizons less than three years, are risk averse, or have already saved enough to meet their goals.

However, this assessment was heavily skewed on the conservative side because of the presence of the huge pile of cash. After I removed the cash from the picture, I got this:

Apparently, now it turned out to be an aggressive mix.

Your portfolio is aggressive. An asset mix such as yours normally generates high long-term returns but can be very volatile. Financial planners typically recommend these types of mixes for investors who have investment horizons longer than 10 years, need high returns, and are comfortable with a high level of risk. Note also that your portfolio has greater exposure to foreign stocks than is typical.

That seems to be more like it. This assessment also correctly describes my current temperament with regards to investing. I am just going to “buy and hold” for as long as it is feasible. With sufficient liquid cash still existing in my portfolio, I think I can let these investments marinate for around 20 years (or even more). However, as I keep converting more cash into stocks, I will probably have to tone down the aggression a bit in future.

So that’s how things are at present. So far, it has been a great learning experience, but there are miles to go before things become all nice and rosy.

Now, a quick summary of the amateur mistakes that I committed during this phase of investing:

1. I jumped into buying the ETFs before clearly understanding what it means by “asset allocation”.
2. Ended up buying too much of foreign stock without realizing it - in a way this may turn out to be good in the end, but I need to understand this better.
3. People who are familiar with ETFs will immediately realize that I have two different ETFs that track the same market subset (emerging market ETFs - VWO and EEM) - one of them (EEM) has a higher expense ratio than the other. I completely overlooked this issue.

I intend to address some of the issues before I go on a buying spree again. Towards that, here are some specific short-term goals that I am setting for myself:

1. Learn more about asset allocation. Understand what is “large cap”, “small cap”, and “mid cap” - and how changing these things will distribution will affect the portfolio’s performance.
2. Understand expense ratios of ETFs properly.
3. Understand what is meant by “rebalancing a portfolio” and figure out how to do it in order to reduce the percentage of foreign based ETFs [right now I am just thinking about buying more US based ETFs to do this - my mind cannot think beyond "buy and hold" at this time, so there won't be any selling].
4. Learn to (properly) use MorningStar’s portfolio X-ray tool to analyze and understand how future buying will affect the nature of my portfolio.

Plenty of work to do here.

By the way, feel free to correct me if I have showed signs of not having understood certain concepts correctly - I am still in the learning phase and all feedback will be appreciated.

Meanwhile, I think I am turning into some kind of a bear … ever since I actively started buying ETFs, I have been hoping that the market goes down - so that I can buy some at discount. Bad bear, no cookie for you.

[A quick note: some of you may remember that I recently spent a boat load of cash on our car. In order to compare apples to apples, I haven't considered that decrease in cash when comparing the two portfolios in the first figure]

Let’s talk a little bit about short term interest rates in a layman’s language. The US Federal Reserve adjusts the short term interest rates according to market conditions. The most *popular* of these rates is the Federal Funds Rate - that’s the one you usually hear about on websites, TVs, and newspapers. This rate determines the interest that a bank pays in order to borrow money from another bank. If the Federal Funds rate goes down, banks can borrow the money (from each other) at a lower cost - and that eventually translates into lower borrowing costs for the customers (on various loans, credit cards, etc.,). If the rate goes up, the cost for borrowing money rises - for the banks and eventually for the customers.

Depending on how the economy is performing, the Federal Reserve attempts to adjust (raise or lower) the interest rate to keep it running in an optimal condition. This leads to sort of a interest cycle [it's more like a feedback control loop] which can be explained as below:

Here is a symbolic representation of the cycle:

Use this key to understand the above symbolic interest rate cycle:

	Bernanke worried		Bernanke happy… yeah right!
	Cramer angry		Cramer normal happy

[Watch this video if you are still confused]

Where are we now in the interest rate cycle?

Here is an excerpt from a CBS News article that succinctly describes the current situation.

The fear is that if credit continues to become harder for people and businesses to get, spending and investment will be crimped. That could hurt overall economic growth. In a worst-case scenario, the country could slide into a recession. Credit is the economy’s life blood. It allows people to finance big-ticket purchases such as homes and cars and can help businesses bankroll expansions and other things that can boost hiring …

… With squeezed homeowners finding it difficult to make their mortgage payments or pay them in a timely fashion, foreclosures and delinquencies are soaring and are expected to get worse. Lenders have been forced out of business, and hedge funds and other big investors in subprime mortgage securities also have taken a big financial hit.

This is pretty much indicative of the fact that we are heading towards a cut in the short term interest rates in the near future. In the present scenario, if this doesn’t happen soon, people are going to worried about recession.

This probably means that the market will have a greater tendency to go down in the coming days if there are no indications of reduction in the interest rates (or if there is no improvement in the housing market situation - which is not going to happen anytime soon, so let’s watch the interest rates instead). I guess we are seeing signs of it already - today’s headline on MarketWatch.com:

Dow industrials plunge 200 as investors give in to fear of recession.

I think i will prepare to buy some more ETFs today and in days to come.

… Then you probably have been through more than a dozen panic attacks and at least one major heart attack within the last 10 years.

Here is why. Look at how the S&P 500 index (SPY Exchange Traded Fund) has performed during the last 10 years:

It certainly doesn’t look like a place to be if you get nervous at every minor fall in share prices.

By the way, if you compare the latest market slide - that tiny drop at the rightmost end of the graph - against the major downturns that have occurred earlier, you can see that it’s really not that big of a deal (at least not yet).

So, take heart and this too shall pass.

On a more sobering note, it looks like the S&P 500 has not performed very well when averaged over the last 10 years… and 10 years is a pretty large span of time (or is it just my perception?).

Forget about the rapid ups and downs in the curve - if you invested at random from a period between 1998 ~ 2002, you probably haven’t made much more money than what you would have made in a high interest savings account. If you invested around the year 2000, you may have even *lost* money after taking inflation into consideration. May be these are the people (who invested a lot during 1998 - 2002) who are worrying more about the recent events (?).

Of course, this doesn’t have any bearing on 20-year or 30-year performances, or some other 10-year performances (different time-frames will result in different returns). It’s just that I am just wondering if it’s not a good idea to put most of your money in such an index fund (or probably the stock market as a whole) if you are intending to keep it there for less than 10 years. Especially if you have a weak heart.

I am not a fancy stock market trader and my current practical knowledge about stock trading does not extend much beyond the “buy and hold” strategy of investing.

A few months ago, I mentioned about my almost-all-cash portfolio. Slowly, but surely, I am trying to move some of the cash into the stock market. Because of this, I am in a buying mode at present.

I am probably naive about analyzing the market fluctuation, but in the current situation (with the “buy and hold” thinking and the eagerness to buy more stocks), a fall in stock prices seems like a “grand sale” for me. So when I read headlines like this:

Dow stumbles 280 pts Friday amid broad market sell-off

I get all excited.

To me, that sounds like “stocks on sale“.

It was too late to act on Friday, because I didn’t read about the sell-off soon enough; but, I did place a buying order for a few SPY (an exchange traded fund (ETF) tracking the S&P 500 index) shares which was executed first thing on Monday morning - right before the rally. I got the shares at $143.61 apiece. During my earlier purchase in June, the price was $151 per share. Apparently, I have now effectively reduced my average buying price for the share.

This sounds like “market timing” - a risky game for frequent traders, but I am not too worried about it right now because I am in the buy-and-hold mode. If the price drops further, I am going to buy more aggressively. If the price increases, I will switch to my normal investing frequency, but still keep buying. I am probably more of an opportunist than a market timer.

Also, I may be playing it too safe by buying SPY in these times (instead of individual stocks), but my comfort zone doesn’t extend much beyond SPY (and at times, VWO - Vanguard Emerging markets ETF), so that’s as much as I could take advantage of the situation.

For now, it seems like a good thing that I don’t know how and when to sell.

By the way, I have to mention that Zecco is really making investing fun - it’s been a rather smooth ride with them till now.

Just sharing some interesting statistics about men and women and their general attitude towards investing. The image below is supposedly based on Sharebuilder’s 2007 “Women and Investing Survey” as reported by Seattle Post-Intelligencer (I tried to search for the original survey on Sharebuilder’s website but could not find this particular (2007) version).

It appears from the survey that more men are “confident” and “optimistic” about investing than women.

Similar findings were published in a Sharebuilder survey last year in which it was reported that, in general, only 35% of women surveyed trust themselves to make good investing decisions; whereas 50% of the men were in that category. Here is some data from that presentation (link to PowerPoint file):

Again, it’s clear that more men consider themselves to be “knowledgeable” and “confident” with their investments than women.

Based on these facts, one might quickly jump to the conclusion that men perform better with all their confidence and optimism. However, if you are thinking along those lines, here are some interesting remarks in the same presentation:

• Men tend to embrace investing with gusto. They are self-confident (perhaps to a fault), prefer to engage in the activity frequently and get enjoyment from it.

• Young men are the most cocky.

• They [women] don’t want or need a pitch of immediate riches through the latest big score or hot stock, nor are they much interested in having to fret over their investments every hour of the day. They are practical and want to invest that way.

This is nicely complemented by findings from some older surveys which state that (source):

• “Men tend to be overconfident about their ability to pick stocks that can beat the market,”
• A study of more than 35,000 discount-brokerage customers by economists at the University of California at Davis found that between 1991 and 1997, women’s portfolios earned, on average, 1.4 percentage points more a year than men’s.
• Records of investment clubs reveal an even wider performance gap: Through the end of 1998, all-female clubs had an average compounded lifetime return of 23.8 percent a year, compared with just 19.2 percent for all-male clubs, according to the National Association of Investors Corp., which represents about 37,000 clubs nationwide.

Considering all the characteristics, it is safe to conclude that women, with all their fear and risk averse behavior, are more efficient when it comes to investing - they aren’t spending as much time as men in tracking (and boasting about) their investments and yet they are getting higher returns.

In fact, even if you forget about efficiency for a while, investing is all about getting good returns - and women are ahead in that game.

There are some subtle lessons here for us, my fellow gentlemen.

Updated: Link to the UC Davis study - thanks to TFB @ The Finance Buff.