Yesterday we looked at buying stocks on take-over companies just after the news of the proposed acquistion was announced. We saw that if one had bought the stock at the closing price on the day of the announcement one could reap an average annual rate of return of around 8.7%. (The data was based on analysis of 57 companies during the period between March through July of last year.) At the end of the article, I wondered if one could do better by buying at the opening price. I crunched through the numbers this morning and here are the results:

One of the holy grails in trading is to find companies that may be potential take-over targets because if one can correctly identify them, the rewards can be considerable. A take-over announcement can boost the acquiree’s stock price by 10%-50%, although share increases in the 10%-25% range are usually the norm. That’s nice work if you can get it, but it’s in the getting them where lies the rub. Factors that go into trying to figure out what companies are ripe for the picking include low price to book value, companies in sectors that are undergoing consolidation, and technical factors such as unusual options volume which can be a sign that people are trading on inside information. (It’s illegal but it’s done every day.)

Correctly identifying a potential take-over candidate can be very time-consuming and ultimately unrewarding. More often than not you will be wrong which could wind up costing you a lot of money on many failed speculations. But I got to thinking, what about playing stocks after the take-over has been announced? Can one make any decent money on them, or will it only amount to chump change?

To test out my hypothesis, I looked at 62 companies that announced they were being taken-over between March through July of last year. I set up my simulation to buy each stock at the closing price of the day the take-over was announced. Then I checked the date the stock was acquired and the price at which it was sold. The results actually surprised me. Before I present them, I have to say that the data is based on 57 companies. Those are the ones where the acquisition was completed. In two instances, the deals fell through completely. In one case, the merger was extended and is still pending. In the last two cases, the mergers are still pending but are on shaky ground because of regulatory hurdles in one and a reduced financial outlook in the other.

So, without further ado, here’s what I found:

1. The average time for a merger to complete (from announcement to the final take-over date) was about 4 months with a standard deviation of around 2 1/2 months. This means that 68% of most mergers occur between 1 1/2 and 5 1/2 months. (For you statistical wonks out there, the median was around 3 months.)
2. The average gain/loss per stock was +2.9% over the holding period. This result assumes that an equal number of shares of each stock were purchased at the closing price on the day of the take-over announcement. (This value would be different if an equal dollar amount were bought.) The standard deviation of the gain/loss was 2.75% which means that two-thirds of the stocks ended up gaining between 0.15% and 5.65%. There was one stock that gained 17% because the original offer price was subsequently raised. Two stocks actually lost value. One was due to a merger battle, and I couldn’t find a reason for the other.
3. If we assume that the average holding time for each stock is four months, then this results in an average annual return of 8.7% (2.9% x 3).

You may yawn at an 8.7% return, but basically this is done without incurring a lot of risk. So far, only two of the proposed mergers have fallen through, which is a 3% failure rate. Not bad. There aren’t many portfolios out there that can boast a number even close to being that low. A major drawback to this strategy is that M&A activity is at the mercy of the markets. This means that during down markets such as now and especially during the current credit crisis, M&A activity is reduced. During bull markets, this certainly isn’t the best strategy to use to increase your returns, but it’s still not a bad one especially for those of you who are highly risk averse.

Final Note: The above data was derived from the closing prices, but if you pounce on these at the open, you can probably do a bit better. Hey, that’s not a bad idea. For tomorrow, I’ll look into this further and see if there’s a measurable difference in the rate of return between using the opening price and the closing price, so stick around!

Today we’re stepping out of the ivory tower and wading back into the market moat. I was hoping that today’s market action would be a follow-through on recent upward movement, but unless there’s an end of day rally, it doesn’t look like we’re going to get it.

Last week the volatility index (VIX), a measure of market fear or risk, dropped below its 200dma and has remained there since. That’s a good thing. For my taste, however, it needs to start moving below 20 and stay there before I’ll be convinced that the worst is over. Also, the S&P (SPX) has been toying with its 1400 resistance level, and it will need to break that on heavy volume for me to be a true believer.

There are two high notes. One is that the Dow Transports (DTX), considered to be a leading indicator of market direction, did break through major resistance of 500 last week and has been in an upward trend since the middle of March. In fact, all of the major indices have been trending up since then, as I’m sure you know. The other bright spot is that the Q’s (QQQQ), the Nasdaq 100 tracking stock, also broke its $46 resistance level. I think that if the market can hold through the next Fed meeting on interest rates scheduled for release this coming Wednesday, we may have the beginning of another bull market, albeit a tepid one considering that energy prices continue to rise, unemployment is rising, and the consumer is spending less. These are all factors that will figure into the equation so be careful about backing up your truck because you just might hit a brick wall.

Being wishy-washy is a way to cover one’s butt and there’s a lot of financial pundits out there who are doing just that, but this time I’m giving them a break since the financial crystal ball is very cloudy indeed. One ray of hope that the market may be turning up is to look at the current movement of the major brokerage firms. They’ve been rising stealthily for the past month, and if recent earnings news is any indication, their futures may indeed be bright.

Ever since the four-eyed credit-crunch ogre began to rear its ugly head early last summer, the brokers got whacked, declining 25-50% in value. Most of them put in a double bottom this January and rushed back up only to get beaten down again. Then came March 17th when JP Morgan shocked the investment community by offering a ridiculously low $2/share for Bear-Stearns. The news tanked all of the brokerage stocks, but since then they’ve been staging a rather nice comeback. Three of the major firms, Goldman-Sachs (GS), Morgan Stanley (MS), and Lehman Bros. (LEH), all just reported earnings that beat estimates. Only Merrill-Lynch (MER) reported earnings that were basically in-line. However, that didn’t seem to hurt the stock much as it, too, has been on the rise.

So should you be a buyer of these brokerages? Except for Goldman, I would wait. All of these stocks are still trading below their 200dmas. I’ll be more interested in them when they break overhead resistance on heavier than normal volume: MS at $55, LEH at $50, and MER at $50-$51. I think it was Guy Adami on CNBC’s Fast Money who said about a month ago that Goldman is a screaming buy. (His words.) The company reported good earnings on March 18th and yesterday broke its all-important $180 resistance level. Today, it’s flirting with its 200dma. You go, Guy! (I really wanted to say that.)

Knight Capital (NITE) is my other favorite. The firm surprised Wall Street last week with better than expected earnings, and recently broke its $18 resistance level. The stock is still climbing higher, trading up over a buck since Monday. [Note that most of the major brokerage stocks pay a low dividend except for Knight which pays none.]

What about the online brokers? Most of them have been rising in sync with the institutions, although their charts aren’t quite as compelling. Perhaps this reflects the fact that they didn’t beat earnings estimates as most reported in-line, except for Etrade (ETFC) which reported worse than expected earnings. Right now I’d stay away from this stock, at least until the company can trim the fat and turn around to profitability which analysts think may take at least two quarters. The star of the group is Interactive Brokers (IBKR) which blew out estimates today causing share prices to jump 10%. This is the best banana of the bunch. Both Schwab (SCHW) and TD Ameritrade (AMTD) are rising, but I can’t really say if they’re good buys at this level. Their performance will probably depend on the direction of the overall market.

If you’re like many investors whose portfolios got whacked this year, maybe one way you can get back at your broker is to buy them. Yeah, that’ll show ’em!

Today is the final installment of Professor Pat’s dissertation on Modern Portfolio Theory (MPT). In it, he’ll be looking at the correlation among asset classes and will also provide you with fund recommendations that you can use as proxies with which to construct your own portfolio. But before I hand this over to the Professor, I want to thank him for providing us with his insight into MPT and for generating these tables which involved research trips to the local university’s business library and many hours of computer modeling. I am deeply grateful for his valuable time, knowledge, and effort.

Today is the third installment of Professor Pat’s dissertation on Modern Portfolio Theory (MPT). In it, he’ll be including three other uncorrelated asset classes that can be added to a portfolio that will not only increase returns, but lower risk as well. The floor is all yours, Prof. Pat!

Adding international stocks, bonds, and REITS to your portfolio
In Part II of this article (yesterday) I presented some options for optimum portfolios using six basic asset classes. Today we will examine the effects of adding more alternative asset classes to the list of portfolio options. We will see in quantitative terms how broadening the diversification of an investment portfolio not only increases returns but also lowers risk. Any additional asset classes added for consideration should preferably be uncorrelated or negatively correlated to the other asset classes for best results. The following asset classes meet those criteria:

1. Real Estate Investment Trusts (REITs) performance per the Dimensional Fund Advisors (DFA) U.S. Real Estate Securities Index.
2. International Large Company Stocks per the DFA International Value Index portfolio of non U.S. Stocks.
3. International Bonds composed of the DFA Five-Year Global Fixed Income Index Fund.

Using annual total return performance data for each of these asset classes from 1927 through 2007 to match the data as for the other basic six asset classes as described yesterday, I applied the mathematics of MPT to come up with the following table:

Today we continue with the column of guest blogger Professor Pat who provides us with the second installment of his treatise on Modern Portfolio Theory. Yesterday’s blog provided an introduction to Modern Portfolio Theory (MPT) and today he’ll be discussing how to optimize your portfolio using the results of MPT. Although the Professor doesn’t like to toot his own horn, I just want to say that some of the data presented in the table today and in the next installment are derived from historical data run through the Professor’s own MPT algorithms and won’t be found anywhere except for perhaps in brokerage firms. So lead on, Professor Pat!

In last Thursday’s blog we looked at the concepts of alpha and beta in terms of maximizing portfolio returns while minimizing risk. Those concepts are an integral part of a larger subject known as Modern Portfolio Theory, or MPT. This theory determines how investors should allocate their holdings to achieve a specified return with the least amount of risk. Since my knowledge of MPT is minimal, I thought I’d turn over today’s blog to Professor Pat, a colleague of mine who is well acquainted with MPT and uses it to allocate his own investment portfolio. For the record, Pat is not technically a professor in the usual sense of the word. He doesn’t teach MPT on the university level but his knowledge on the subject is so vast that he probably could. I’m using the term here in its second definition as one who professes or instructs. So, without further ado, I’ll let Professor Pat take it away and perhaps we’ll all learn something from his elegant discourse.

Modern Portfolio Theory (MPT): The Background
Thanks, Dr. K, for letting me present the ideas behind MPT. Since this is such a large subject, I’m going to split it up into several segments. Today, I want to describe the theory in general and its importance to you, the investor. In subsequent columns, I’ll present concrete strategies using results that have not been published anywhere that you can easily implement in constructing your own investment portfolio.

Modern Portfolio Theory (MPT) was first conceived by Harry Markowitz in 1952. For his inspiration and hard work he was awarded the 1990 Nobel Prize in Economics. Markowitz proposed that investors should be concerned not just with investment returns but also with investment risk, and put forth a strategy on how to achieve optimum performance using a mathematically derived allocation of asset classes.

MPT asserts that investors could and should balance the returns they receive on their investment portfolios with the risks those investments present. As such, and for the first time, a way to actually quantify the notion of risk was available. The new idea was that risk could be equated with volatility or the variation in returns from one time period to the next. The beauty of MPT is that it was also now possible to take this one step further and mathematically determine an optimum investment portfolio that delivers the desired long-term rate of return while simultaneously minimizing risk. The benefits of portfolio diversification in terms of risk reduction could now be mathematically derived. [Note from Dr. K: The math used in MPT is quite hairy and is beyond the scope of this discussion. For those of you who are mathematically inclined, you can research this further. Wikipedia gives a good overview of the math used in MPT. Good luck!)

An investment portfolio consists of various asset classes, some of which appreciate and some of which may depreciate within any specified time interval. The rate of change, or volatility, in the value of each class varies as well. Some investments move up and down together, some move up when others move down, while others are completely uncorrelated to each other. MPT takes advantage of this fact to determine not only which investments to invest in but how much of each you should hold relative to one another.

MPT can also be thought of as a type of portfolio insurance. As an investor, you hope that all of your investments will increase but you also know that this is an unrealistic expectation. MPT insures your portfolio against unreasonable losses by holding asset classes that can counteract losses in one class with gains in another. The way to achieve this is to select investment vehicles that are uncorrelated with each other. (More on that later.) A properly diversified portfolio also includes relatively low yielding assets (like treasuries) that can be counted on to produce steady and reliable gains. An important assumption of MPT is that the future will, on average, be just like the past.

MPT: The Theory
The techniques that are used in MPT to solve the optimum asset allocation problem is a branch of mathematics known as quadratic programming. There are two inputs to this program: 1. The actual historical returns of the various candidate assets input as a time series, and 2. The desired average rate of return that portfolio is expected to produce. The output of the calculations is the percentage to be ascribed to each asset class so that the entire portfolio will produce the input return while minimizing risk. MPT quantifies that level of risk with a number called the standard deviation.

The standard deviation, denoted in statistical terms by the Greek letter σ, is a number that provides a bracket range for the desired return. One standard deviation represents approximately 68% of the values around the the expected outcome. A basic assumption in MPT is that investment returns follow a pattern known as a normal distribution commonly found in natural processes.* Graphically, it forms a shape that looks like a bell as depicted in the illustration below. For example, if the desired annual rate of return is 10%, MPT might reveal a certain asset allocation strategy that would result in a minimum standard deviation of 11.7%. This means that approximately 68% of the time the actual return in any one year would fall in a range from -1.7% to +21.7%. (10% +/- 11.7%) The normal distribution also tells us that about 95% of the time the return will be the average return plus or minus two standard deviations, or between -13.4% to 33.4% in this example. The image below depicts these concepts. The dark blue region is one standard deviation,and the light blue region extends to two standard deviations. The symbol μ on the image is the average rate of return, or 10% in our example.

MPT is a useful tool for investors who prefer to remain somewhat passive in their investment activities. That is, they are not concerned with market timing. The optimum asset allocation technique tells them that they can remain comfortable with fluctuations in the market and limit their activities to quarterly rebalancing to preserve the correct allocations following increases or decreases in the value of individual assets held.

When we get to presenting the reality of these results, the data will confirm what everyone already knows: there is no such thing as a free lunch. That is, the higher the rate of return you wish to achieve, the more risk you have to be willing to take on. But we will see with numbers just how much more risk we’ll have to take to achieve those higher returns or how much return we need to give up to achieve more safety.

The next installment in this series will present actual results using common investment classes and will show you how to assemble a portfolio needed to achieve your desired rate of return. Stay tuned!

*Dr. K Note: Post-Modern Portfolio Theory (PMPT) challenges this assumption, but for right now, it’s a good-enough one.

In my blog on March 17th, I constructed a portfolio of six high-paying dividend stocks and wrote the April covered calls against them. Since today is options expiration, I want to examine the portfolio and see how we did.

Since all of our options expired in the money, all of our stocks will be assigned. That means that if we want to own them again, we’ll have to go out and buy more. It also means that we didn’t get to participate in any price movement above the strike price which is unfortunate since all of the stocks did very well.

So what have we learned from this lesson? That covered calls aren’t such a good idea? Well, yes and no. We would have done a lot better if we had waited to sell calls when the stock was making a new high, but if course one never knows when a stock is at a local high or is poised to go higher. Certainly, when the stock is taking a breather is not the best time to cover.

If you watch CNBC or read some of the financial journals, you’ve probably stumbled across the word alpha. Most non-institutional investors don’t know what it means but they should since the attainment of alpha is the goal of every investor, whether he or she realizes it or not. So what is alpha? Alpha is nothing more than the excess return of a stock, portfolio, or fund over a given benchmark. I won’t bore you with the mathematical equation for alpha, but it takes into account the price risk, or volatility of the stock or fund and compares its risk-adjusted performance to a benchmark, usually the S&P 500. The price risk is given by a coefficient named beta. Sometimes you’ll see the beta of a stock listed under the company’s profile. Beta is a measure of a stock price’s volatility as compared with the overall market. Since the S&P is the typical benchmark, it has a beta of 1. A beta of 2.50 represents price movement that is 150% more volatile than the market; a beta of 0.50 represents a movement that is half as volatile as the market. Beta can be viewed as a measure of risk so that riskier stocks such as high-tech stocks typically have beta’s greater than 1 while less risky stocks like utilities have betas less than 1. With me so far? Good.

Now let’s get back to alpha. In the hedge fund world, alpha is of primary importance. Hedge fund managers are rated according to how much alpha their fund generates. (They’re also rated according to their Sharpe ratio which is defined below.) A positive alpha of 1.0 means that the fund outperformed its benchmark index by 1%, and a negative alpha of -1.0 means that it underperfomed it by 1%. Alpha can be viewed as a measure of the fund manager’s ability to generate profits in excess of market returns. This isn’t that easy to do and sometimes the process of seeking alpha requires taking substantial risks which is why a lot of hedge funds that have invested heavily in mortgage-backed debt are in serious trouble right now.

Fund managers are usually paid in accordance to how much alpha their fund generates. The higher the alpha, the higher their fees (usually). Hedge fund managers with stellar alphas and high Sharpe ratios can take up to 50% of the profits! That’s why many of them have homes in the Hamptons worth tens of millions of dollars, bid up oil paintings to ridiculous prices at Sotheby’s, and flitter to and fro on private jets. But hey, if you’re a high net worth individual with money in their funds, you’re probably hob-nobbing with them, too.

If you’re not a part of the jet-set, is there a way that an individual investor can increase alpha without increasing portfolio risk? Yes, via the theory known as “portable alpha.” In essence what this means is that an investor would invest some of his portfolio in securities (or other instruments) that have no correlation with the existing portfolio. (They’re separating beta from alpha.) This typically involves leveraging part of the portolio using futures. I know that most people shy away from futures, but it’s not as formidable as it sounds. Really. Let’s look at an example.

Adding Alpha without Adding Risk
Let’s say you have a portfolio of $200,000 invested in Treasury bonds (which are essentially risk-free) that are currently yielding 4%. You’re not happy with that rate of return and would like to increase it without adding risk. You think that although the S&P has been lousy, things might be looking up and you’d like to invest 30% of your portfolio into the index. You believe that a 10% return on the S&P for this year is reasonable, if not even a bit conservative. So, instead of investing $60,000 into an S&P index fund, a better approach is to buy $60,000 worth of the S&P Emini futures. Although margin requirements for buying futures varies among brokers, we’ll use 10% here. (My broker charges about 7%.) What this means is that you’ll only need $6000 to buy the futures. So what do you do with the leftover $54,000? You buy more treasuries.

These leaves us now with a portfolio of $194,000 in treasuries and $6000 allocated to margin for the futures. At the end of the year assuming everything works out as planned, your rate of return will be 6.9% instead of 4% had you only owned treasuries. (4% x $194000 + 10% x $60000) You’ve increased your return by nearly 3% without adding portfolio risk. (Actually, your return will be slightly less since there’s a built-in premium to futures contracts.)

However, you do take on another risk–that of event risk. If the stock market takes a nasty drop, you might be faced with a margin call in your futures account. In the event that this happens, you’ll need to deposit more money into your margin account. To do this will require you selling some of your T-bonds to make up the difference. If the market corrects and you have now excess capital in your margin account, you can reinvest that into treasuries. Your new projected rate of return will be different and probably less than expected depending on the going T-bill rates.

That’s it for the example. I want to emphasize that I’ve only scratched the surface on the discussion of alpha and beta. People have won Nobel prizes developing these concepts, so take heart if you don’t quite understand them, but be assured that institutions do.

Portable alpha is used regularly by fund managers to add alpha to their funds without increasing risk. They do this by using futures to generate money that they can use to purchase other instruments they feel will generate positive returns, thus increasing alpha. And now, so can you!

The Sharpe Ratio
The Sharpe ratio is a measure of risk-adjusted return. Essentially, the Sharpe ratio tells us whether returns are due to smart investment decisions or are a result of excess risk. The higher the ratio, the safer the strategy. (Sharpe ratios greater than one are considered to be good.) It can viewed as a measure of the fund manager’s consistency. Two funds may have the same alpha, but the one with the higher Sharpe ratio has better risk-adjusted performance. If you’re comparing funds with similar focus and performance, look at their Sharpe ratios. The ones with the highest ratios will be the safer investments, although past performance is no guarantee of future results…