tag:blogger.com,1999:blog-33951639885503220092017-07-23T02:04:25.818-07:00Stock ArcherShooting for consistent investment returnsChenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.comBlogger18125tag:blogger.com,1999:blog-3395163988550322009.post-43302279114317586432014-02-10T14:00:00.000-08:002014-02-10T14:00:02.383-08:00Front-loading your 401kThe most common way of contributing towards your 401k is by setting aside a percentage of each paycheck. With a bi-weekly paycheck (once every two weeks), to max out the annual contribution limit of $17,500 (as of 2014), you would put in $673.08 per paycheck. While this strategy has many benefits in its simplicity and amortization, it is not the most optimal in terms of maximizing the long-term value of your retirement account. <br /><br />Time is your most valuable asset in both saving and investing. If you are certain about how much you will contribute this year, then it is better to make that contribution as early on in the year as possible. This will give you a little extra time to let that money grow. <br /><br />How much growth? Let's compare the two extreme examples: loading your 401k at the beginning of year versus loading it all at the end of the year. The difference between the two is <b>a whole year of compounding</b>. At a 10% growth rate, a front-loading a $10,000 contribution would net you an extra $1,000 by the end of the year. Assuming a consistent growth rate, that extra $1,000 will become over $2,593 in 10 years and over $17,000 in 30 years. And not only that, but you'll be able to reap the same rewards each year. <br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-o2wLjoNCl5w/UvilLeaVPTI/AAAAAAAAARg/BekFYTI-Ryg/s1600/401k_contribution_strategies.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-o2wLjoNCl5w/UvilLeaVPTI/AAAAAAAAARg/BekFYTI-Ryg/s1600/401k_contribution_strategies.png" height="275" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Example graph of net 401k value using each of the three contribution strategies assuming the same total yearly contributions.</td></tr></tbody></table><br />If you compare front-loading to an amortized contribution over the course of a year, the benefit is approximately half of the above - still a very significant amount. <br /><br />However, there are a few drawbacks that come with this more aggressive strategy: <br /><ol><li>You must know how much you will contribute ahead of time.</li><li>You must have an adequate amount of money saved up at the beginning of the year since your paycheck will be significantly diminished.</li><li>Negative economic growth will also be amplified.</li></ol>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com4tag:blogger.com,1999:blog-3395163988550322009.post-414708666984957562014-01-28T17:26:00.002-08:002014-01-28T17:32:29.912-08:00Optimizing the asset allocation of your portfolio (part 1)Suppose you have \( n \) investment opportunities, each with its own rate of return distribution. How should you allocate your resources so that you maximize your long-term return?<br /><br />At first glance, it seems optimal to put everything into the investment with the highest average ROI. It is the best performer after all and so we'd expect it to do just well in the future. The issue with this allocation strategy is that it is highly susceptible to <a href="http://mathworld.wolfram.com/GamblersRuin.html">gambler's ruin</a>. That is to say, one bad day or year in that particular investment can completely wipe your whole portfolio out. It is this multiplicative nature of the rate of return that makes investing both a highly lucrative and a highly volatile business.<br /><br />So what is the correct allocation strategy so that you minimize your risk and maximize your overall return? The answer is in the generalization of the <a href="http://en.wikipedia.org/wiki/Kelly_criterion">Kelly criterion</a>.<br /><br />For this first part, let's restrict the problem to that of one investment opportunity. That is to say, you have the choice of what fraction \( f \) of your portfolio to put into this one investment (keeping the rest in cash). It turns out that the optimal solution is of the form \[ f = \frac{\mu}{\sigma^2} \] where \( \mu \) is the mean rate of return and \( \sigma^2 \) is the standard deviation.<br /><br />Suppose we start out with \( V \) dollars and this investment has a randomly distributed rate of return of \( R \) over a given time period. We wish to find the allocation fraction \( f \) that maximizes our expected long-run rate of return. Let \( r_1, r_2, \dots \) denote the portfolio return for each time period. Then our asset value after \( t \) periods is \[ V_t = V \times (1 + r_1) \times (1 + r_2) \times \dots \times (1 + r_n) \] As usual, multiplication is difficult, so let's maximize the expected log value \[ \log V_t = \log V + \sum_{i=1}^t \log(1 + r_i) \] Taking the expectation of this (letting \( X \) be a random variable representing our portfolio return), we get \[ \begin{align*} E[\log V_t] &= \log V + \sum_{i=1}^t E[\log(1+X)] \\ &= \log V + t \times E[\log(1+X)] \end{align*} \] Since \( \log V \) and \( t \) are constant, we simply need to maximize \( E[\log(1+X)] \). Expressing \( X \) in terms \( f \) and \( R \): \[ \begin{align*} 1 + X &= (1-f) + (1 + R) \times f \\ &= 1 + fR \\ E[\log(1+X)] &= E[\log(1 + fR)] \end{align*} \] To simplify this further, we will use the second-order Taylor expansion of the logarithm \( \log(1+x) = x - \frac{1}{2} x^2 + O(x^3) \). Thus we have that \[ \begin{align*} E[\log(1 + fR)] &= E\left[ fR - \frac{1}{2} (fR)^2 + O((fR)^3) \right] \\ &= E[R] f - \frac{E[R^2]}{2} f^2 + O(f^3) \end{align*} \] To maximize this, we take the derivative with respect to \( f \) and set it equal to 0 \[ \begin{align*} 0 &= \frac{\partial}{\partial f} E[\log(1 + fR)] \\ &= E[R] - E[R^2] f + O(f^2) \end{align*} \] To a first-order approximation, we have that \[ \boxed{f \approx = \frac{E[R]}{E[R^2]}} \] i.e. you should allocate according to the ratio of the first and second raw moments of the distribution of returns. A quick sanity check verifies this approximation since a higher mean and lower variance leads to a higher allocation fraction.<br /><br />If you have the third-moment, you can solve the quadratic to go up to a second-order approximation.<br /><br />Also note that there are two other critical points for the boundaries: \( f=0 \) and \( f=1 \), which may be the correct solutions for some extreme distributions.Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-71824288716701286672014-01-06T14:33:00.000-08:002014-01-06T14:44:41.661-08:00Dividend Discount Model<i>This is part of a series on <a href="http://www.stockarcher.com/2012/08/valuation-techniques.html">valuation techniques</a>.</i><br /><br />The fundamental reason why stocks are a vehicle for investment is that they represent a fractional ownership of a company and thus allow you to partake in that fraction of the profits. These profits, called dividends, are typically distributed once per quarter (i.e. four times a year) and are directly proportional to the number of shares that you own. If we have perfect information of future dividends, then we can compute the present value of a share of the company via discounting. <br /><br />Suppose I have a constant <a href="http://en.wikipedia.org/wiki/Cost_of_capital">cost of capital</a> (also called the discount rate) of \(r\), i.e. the opportunity cost of 1 dollar over one year is \(1+r\) dollars. And for simplicity, let's say dividends are distributed yearly, starting tomorrow, at \(D_0, D_1, D_2, \dots\) dollars per share. Then the value (to me) of a share is \[ V = D_0 + \frac{D_1}{1+r} + \frac{D_2}{(1+r)^2} + \dots \] If the dividends are constant at \(D\), then this simplifies to a simple geometric series \[ \begin{align*} V &= D \left(1 + \frac{1}{1+r} + \frac{1}{(1+r)^2} + \dots\right) \\ &= \left(\frac{1}{1 - \frac{1}{1+r}}\right) D \\ &= \boxed{\left(\frac{1+r}{r}\right) D} \end{align*} \] If instead the dividends grow linearly at a rate of \(m\), then we have that \[ V = D + \frac{D+m}{1+r} + \frac{D+2m}{(1+r)^2} + \dots \] Then we use the standard technique for simplifying such expressions \[ \begin{align*} \left(\frac{1}{1+r}\right) V &= \frac{D}{1+r} + \frac{D+m}{(1+r)^2} + \dots \\ \left(1 - \frac{1}{1+r}\right) V &= D + \frac{m}{1+r} + \frac{m}{(1+r)^2} + \dots \\ \left(\frac{r}{1+r}\right) V &= D + \frac{m}{r} \\ V &= \boxed{\left(\frac{1+r}{r}\right) \left(D + \frac{m}{r}\right)} \end{align*} \] Finally, let's consider the case where the dividends grow exponentially at a rate of \(g\) \[ \begin{align*} V &= D + \frac{(1+g) D}{1+r} + \frac{(1+g)^2 D}{(1+r)^2} + \dots \\ &= D \left(1 + \frac{1+g}{1+r} + \frac{(1+g)^2}{(1+r)^2} + \dots \right) \\ &= \boxed{\left(\frac{1+r}{r-g}\right) D} \end{align*} \] It is worth noting that these computations only reflect the value of a stock for a given person's or organization's discount rate. The actual price of a stock is a function of supply and demand, i.e. the distribution of values as computed by everyone in the market.<br /><br />Furthermore, having perfect knowledge of future dividend distributions is, of course, impossible. However, it can be reasonably approximated for certain classes of stocks, such as blue chips. For example, energy companies like Pepco (POM) and PG&E (PCG) have had very consistent dividends over the course of their lifetimes and can be expected to continue such trends in the future.<br /><br />Perhaps also of interest, we assumed that the first dividend would be distributed the very next day. This reflects the <i>maximum value</i> of the stock to me. The minimum value is achieved the day after a dividend distribution. And the difference between these two values is given by \(D_i\) (i.e. the value will fall by \(D_i\) after the dividend is distributed). This can give rise to some arbitrage opportunities if the market is inefficient at such pricing.Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-87104589176750689082013-02-13T23:12:00.000-08:002013-02-13T23:30:58.354-08:00Portfolio Update (6 months later)<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-nO4VwKE5nHk/URyL6DwIpQI/AAAAAAAAAQA/FrOecNKx1DY/s1600/6months.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="216" src="http://3.bp.blogspot.com/-nO4VwKE5nHk/URyL6DwIpQI/AAAAAAAAAQA/FrOecNKx1DY/s400/6months.PNG" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">My portfolio gains versus the S&P, Dow, and NASDAQ.</td></tr></tbody></table>It's been about 6 months now after I bought <a href="http://www.stockarcher.com/2012/08/the-first-stocks.html">my first round</a> of stocks. Overall, my portfolio has performed consistently well and netted a total return of 12% so far, which amounts to about $600 of passive, tax-free income. In this post, I will summarize the results below with a bit of commentary.<br /><br />First, let me go over my current portfolio as well as some positions that I've closed since my initial purchase.<br /><br /><table class="mytable"><thead><tr><th>Company</th><th>Ticker</th><th>Status</th><th>% Gain</th></tr></thead><tbody><tr class="green"><td>Cisco Systems Inc.</td><td>CSCO</td><td>Closed</td><td>16%</td></tr><tr class="green"><td>Citigroup Inc.</td><td>C</td><td>Closed</td><td>14%</td></tr><tr class="red"><td>Hewlett-Packard Company</td><td>HPQ</td><td>Open</td><td>-3%</td></tr><tr class="red"><td>Intel Corporation</td><td>INTC</td><td>Open</td><td>-8%</td></tr><tr class="green"><td>JetBlue Airways Corporation</td><td>JBLU</td><td>Open</td><td>21%</td></tr><tr class="green"><td>JPMorgan Chase & Co.</td><td>JPM</td><td>Closed</td><td>8%</td></tr><tr class="green"><td>Knight Capital Group Inc.</td><td>KCG</td><td>Open</td><td>24%</td></tr><tr class="green"><td>NRG Energy Inc.</td><td>NRG</td><td>Open</td><td>17%</td></tr><tr class="green"><td>Office Depot Inc.</td><td>ODP</td><td>Closed</td><td>14%</td></tr><tr class="green"><td>Pepco Holdings, Inc.</td><td>POM</td><td>Open</td><td>2%</td></tr><tr class="red"><td>PG&E Corporation</td><td>PCG</td><td>Open</td><td>-7%</td></tr><tr class="green"><td>Safeway Inc.</td><td>SWY</td><td>Open</td><td>32%</td></tr><tr class="green"><td>Staples, Inc.</td><td>SPLS</td><td>Closed</td><td>9%</td></tr><tr class="green"><td>Xerox Corporation</td><td>XRX</td><td>Open</td><td>16%</td></tr></tbody></table><br />As you can see, I closed positions in Cisco, Citigroup, JPMorgan Chase, Office Depot, and Staples. <a name='more'></a><br /><br />Cisco was one of the very first companies that I invested in and was mainly for testing the waters. I sold it at about $19 once I hit the 15% profit mark. While it currently sits at $21, I didn't really do a thorough valuation so I have no qualms about selling it early so that I can reinvest my cash elsewhere.<br /><br />I bought Citigroup in August 2012 when the price had stabilized after falling significantly. That caught my attention and after doing an initial valuation, I found it to have very solid fundamentals. Plus, as a Citibank customer, I have been extremely satisfied with their banking service and their technology. I sold it shortly thereafter in October after a modest gain at $35. Currently it sits at $44. I'm not sure what to make of this. I sold it because I read that the financials of financial firms can be misleading due to the various ways that the balance sheet can be manipulated. I didn't want to take a risk so I sold it early. Maybe a slight regret after seeing how the stock has been doing, but I'd rather play it safe.<br /><br />JPMorgan was a similar situation to Citigroup. I did not want to be involved in any company whose business I do not fully understand.<br /><br />I bought Office Depot and Staples in August 2012 after office supply stocks had been falling steadily for 6 months. I happened to get extremely lucky and bought just as they started rising again. But regardless, I found that they were significantly undervalued at the time despite concerns of losing business to things like online retailers. I sold them after they had risen past my margin of error. In retrospect, they had risen <i>far</i> further than that, but again, hindsight is 20-20.<br /><br />Most of my currently open positions that have netted gains are pretty straightforward: JetBlue, NRG Energy, Pepco, Safeway, Xerox. All of them had solid fundamental numbers, a good outlook, and (aside from NRG) products and services that I am personally happy with.<br /><br />You may have noticed that I left out Knights Capital Group. I will admit, this particular stock was my little "experiment" (read: gamble). There was a huge fiasco regarding the company on August 1, 2012 that disrupted several companies in the NYSE and caused them to lose over $400 million. As a result, the stock price plummeted and I wanted to test to see if it was a market overreaction. I figure that as one of the largest trading firms on Wall Street, it must be able to get back on its feet and resume its business. This was completely my intuition and it happened to be correct.<br /><br />Now, we arrive at the trickiest and most important part of the portfolio: the losses. I have three stocks that are currently sitting on losses: HP, Intel, and PG&E.<br /><br />I bought HP after doing some <a href="http://www.stockarcher.com/2012/08/hewlett-packard-hpq-qualitative-analysis.html">basic fundamental analysis</a>. The company has been plagued with a lot of problems, both external market forces and internal organizational issues. I found that the market forces (i.e. declining PC and printer sales) were not enough to justify its low price. However, a lot of organizational changes within the company in addition to some weak earnings in the past two quarters have caused the price to dip quite far down. However, it has been recovering steadily since December 2012 so I am still optimistic and confident in my analysis. Despite all of the financial problems HP faces, it still gives out a regular 1% quarterly dividend, which is a positive sign and offsets some of the recent losses. I plan to invest in the long term, so I'm not particularly worried. I will hold onto the stock for 20 years if I have to.<br /><br />Intel also faced some earnings disappointments in the past quarter or so. The price dipped significantly before I bought it so I figured it would be a good time to enter. Intel has proven to be at the forefront of semiconductor technology time and time again and I don't see any good reason why it would not be a solid investment for the future. The CPU isn't going anywhere and Intel has also had big successes with their integrated graphics cards. It also gives out a 1% quarterly dividend as icing on the cake.<br /><br />Finally, we have PG&E. I wanted about 20% of my portfolio to be in very consistent, solid companies with a nice dividend. I figured that energy would be a good place to put that money. I suspect that I just got unlucky with the timing of buying the stock. These minor price fluctuations aside, it gives over 1% in dividends quarterly. I am happy with their service and think that the energy needs of the West coast isn't going to alter considerably. If anything, it will go up in the coming years. There are some government regulations surrounding energy companies, so it is unclear to me how this will affect the company's profits. All-in-all, this was just a money dump for me.<br /><br />Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-13817768748024894632012-09-18T20:02:00.000-07:002012-09-19T01:44:31.009-07:00Modeling Price FluctuationsThe premise of this post is that the movements in price of a security (e.g. stocks, bonds) can be viewed as a random process. Whether or not this is a valid assumption is somewhat of a philosophical question. The price of a security entirely depends on the factors of supply and demand, which are in turn deterministically governed by a multitude of more subtle factors. But like the outcome of a flip of a coin, which is completely determined by the equations of physics and the parameters of the system, such processes are much to complex to analyze in full generality. As a result, we model it as a stochastic process whose variance comes from all of these latent factors.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-etp7BaTvYKE/UFkf5qU3KoI/AAAAAAAAAOg/gONCmPe7gFo/s1600/10walks.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="209" src="http://1.bp.blogspot.com/-etp7BaTvYKE/UFkf5qU3KoI/AAAAAAAAAOg/gONCmPe7gFo/s320/10walks.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">An illustration of random walks</td></tr></tbody></table> <h3>Problem Statement and Assumptions</h3>We are given the initial price \(P_0\) and we want to make inferences about the future stock price \(P_T\). The random variables \(P_i\) must also be non-negative. The time scale here is arbitrary and can be made as large or small as necessary.<br /><br />Our key assumption here is that the changes in price are <a href="http://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables">independent and identically distributed</a> (iid). We characterize the price change as the ratio \[C_i = \frac{P_i}{P_{i-1}}\] Note that we didn't use a straightforward difference (\(P_i-P_{i-1}\)). The reason is because the difference most certainly isn't iid (a price of $1 has <a href="http://en.wikipedia.org/wiki/Support_(mathematics)">support</a> on \([-1,\infty]\) whereas a price of $2 has support on \([-2,\infty]\)). You'll notice that our characterization corresponds to a <i>percentage</i> difference (plus one).<br /><br /> <h3>The Normal Distribution</h3>The <a href="http://mathworld.wolfram.com/NormalDistribution.html">normal distribution</a> (also known as the bell curve, the Gaussian, etc.) is ubiquitous in modeling random variables. And so it would be reasonable to conjecture that \(P_T\) is normally distributed. \[ f_{\mu,\sigma^2}(x) = \frac{1}{\sqrt{2\pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} \] <table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-aMXsiXjm9to/UFkfjM9z-mI/AAAAAAAAAOU/2BA8FzMa_zA/s1600/normal.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="http://3.bp.blogspot.com/-aMXsiXjm9to/UFkfjM9z-mI/AAAAAAAAAOU/2BA8FzMa_zA/s320/normal.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">The normal distribution</td></tr></tbody></table><br />However in a similar vein as to why we didn't use the difference in price as our characterization of change, the normal distribution doesn't have the correct support. If we had used the distribution as our model, we would have found that the model would assign a positive probability to the future price being less than 0.<br /><br /> <h3>Logarithms to the Rescue</h3>Okay, let's actually do the math without resorting to guessing. The price \(P_{1}\) can be expressed as \(C_1 \times P_0\), and \(P_{2}\) as \(C_2 \times P_1\), and so on. Inductively continuing this process yields \[ P_T = C_T C_{T-1} \dots C_1 P_0 \] Thus we have that \(P_T\) is proportional to the product of \(T\) iid random variables. The trick is to turn this product into a sum so then we can apply the <a href="http://mathworld.wolfram.com/CentralLimitTheorem.html">central limit theorem</a>. We do this by taking the logarithm of both sides \[ \begin{align*} \log P_T &= \log(C_T C_{T-1} \dots C_1 P_0) \\ &= \log C_T + \log C_{T-1} + \dots + \log C_1 + \log P_0 \\ &\thicksim N(\mu,\sigma^2) \end{align*} \] Since the \(C_i\)s are iid, their logarithms must also be iid. Now we can apply the central limit theorem to see that \(\log P_T\) converges to a normal distribution! The exponential of a normal distribution is known as the <a href="http://en.wikipedia.org/wiki/Log-normal_distribution">log-normal distribution</a> so \(P_T\) is log-normal. \[ g_{\mu,\sigma^2}(x) = \frac{1}{x\sqrt{2\pi \sigma^2}}e^{-\frac{(\log x-\mu)^2}{2\sigma^2}} \] <table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-3lkJ_F8iGCI/UFke17h7mYI/AAAAAAAAAOI/vPjVVxTvqZw/s1600/Lognormal.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="199" src="http://2.bp.blogspot.com/-3lkJ_F8iGCI/UFke17h7mYI/AAAAAAAAAOI/vPjVVxTvqZw/s320/Lognormal.gif" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">The log-normal distribution</td></tr></tbody></table><br />As a sanity check, we see that the support of the log-normal is on \((0,\infty]\) as expected.<br /><br /> <h3>But wait there's more!</h3>In the beginning we noted that the choice of time-scale is arbitrary. By considering smaller time scales, we can view our \(C_i\)s as the product of finer grained ratios. Thus by the same argument as above, each of the \(C_i\)s must also be log-normally distributed.<br /><br /> <h3>Experimental Results</h3>I took ~3200 closing stock prices of Microsoft Corporation (MSFT), courtesy of <a href="http://finance.yahoo.com/">Yahoo! Finance</a> from January 3, 2000 to today. I imported the data set into <a href="http://www.r-project.org/">R</a> and calculated the logarithms of the \(C_i\)s. I then plotted a normalized histogram of the results and overlaid the theoretical normal distribution on top of it. The plot is shown below:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-0MraPTGZNN8/UFkqB6EQOaI/AAAAAAAAAO0/cwmVj0tSc1I/s1600/logC.png" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="262" width="320" src="http://3.bp.blogspot.com/-0MraPTGZNN8/UFkqB6EQOaI/AAAAAAAAAO0/cwmVj0tSc1I/s320/logC.png" /></a></div><br /> <h3>Discussion</h3>As you can see, the theoretical distribution doesn't fit our data exactly. The overall shape is correct, but our derived distribution puts too little mass in the center and too little on the edges.<br /><br />We now must go back to our assumptions for further scrutiny. Our main assumption was that the changes are independent and identically distributed. In fact, it has been shown in many research papers (e.g. <a href="http://schwert.ssb.rochester.edu/jfin89.pdf">Schwert 1989</a>) that the changes are <i>not</i> identically distributed, but rather vary over time. However, the central limit theorem is fairly robust in practice. Especially under a sufficiently large of samples, each "new" distribution will eventually sum to normality (and the sum of normal distributions is normal).<br /><br />I suspect that the deviation from normality is primarily caused by dependence between samples. The heavy tails can be explained by the fact that a large drop/rise in price today may be correlated to another drop/rise in the near future. This is particularly true during times of extreme depression or economic growth. A similar argument can be made about the excess of mass in the center of the distribution. It is conceivable that times of low volatility will be followed by another time of low volatility.<br /><br /> <h3>Conclusion</h3>While our model might not be perfect in practice, it is a good first step to developing a better model. I think what you should take from this is that it is important to experimentally verify your models rather than blindly taking your assumptions as ground truths. I'll conclude this post with a few closing remarks: <ul><li>Many people actually do use the normal distribution to model changes in prices despite the obvious objections stated above. One can justify this by noting that the distribution of \(C_i\) in practice is usually close to 0. Thus the first order approximation \(e^x \approx 1+x\) is fairly accurate.</li><li>The histogram and fit shown above can be reproduced for almost any stock or index (e.g. S&P 500, DJIA, NASDAQ)</li><li>R is a great piece of software but has god awful tutorials and documentation. I am not in a position to recommend it yet because of this.</li></ul>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-65202177342269106852012-08-31T14:48:00.001-07:002012-08-31T18:32:48.303-07:00Valuation Techniques: Liquidation value<i>This is part of a series on <a href="http://www.stockarcher.com/2012/08/valuation-techniques.html">valuation techniques</a>.</i><br /><br />When we talk about the value of a company, there are two fundamental components associated with it: assets and income. Very simplistically, we can view a company as a black box holding assets that grow over time in a stochastic manner.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-3pYzioNOg9o/UEFCK2dBz_I/AAAAAAAAAN0/sM-piAA7L1c/s1600/going-out-of-business1.JPG" imageanchor="1" style="clear:right; float:right; margin-left:1em; margin-bottom:1em"><img border="0" height="240" width="320" src="http://4.bp.blogspot.com/-3pYzioNOg9o/UEFCK2dBz_I/AAAAAAAAAN0/sM-piAA7L1c/s320/going-out-of-business1.JPG" /></a></div>I will define the <b>liquidation value</b> of a company as the net worth of a company's tangible assets in event of a bankruptcy.<br /><br /><h3>How it useful?</h3>Unfortunately, liquidation value isn't an accurate measurement of the intrinsic value of a company. Then how is it at all useful to an investor?<br /><br />Neither accuracy nor precision are necessary conditions to make a profit in investing. The only necessary condition to successful investing is <b>arbitrage</b>. As long as we can buy a security for less than what it's worth, a profit can be made. Even if we don't know precisely what a security is worth, we need only to establish sufficiently tight <b>lower bounds</b> on the price to determine if it is a worthwhile investment.<br /><br />That is exactly what the liquidation value is meant to provide. While it is difficult to predict the future earnings of a company, we still have a lower bound given by what the company currently holds. These figures are reported regularly on the balance sheet in financial statements.<br /><br /><a name='more'></a><h3>Looking at the balance sheet</h3>Most financial services (Google Finance, Yahoo Finance, Bloomberg, etc) will provide a summary of a company's recent balance sheets. Knowing how to properly read a balance sheet is critical to evaluating the current assets of a company.<br /><br />Let's consider a snippet of Wal-Mart's Q2 of fiscal year 2013 balance sheets:<br /><br /><style>.finstate td, .finstate th { padding: 5px; text-align: left; } </style> <br /><table class="finstate mytable"><thead><tr> <td>(Amount in Millions of USD)</td> <th>July 31, 2012</th></tr></thead><tbody><tr> <th>Cash and cash equivalents</th> <td>7,935.00</td></tr><tr> <th>Total Receivables, Net</th> <td>5,365.00</td></tr><tr> <th>Total Inventory</th> <td>40,558.00</td></tr><tr> <th>Property and equipment</th> <td>159,919</td></tr><tr> <th>Goodwill</th> <td>20,081</td></tr><tr> <th>Total Assets</th> <td>195,661.00</td></tr><tr> <th>Total Liabilities</th> <td>125,383.00</td></tr><tr> <th>Total Equity</th> <td>70,278.00</td></tr><tr> <th>Total Common Shares Outstanding</th> <td>3,383.54</td></tr></tbody></table><ul><li>Cash and cash equivalents - amount of cash in the bank or stored in no risk, liquid securities like Treasury bills</li><li>Total Receivables - unpaid debt owed to the company by customers due within a year</li><li>Total Inventory - value of raw materials, goods in progress, and unsold finished goods</li><li>Property and equipment - value of land, buildings, equipment, etc</li><li>Goodwill - intangible amount of money put onto the balance sheet after an acquisition</li><li>Total Assets - sum of all assets (in this example, it doesn't add up perfectly since I left out some more detailed lines)</li><li>Total Liabilities - sum of all debt, both short-term and long-term</li><li>Total Equity - total assets minus total liabilities</li><li>Total Common Shares Outstanding - number of shares traded on the market</li></ul><br />This should provide a general gist of things, though I left out a significant number of more detailed (and less significant) lines.<br /><br /><h3>Estimating the Liquidation Value</h3>So now that we have the company's balance sheet, it appears at first glance that the number we want is the <b>total equity</b>. After all, the total equity is the total assets minus total liabilities, a reasonable estimate for what a company would liquidate for.<br /><br />Unfortunately the story isn't so simple. For example, in the event of a bankruptcy, there is no chance that the company will be able to liquidate the items in its inventory at its full value (e.g. out of business sales). In addition, not every item will be sold.<br /><br />And so we must <i>discount</i> the assets in an appropriate fashion so as to come up with an accurate lower bound. Every company has assets in different proportions and types and so there's no catch-all discount factor. However, we can use some general guidelines (and tweak them on a per-company basis) for each individual asset type to provide a more accurate estimate.<br /><br />Benjamin Graham proposed the following formula:<br />\[NNWC = C + 0.75AR + 0.5I - L\] where \(C\) is the total cash, \(AR\) is the total accounts receivable, \(I\) is the total inventory, and \(L\) is the total liabilities. This formula is commonly known as net-net working capital (NNWC).<br /><br />The original NNWC formula is rather too crude in my opinion and should include other assets like property and equipment.<br /><br />I believe that each company requires its own tuned coefficients depending on the type of business. So in the general case, we have: \[ \begin{align*} LV &> D_1 B_1 + D_2 B_2 + \dots + D_n B_n \\ &= \mathbf{D} \cdot \mathbf{B} \end{align*} \] where \(LV\) is the liquidation value, \(D\) is the discount vector, and \(B\) is the vector of balance sheet items. Typically, we can impose some additional constraints on \(\mathbf{D}\) such as: \[D_i < 1 \\ D_{liabilities} < -1 \\ D_{cash} = 1\] Once a lower bound on the company value is established, simply divide it by the total number of shares outstanding to get a lower bound on the share price.<br /><br /><h3>Determining Discount Coefficients</h3>As I mentioned before, I don't believe there is a general method of determining these coefficients. It is mostly an art that involves a whole lot of research about the company and a strong intuition about the market. Not all available information is divulged in a company's financial statements.<br /><br />If you scour the internet, you can find more specific information about particular allocation of assets. From this, you can make more educated estimates.<br /><br />But one thing is certainly true, it is always better to err on the side of pessimism and caution. Remember, you are trying to establish a lower bound. Being overly optimistic or rushed can lead to bad investments.<br /><br /><h3>Shortcomings</h3>The primary issue with this technique is that it only provides a very loose lower bound. As such, it rules out the vast majority of stocks, leaving you with only a few potential winners. In more technical terms, you sacrifice a lot of <a href="http://en.wikipedia.org/wiki/Statistical_power">statistical power</a> in order to minimize the rate of <a href="http://en.wikipedia.org/wiki/Type_I_and_type_II_errors">Type I errors</a>. By ignoring revenue, you are glossing over a large part of a company's value in hopes that it does not matter.<br /><br />Another issue is that after filtering out companies based on this criterion, you must be very skeptical of the results. You should go ahead and verify that these companies are indeed worth investing in. Extraordinary circumstances can occur such as incorrect balance sheet reporting, money laundering, etc.<br /><br /><h3>Getting Started</h3>There are thousands of stocks out there so it's impossible to go through them one by one to apply this technique. The first step is to weed out stocks that cannot possibly satisfy this criterion. For this valuation technique, you can ignore all stocks with a P/B ratio greater than one. Most stock screeners will allow you to do this, including <a href="http://www.google.com/finance#stockscreener">Google Finance</a>.Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-1541568876657756592012-08-31T14:48:00.000-07:002014-01-06T14:45:47.032-08:00Valuation TechniquesInvesting ultimately comes down to the ability of an individual to value a company and the associated risks of such a valuation. There are hundreds of different models and techniques in use today, both simple ones devised by humans and enormously complex ones used in <a href="http://en.wikipedia.org/wiki/Algorithmic_trading">algorithmic trading</a>.<br /><br />I don't believe that there is one magic, all-encompassing, algorithm that will perform optimally in all (or even most) scenarios. The issue is that every company has a different business model, each of which would require a different model for valuation. This task is rather intractable, and so it is the job of the investor to be able to create robust models that hold under reasonable approximations. In addition, he must be able to understand which approximations hold for which businesses, and use the appropriate model.<br /><br />Many present models involve looking at one aspect of a business, such as dividends, cash flow, earnings, etc. From these, you can derive <a href="http://en.wikipedia.org/wiki/Dividend_discount_model">dividend discount model</a>, <a href="http://en.wikipedia.org/wiki/Discounted_cash_flow">discounted cash flow</a>, and P/E relative valuations, respectively. But naturally, these are rather crude in the sense that they don't look at all of the variables. And combining different valuation schemes is a non-trivial process.<br /><br />In this series of articles, I will start with a set of assumptions and derive some models for valuation using these approximations. This post will be edited as articles are added.<br /><ol><li><a href="http://www.stockarcher.com/2012/08/valuation-techniques-liquidation-value.html">Liquidation value</a></li><li><a href="http://www.stockarcher.com/2014/01/dividend-discount-model.html">Dividend Discount Model</a></li></ol>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-73756821162003411052012-08-28T21:27:00.001-07:002012-08-28T21:54:10.256-07:00Hewlett-Packard (HPQ) Qualitative AnalysisOver the past week, Hewlett-Packard Company (ticker: <a href="https://www.google.com/finance?client=ob&q=NYSE:HPQ">HPQ</a>) has fell over 17% to the current price of $16.83 per share. This drop was largely due to the company's recent 2012 Q3 earnings report released after hours on August 22, where they reported a net earnings loss of 8.9B.<br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-tdiOEhjuaKM/UD2Z8kppaJI/AAAAAAAAANg/jDil9JvtHh4/s1600/hp.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="136" src="http://2.bp.blogspot.com/-tdiOEhjuaKM/UD2Z8kppaJI/AAAAAAAAANg/jDil9JvtHh4/s200/hp.jpg" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">The PC isn't going away any time<br />soon</td></tr></tbody></table><br />On the surface, I think it is quite natural to feel grim about the company's prospects after such a dramatic loss. In my personal portfolio, if I had sold my shares before the earnings report, I would have realized a 12% gain, whereas now I am sitting on a 7% loss. So while emotionally I am obviously not happy with the turn of events, that should not impact the underlying analysis on which I base my trades.<br /><br />In fact, it is precisely bear-ish sentiments like these that give investors arbitrage opportunities like this.<br /><br />As such, I stick by original positive prospects for HP and would buy even more shares if I had the cash and sufficient diversification to do so. Here is why:<br /><br /><a name='more'></a><h3>Company Overview</h3>Most people associate HP with two primary segments: personal computers and printers. However, while these two certainly play a large role in the company, HP also has a hand in several other markets.<br /><br /><ol><li>Imaging and Printing Group (IPG) - printers, scanners, printing supplies, digital cameras</li><li>Personal Systems Group (PSG) - personal computers for businesses and consumers, PC accessories</li><li>Enterprise Business (EB)</li><ol><li>Enterprise Storage, Servers, and Networking (ESSN) - servers, data storage</li><li>Enterprise Services (HPES) - IT outsourcing</li><li>Software Division - enterprise software including SaaS, cloud computing</li></ol></ol><div>HP also runs the advanced research group <a href="http://www.hpl.hp.com/">HP Labs</a>.</div><div><br /></div><div>Number of Employees: ~340,000</div><div>Market Cap: $34B</div><div>Total Equity: $32B</div><div><br /></div><h3>Similar Companies</h3><div>On the PC side of things, we have a direct competitors Dell (ticker: <a href="https://www.google.com/finance?q=NASDAQ:DELL">DELL</a>) and Apple (ticker: <a href="https://www.google.com/finance?q=NASDAQ:AAPL">AAPL</a>) in both business and consumer markets.</div><div><br /></div><div>HP currently dominates the consumer printing and imaging market. However for enterprise solutions, Xerox (ticker: <a href="https://www.google.com/finance?q=NYSE:XRX">XRX</a>) comes into play.</div><div><br /></div><div>In terms of providing enterprise software, there is IBM (ticker: <a href="https://www.google.com/finance?q=IBM">IBM</a>), SAP (ticker: <a href="https://www.google.com/finance?q=NYSE:SAP">SAP</a>), and Oracle (ticker: <a href="https://www.google.com/finance?q=NASDAQ:ORCL&ei=yYo9UMiaGae6lAPVZA">ORCL</a>).</div><div><br /></div><h3>Analysis</h3><h4>Total Equity</h4><div>The total equity, or book value, is the net assets minus liabilities. HP is trading at approximately 1.06 times its book value (P/B ratio). Comparing this to other company's in the sector, Dell is trading at 2.2, Apple at 8.2, Xerox at 0.8, IBM at 11.3, SAP at 4.9, and Oracle at 3.6.</div><div><br /></div><div>Only Xerox is comparable in terms of having a low P/B ratio. While this may be a feature of the print services, the PC and enterprise solutions segments of HP should certainly bring its P/B ratio up to at least 2.</div><div><br /></div><div>Looking at the balance sheet, we see a healthy amount of cash on hand (9.5B) and both inventory and accounts receivable. One particularly worrisome aspect here is the large amount attributed to goodwill and intangibles. I haven't fully analyzed HP's recent acquisitions, but they certainly look at least a bit overpriced and that attributes to the large amount written off to goodwill. I'll come back to this in the next section.</div><div><br /></div><div>Because of the large amount of goodwill, we cannot simply say HP is a definite good buy just based on book value. Goodwill tends to obscure the true book value and in many cases it is better to completely remove it from consideration.</div><h4>Income</h4><div>So I think what worries most people is HP's ability to generate sufficient earnings. In particular, this past quarter has been absolutely dismal in terms of net income. But let's break down exactly what happened.</div><div><br /></div><div>Net earnings is is the total revenue, minus cost of revenue, operating expenses, and taxes. From Q2 to Q3, earnings fell from 1.6B to -8.9B.</div><div><br /></div><div>However, revenue stayed fairly consistent at 29.6B compared to Q2's 30.5B and Q1's 29.9B. The cost of revenue similarly stayed the same, resulting in steady gross profits.</div><div><br /></div><div>If we look at the standard GAAP reported income statement (e.g. as provided by Google Finance), we see a whopping 11B under the line "Unusual Expense", compared to previous quarter's 70M. So in order to find out what this constitutes, I dug into the actual earnings report released by HP. It turns out that this 11B reported loss comes from goodwill impairment charges in regards to in the services segment and intangible asset impairment charges for the Compaq trade name.</div><div><br /></div><div>As I mentioned earlier, the goodwill line of the balance sheet causes a bit of worry. However in some sense, the negative effect is double counted in the income statement. If we view goodwill as a bad thing in the balance sheet, we shouldn't readjust for it when reading the income statement. In fact, if we ignore impairment charges, HP actually <b>earned</b> 2B this past quarter.</div><div><br /></div><div>In terms of P/E, HP is sitting at around 4. By comparison, similar companies are sitting on P/E ratios of around 10-15. Even if earnings dip further in the future, I don't think it justifies such a low P/E ratio.<br /><h4>Dividends</h4>Despite income related headwinds, HP maintains strong, consistent dividends between 2-3% per year. That is an additional bonus on top of any capital gains. While shareholders aren't guaranteed dividends, historically speaking HP has been very kind to shareholders in the dividends department.<br /><br />This factor should play a huge role in future valuations of the company.</div><h4>Restructuring Changes</h4><div>If you're following HP related news, you will see a lot statements being thrown around about restructuring changes in the company. About 1.8B in the income are attributed to restructuring charges. This is also rather superficial and has very little to do with the core business of HP.</div><div><br /></div><div>These changes include laying off about 27,000 employees and moving towards emphasizing their services segment as opposed to PC and print segments. This is largely due to the general slowdown in PC sales and printer sales. I find these changes good and will likely play out well for HP in the long run.</div><h4>Optimism</h4><div>I also feel that investors are too pessimistic about the future of the PC market. While smartphones and tablets are all well and good, I highly doubt that they will replace the PC in any sense. Sales may have slowed down recently because of all these new gadgets on the market, I believe that the drop will level off soon enough. The buy cycle for the PC may have increased slightly, but people will always need newer computers.</div><div><br /></div><div><br /></div>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-43343001630181149762012-08-23T19:35:00.000-07:002012-08-23T19:36:30.603-07:00Value vs. Growth InvestingIf you have done any research on stocks, mutual funds, etc., you have probably heard the terms <i>value stocks</i> and <i>growth stocks</i>. These two adjectives are used to describe the underlying motivation and strategy for investing in a particular security. Many (if not most) investors and the media portray these two as distinct camps with clashing investment ideologies.<br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-J5sZQQxJMqU/UDbnuYJq1BI/AAAAAAAAANQ/X0FmKYt-W0M/s1600/benjamin_graham.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://4.bp.blogspot.com/-J5sZQQxJMqU/UDbnuYJq1BI/AAAAAAAAANQ/X0FmKYt-W0M/s200/benjamin_graham.jpg" width="149" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Benjamin Graham (1894-1976) is hailed as the<br />father of value investing</td></tr></tbody></table>Proponents of value investing favor low priced stocks, selling below their intrinsic value. Typical characteristics of value stocks are low price/earnings (P/E), price/book (P/B), and high dividends. The idea is that over time, the overall market will realize that the stock is undervalued and correct itself accordingly. As such, it is associated long term investors.<br /><br />On the other hand, growth investing is a matter of investing in companies with higher than expected growth rates. The premise is that the stock price reflects the opinions of Wall Street analysts on earnings and cash flow. If the company beats these expectations, then the stock price will move up. In order to facilitate high earnings growth, these stocks typically have low or no dividend yields.<br /><a name='more'></a><h4>Now let's take a step back...</h4><div>So far, we know that the stock price is the market's valuation of a company. Thus we should always invest in companies that are currently being undervalued in order to make a profit. This sounds exactly like value investing.</div><div><br /></div><div>The question then becomes, how do we determine the value of a company? Well at first glance, we can take into consideration the company's physical assets like land, equipment, and inventory. That gives us the book value. But a company isn't a static entity; the whole purpose is to generate revenue and profits. Thus the value of a company must inherently take into account the future cash flow, <i>including all growth of said cash flow</i>.</div><div><br /></div><div>And so we arrive at the conclusion that the value investing must necessarily use principles of what's known as growth investing.</div><h4>Vice-Versa</h4><div>The same conclusion can be drawn about growth investing. During the late 1990's and early 2000's of the dot-com bubble, a common investment principle was "growth at any price." The faulty premise being that as long as the company will grow, any stock price is justified. As a result, stock prices of technology companies like Amazon skyrocketed far past their intrinsic value.</div><div><br /></div><div>Since then, "growth at any price" has fallen out in favor of "growth at reasonable price". But what constitutes reasonable? In order to determine a reasonable price, one must evaluate the value of a company, taking into account both potential for growth and assets. Then, like value investing, you buy stocks are are undervalued according to your calculations.</div><h4>Conclusion</h4><div>In Warren Buffett's own words: "growth and value investing are joined at the hip". You cannot be one, without being the other because growth is tied into value. Fundamentally speaking, there is absolutely no point in differentiating the two.<br /><br />And here's another quote from Buffett:</div><div><blockquote class="tr_bq"><i>Market commentators and investment managers who glibly refer to growth and value styles as contrasting approaches to investment are displaying their ignorance, not their sophistication.</i></blockquote></div><div><br /></div>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-72911940237172471392012-08-21T14:42:00.001-07:002012-08-21T14:48:57.504-07:00Day trading and why you shouldn't do itDay trading is when you try to take advantage of the intraday fluctuations in prices of financial instruments like stocks and bonds. The idea is that even though the overall daily price may decrease, the price will increase at some points throughout the day. If a trader can time his buys right before the increases and sell right before it starts decreasing, he can make a profit.<br /><br />Consider the following intraday time series for a stock:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-0rysqZ7XgEI/UDPdKnFJHiI/AAAAAAAAANA/xbp1VevMLJc/s1600/graph.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="247" src="http://2.bp.blogspot.com/-0rysqZ7XgEI/UDPdKnFJHiI/AAAAAAAAANA/xbp1VevMLJc/s320/graph.PNG" width="320" /></a></div><br />Overall, the stock price dropped from $10 to $8, a 20% loss. However, an omniscient investor could in theory buy the stock at 10 AM, sell at 11 AM, buy again at 1 PM, sell at 2 PM, buy at 3 PM, and finally sell at 4 PM. The net result is a $3/share, a 30% gain.<br /><br />This kind of arbitrage can almost always occur, regardless of market conditions or time scale. This is because while the overall trends are consistent and can be predictable, the small fluctuations caused by people buying and selling shares is inevitable. There will almost always be both buyers and sellers throughout the day and if at any given point the number of supply exceeds the demand, the price will go up temporarily.<br /><a name='more'></a><br />The potential for profits are huge as our previous example illustrates, but how does one go about realizing that potential?<br /><br />There are a number of techniques that traders use to try and predict these upswings and downturns.<br /><br />One simple one is to monitor the news. When good news comes out, the stock price can be expected to go up in the near future as other traders are enticed into buying. Similarly when bad news comes out, the price is expected to go down. Important news reports like quarterly earnings can result in huge changes in stock price like when Chipotle Mexican Grill (<a href="https://www.google.com/finance?client=ob&q=NYSE:CMG">CMG</a>) plummeted over 20% on July 19th when it's second quarter earnings of 2012 failed to meet analyst expctations. Analysts publish their own "buy/sell" ratings which in turn influence the public's perception of a company. Companies also announce things like new products, price cuts, etc. which affect the stock price.<br /><br />You can also enter into the realm of technical analysis, which involves looking at charts and time series of a stock to predict it's future behavior. Proponents of technical analysis try to take advantage of history repeating itself and looking for patterns of stock price movements. For example, I'm sure most stock traders have thought about or tried buying a stock simply because it has reached a 52 week low. The thought process is that the price must go up afterwards, or at least one can reasonably have a positive expected value by gambling on that.<br /><br /><h3>Criticism</h3>I am of the opinion that one should not attempt day trading. My reasoning is as follows:<br /><h4>Trade Commissions</h4><div>Whenever you buy or sell a stock, you typically pay a fee to your broker for completing the trade on your behalf. The fee is usually on the order of $8 per trade, or $16 total for both buying and selling a stock. If we look at the intraday swings of a stock, they are typically on the order of 1% of the price. This means that if we make the optimal trade decisions, we would have to invest over $1,600 in a single stock to simply <i>break even</i>.</div><div><br /></div><div>More reasonably speaking, even the most well-informed traders cannot hope to accurately pinpoint the optimal time to buy and sell, reducing the profit margin even more. I would conservatively estimate the average profit margin for each day trade to be about 0.5% at best.</div><div><br /></div><div>Also by investing so much money into a single stock, you are losing a lot in the way of diversity. An individual investor simply cannot afford the risk of dumping all his money into one stock. For sufficient diversity and margin of safety, an investor would likely need over $500,000 in trading capital to potentially make any semblance of a profit.</div><div><br /></div><div>Note that most stock brokers require a minimum account balance of only around $25,000 to day trade.</div><h4>Opportunity Cost</h4><div>Suppose I felt lucky and decided to spend $100,000 today on 10 day trades, making a 0.5% gross profit. This would amount to $500. The 10 day trades would result in a $320 commission fee, leaving me with a $180 net profit for the day or a little over $20/hour.</div><div><br /></div><div>Well if I had $100,000 of spare cash lying around I was probably already making over $50/hour at a regular day job with almost no risk, additional benefits, and probably a more fulfilling position. With the my spare cash, I could invested that in a less risky and simpler manner for a significant additional source of income.</div><h4>You Can't Beat the Machine</h4><div>Many financial firms are participating in <a href="http://en.wikipedia.org/wiki/High-frequency_trading">high frequency trading</a> (HFT) which use computers to day trade. They use various algorithms to let computers analyze stocks and make trades faster than a human can blink. It is likely that these computers already beat a human day trader to the potential arbitrage opportunity when the information or signs become available.</div><div><br /></div><div>I don't think day trading is necessarily bad, but I believe that it is now outside the scope of human traders. In fact, it is absolutely essential by providing liquidity to the market and making the price reflect the value of a company more quickly.</div><div><br /></div><div>I would associate day trading with arithmetic and long term investing with mathematics. One is better left to computers while the other to humans.</div><div><br /></div>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com2tag:blogger.com,1999:blog-3395163988550322009.post-26240558835051634252012-08-16T18:32:00.002-07:002012-08-16T18:34:08.198-07:00#1 Fallacy in Investing<a href="http://4.bp.blogspot.com/-P5KP6SkSHGI/UC2fBB0bZqI/AAAAAAAAAMs/ywK57eiLu1o/s1600/growth_investing.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://4.bp.blogspot.com/-P5KP6SkSHGI/UC2fBB0bZqI/AAAAAAAAAMs/ywK57eiLu1o/s200/growth_investing.jpg" width="177" /></a>Whenever I talk with people or read about investing, the same misconception comes up over and over. Many, if not most, people believe that rapid growth of a business will equate to a higher stock price in the future. The reasoning being if a company's value increases, the stock price will necessarily reflect that growth since a stock is portion of the company.<br /><div><br /></div><div>The problem is very subtle because the reasoning is 100% correct. So where is the fallacy?</div><div><a name='more'></a><br /></div><h3>Time is Money</h3><div>The issue comes when people equate a company's present <b>value</b> with its present <b>book value</b>. When a business grows, its net assets (e.g. cash, inventory) increases at a rate greater than its liabilities (e.g. debt). The difference between assets and liabilities is the company's equity or book value (this is known as the <a href="http://en.wikipedia.org/wiki/Accounting_equation">accounting equation</a>).</div><div><br /></div><div>However, the value of a company also incorporates <i>future</i> growth. If a company has a book value of $1 million and has a steady income of $100,000 per year, it's present value is certainly going to be greater than $1 million. This is just as if I had $100 of cash that doubled each year, I certainly wouldn't sell it for $100.</div><div><br /></div><div>So it is true that if the value increases, the stock price increases. But the present value of a company <u>already takes future growth into account</u>. By buying the stock of a growing business, you are betting your money on the business growing faster than current market expectations, not on the fact that it will grow at all.</div><div><br /></div><h3>Growth Investing</h3><div>An investment strategy based around these "above expected" growth rates is known as <a href="http://en.wikipedia.org/wiki/Growth_investing">growth investing</a>. Growth related strategies generally target smaller, up and coming businesses whose potential isn't well known or analyzed. Internet and technology stock typically fall under this category. The same goes with emerging markets (e.g. foreign companies in growing countries like China and India).</div><div><br /></div><h3>Conclusion</h3><div>Growth investing isn't necessarily bad, but it is misunderstood by many people. I find that in particular, people get overly excited about technology stocks. They see an excellent product, a rapidly growing user base, and a lot of hype surrounding a tech company. But then they fail to realize that other investors have already taken that into account and bought the stock up to it's current price. That is to say, the current stock price may already reflect everything that you considered.</div><div><br /></div>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com1tag:blogger.com,1999:blog-3395163988550322009.post-28452870733906568332012-08-15T12:22:00.002-07:002012-09-18T20:12:17.297-07:00Diversity is SafetyToday, I sold about 30% of my shares of CSCO at a 10% gain. The reason why I sold is not because I am happy with the return or I think the price will go down, but rather because I feel that my portfolio is not diverse enough.<br /><br />As you can see from my <a href="http://www.stockarcher.com/2012/08/the-first-stocks.html">previous post</a>, I currently own positions in 6 stocks. About 20% of my portfolio value was in CSCO. Why is this a bad thing? If the stock performs well, my portfolio does proportionally well. The flip-side is that if it performs poorly, my portfolio will also do poorly. That single fact is what concerns me the most.<br /><br /><div style="text-align: right;"><a href="http://1.bp.blogspot.com/-axbehv97VvU/UCvsJXCsAfI/AAAAAAAAAMU/aCMPvyFIVOU/s1600/normal1.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-axbehv97VvU/UCvsJXCsAfI/AAAAAAAAAMU/aCMPvyFIVOU/s1600/normal1.PNG" /></a></div>To illustrate the problem, let's consider a more extreme situation. Suppose I had all of my wealth invested equally in a single stock, which we will call AAA. Now let's say our 1 year prospects for this stock is normally distributed an expected value of 10% gain and a standard deviation of 20%.<br /><br />We can expect a 10% gain <i>on average</i>. However the <a href="http://en.wikipedia.org/wiki/Law_of_large_numbers">law of large numbers</a> only holds true over the course of many samples. In this case, there is 34% that you will <i>lose</i> money this year. In fact, there is a 1% chance that you will lose over half of your money. The risk is simply too high to justify this kind of investment strategy.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-rZzuJL4f-3U/UCvsx9NkOqI/AAAAAAAAAMc/hmDJsQPvz2w/s1600/normal2.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-rZzuJL4f-3U/UCvsx9NkOqI/AAAAAAAAAMc/hmDJsQPvz2w/s1600/normal2.PNG" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">The probability that you will lose money</td></tr></tbody></table><a name='more'></a><h3>Diversifying</h3>However, we can lower this risk by taking a greater number of samples. One way of doing this is by investing in multiple independent stocks with positive expected returns. So now suppose we have two stocks, AAA and BBB, both with expected yearly returns of 10% and a standard deviation of 25%. We'll call these two random variables \(A\) and \(B\), and our portfolio return \(P\).<br />\[ P = 0.5A + 0.5B \] We scale \(A\) and \(B\) by 0.5 because we are now investing only 50% of our portfolio in each.<br />\[ \mu_{0.5A} = 0.5\mu_A = 5 \\ \sigma_{0.5A} = 0.5 \sigma_A = 12.5<br />\] The sum of two independent, normally distributed random variables is also normally distributed with<br />\[ \mu = \mu_X + \mu_Y \\ \sigma^2 = \sigma_X^2 + \sigma_Y^2 \] So in our case<br />\[ \mu_P = 5+5 = 10 \\ \sigma_P = \sqrt{12.5^2 + 12.5^2} \approx 17.7<br />\] As you can see, by simply investing in two independent stocks, we can reduce our standard deviation by 30% while still maintaining the same expected value. Now the probability of losing more than 50% of your portfolio value is less than \(3.5 \times 10^{-4}\).<br /><br />So what happens when you diversify even more? Here is a table illustrating the effects:<br /><br /><table class="mytable"><thead><tr><th># of Stocks</th><th>Mean</th><th>Std Dev</th><th>Prob. Losing Money</th><th>Prob. Losing Over Half</th></tr></thead><tbody><tr><td>1</td><td>10</td><td>25.0</td><td>0.34</td><td>\(8.2 \times 10^{-3}\)</td></tr><tr><td>2</td><td>10</td><td>17.7</td><td>0.29</td><td>\(3.5 \times 10^{-4}\)</td></tr><tr><td>3</td><td>10</td><td>14.4</td><td>0.24</td><td>\(1.6 \times 10^{-5}\)</td></tr><tr><td>5</td><td>10</td><td>11.2</td><td>0.19</td><td>\(4.0 \times 10^{-8}\)</td></tr><tr><td>10</td><td>10</td><td>7.9</td><td>0.10</td><td>\(1.5 \times 10^{-14}\)</td></tr><tr><td>100</td><td>10</td><td>2.5</td><td>\(3.2 \times 10^{-5}\)</td><td>\(1.4 \times 10^{-127}\)</td></tr></tbody></table><br /><h3>Additional Considerations</h3><div><ul><li>While you are protected from losing a large sum of money, you are also preventing yourself from having an extraordinary return.</li><li>The above analysis only holds when the variables are independent. This is not always true in the stock market. In particular, market sectors like "tech" or "automotive" are highly correlated.</li><li>We used the normal distribution as an example. In reality, the distribution varies (and in particular, the tails of the distribution are much higher than theoretical models suggest). On the other hand, by the <a href="http://en.wikipedia.org/wiki/Central_limit_theorem">central limit theorem</a>, the sum of iid random variables will converge to a normal distribution.</li><li>Different stocks have different expected returns and standard deviation. You should take this into account when diversifying of your portfolio.</li><li>When stock prices change, the proportions of your portfolio also changes. You must rebalance regularly.</li><li>This applies not only to stocks! Diversifying can also mean investing in bonds, real estate, education, or anything at all!</li></ul></div>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com2tag:blogger.com,1999:blog-3395163988550322009.post-41412121262427536062012-08-14T00:07:00.000-07:002012-09-22T12:09:38.844-07:00Do stock prices matter?Do stock prices by themselves have any impact on whether or not you should buy it?<br /><br /><b>TLDR</b>: No.<br /><br />As an example, consider the two stocks: General Electric and Berkshire Hathaway Class A.<br /><br /><table class="mytable"><thead><tr><th>Stock</th><th>Ticker</th><th>Price</th><th>Market Capitalization</th></tr></thead><tbody><tr><td>General Electric Company</td><td>GE</td><td>20.99</td><td>221.63B</td></tr><tr><td>Berkshire Hathaway Inc.</td><td>BRK.A</td><td>127,380.00</td><td>210.91B</td></tr></tbody></table><br />As you can see, GE's stock costs less than 6000 times less than Berkshire Hathaway's, yet the two companies have about the same market value. The reason behind this is that GE has 10.56 billion shares outstanding while Berkshire Hathaway has a only 1.66 million shares.<br /><br />Yet from a psychological standpoint, people will drawn more towards low priced shares. However, the raw share price has <i>nothing</i> to do with the market value of the company.<br /><br />Does that mean the share price should be completely taken out of consideration when picking stocks? For most companies, the answer is yes. There are two cases where it does matter: when the share price is extremely high (e.g. BRK.A at $127,380) or extremely low (e.g. SPEX at $0.48).<br /><br />In the first case, it's important because the share price may simply be so high that you cannot afford to buy a single share (there is no such thing as a fractional share). If you want a piece of Warren Buffett's BRK.A, you'll have to pay generously for even the smallest portion of his wealth.<br /><br />In the latter case, the stock is considered a penny stock (less than $1). Many stock brokers charge an additional fee for trading penny stocks. This fee may cut significantly into your profits or worsen your losses.Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-61995437703258836382012-08-11T19:50:00.000-07:002012-08-31T15:03:01.915-07:00The first stocksMy initial stock purchases were made on August 1, 2012. Exactly a 10 days has elapsed between then and the market close yesterday. Here is a summary of what I invested in and what they are worth now. <br /><table class="mytable"><thead><tr><th>Company</th><th>Ticker</th><th>Bought Price/Share</th><th>Current Price/Share</th><th>% Gain</th></tr></thead><tbody><tr class="green"><td>Cisco Systems Inc.</td><td>CSCO</td><td>15.86</td><td>17.70</td><td>11.60%</td></tr><tr class="green"><td>Hewlett-Packard Co.</td><td>HPQ</td><td>17.87</td><td>19.41</td><td>8.62%</td></tr><tr class="green"><td>JP Morgan Chase</td><td>JPM</td><td>36.06</td><td>36.92</td><td>2.38%</td></tr><tr class="green"><td>NRG Energy</td><td>NRG</td><td>19.81</td><td>20.88</td><td>5.40%</td></tr><tr class="red"><td>PG&E Corp.</td><td>PCG</td><td>45.85</td><td>45.39</td><td>-0.99%</td></tr><tr class="green"><td>Xerox Corp.</td><td>XRX</td><td>6.94</td><td>7.17</td><td>3.31%</td></tr></tbody></table><br />So far, I have a 4.51% return overall. If we compound that 36 times to extrapolate my portfolio's worth in a year, we arrive at a staggering 490% yearly growth! <br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-3TIldKqSb6A/UCcGSicY5kI/AAAAAAAAALg/bVj_nb1bmcU/s1600/success_kid.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="183" src="http://2.bp.blogspot.com/-3TIldKqSb6A/UCcGSicY5kI/AAAAAAAAALg/bVj_nb1bmcU/s200/success_kid.png" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Like a boss</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"></div><a name='more'></a>Ok, while that will never happen, it's certainly an interesting prospect...<br /><br />Now that we're back to reality, let's talk about something more interesting like why I chose those stocks in the first place. I think one of the best ways to illustrate my strategy is look at some of key financial statistics. Below I have listed both stocks that I currently own and a some hot stocks that I did <b>not</b> buy. Go ahead and take a gander and see if you can notice any patterns. <br /><br /><table class="mytable"><thead><tr><th>Company</th><th>Price/Share</th><th>Price/Book</th><th>Price/Earnings</th></tr></thead><tbody><tr><td>Cisco Systems Inc. (CSCO)</td><td>15.86</td><td>1.8</td><td>11.8</td></tr><tr><td>Hewlett-Packard Co. (HPQ)</td><td>17.87</td><td>0.93</td><td>7.0</td></tr><tr><td>JP Morgan Chase (JPM)</td><td>36.06</td><td>0.77</td><td>8.1</td></tr><tr><td>NRG Energy (NRG)</td><td>19.81</td><td>0.59</td><td>19.1</td></tr><tr><td>PG&E Corp. (PCG)</td><td>45.85</td><td>1.4</td><td>24.8</td></tr><tr><td>Xerox Corp. (XRX)</td><td>6.94</td><td>0.78</td><td>7.7</td></tr><tr class="black"><td>Facebook Inc. (FB)</td><td>21.04</td><td>10.88</td><td>121.74</td></tr><tr class="black"><td>Zipcar Inc. (ZIP)</td><td>10.17</td><td>1.45</td><td>417.79</td></tr><tr class="black"><td>Apple Inc. (AAPL)</td><td>611.21</td><td>7.54</td><td>14.61</td></tr><tr class="black"><td>Zynga Inc. (ZNGA)</td><td>2.84</td><td>1.22</td><td>~200</td></tr></tbody></table><br />Let's focus on one column at a time.<br /><br /><h3>Price/Share</h3>This one is pretty simple. The price per share is simply how much you pay for a single share of the company. Different companies have a different total number of shares, so a share of each company represents a different percent ownership.<br /><br />In this case, I did not even consider buying Apple because the price was simply too high. The minimum amount I could invest in Apple is one share (there is no such thing as fractional shares), which would already run me for over $600.<br /><br /><h3>Price/Book</h3>The book value of a company is the value of all its assets minus liabilities. Roughly speaking, this measures how much the company if it were to sell everything it owns (inventory, equipment, land, etc) and pay off all debts.<br /><br />The price/book (P/B) ratio is defined as<br />\[<br />P/B = \frac{\text{Market capitalization}}{\text{Book value}}<br />\]<br /><br />Market capitalization is just a fancy term for what the entire company is worth on the market (i.e. price per share times total number of shares).<br /><br />A low P/B ratio is generally a good thing. It means that a large percentage of the company's price is backed by real assets and low debt. You'll notice that most of the stocks I own have a low P/B ratio, some of then even less than 1... This means that I bought the company less than what it would be worth if it liquidated everything (roughly speaking).<br /><br /><h3>Price/Earnings</h3>The price/earnings (P/E) ratio is one that you hear about a lot. As you can probably tell by the name, it's simply the price of the company divided by it's earnings (over one year).<br />\[<br />P/B = \frac{\text{Market capitalization}}{\text{Yearly earnings}} <br />\]<br />A low P/E ratio means that with the current earnings rate, it will earn back what you paid for sooner than a company with a high P/E ratio. Thus a high P/E ratio means that investors are expecting an increase in earnings in future.<br /><br />Facebook, Zynga, and Zipcar have an obscenely high P/E ratios. At their current earnings, I would have to wait 400 years before Zipcar makes enough money for their bank account to break even with what I paid for. I think it is folly to believe that they can justify a high growth to make up for this.<br /><br /><br />Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com2tag:blogger.com,1999:blog-3395163988550322009.post-50892507396568997902012-08-10T09:32:00.000-07:002012-08-10T11:41:48.906-07:00Are stocks a Ponzi scheme?The premise behind investing in stocks is simple: buy low and sell high. You should be wondering, why should stock prices increase at all? Ultimately the reason is because other investors want to invest in it, in hopes of selling their shares at an even higher price than what they paid for.<br /><br />But wait, isn't this just an elaborate Ponzi scheme? Let me explain.<br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-LqymLYSD5Us/UCU6_rXObJI/AAAAAAAAAKs/YfwmMTLXSTI/s1600/ponzi.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="135" src="http://3.bp.blogspot.com/-LqymLYSD5Us/UCU6_rXObJI/AAAAAAAAAKs/YfwmMTLXSTI/s200/ponzi.jpg" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Puts Nigerian scammers to shame</td></tr></tbody></table><h3>Ponzi Schemes</h3>For those who are not familiar with the Ponzi scheme, it is a rather simple, yet clever scam. It is named after Charles Ponzi (1882-1949) who successfully employed the scheme to scam thousands of New Englanders back in the 1920's [1].<br /><br /><br /><a name='more'></a>The scheme starts with a claim of an investment opportunity with lucrative returns (like 50%/month), open to anyone who wishes to partake in it. Initial investors are drawn in by the prospects and unsuspectingly throw some money into the pot. As more investors do this, the early adopters are given their expected returns using the money of later investors.<br /><br />With the increased confidence, many new investors are drawn in and the cycle repeats itself. The <a href="http://en.wikipedia.org/wiki/Bandwagon_effect">bandwagon effect</a> takes over and before long, the initiator of the scam ends up with a huge sum of cash and a lot of debt.<br /><br />At some point, the scammer will simply disappear with all of the invested money, leaving everyone else penniless. You may think that the early adopters still came out ahead (since they received their promised returns); however it is usually precisely those first investors who come back and <i>reinvest</i> even more money into the scheme.<br /><br /><h3>Stocks are not Ponzis</h3>As you can see, the stock market shares many of the same characteristics as a Ponzi scheme. Money is put into an security whose returns are backed by the investments of future investors. Eerily similar isn't it?<br /><br />However, it is important to realize that the entire scheme is only a scam because it eventually unravels and the truth comes out. The mechanism behind this is usually caused by a slowdown of new investments. Once the fraud has been saturated as much as possible and people start asking for their returns, there is no one left to turn to. At this point, investors would realize the issue and attempt to withdraw in what is similar to a <a href="http://en.wikipedia.org/wiki/Bank_run">bank run</a>. Unfortunately it is usually too late and the money is already gone.<br /><br />A stock on the other hand is backed by a real physical asset: the company and its business. If a company has $1 million on hand, the stock price should never drop below that million divided by the number of shares outstanding. So as long as a stock price stays in check and close to reality, there is little risk of it becoming a Ponzi scam.<br /><br /><h3>sometimes...</h3>Unfortunately this isn't always the case as has been proved many times throughout the course of history. The <a href="http://en.wikipedia.org/wiki/Dot-com_bubble">dot com bubble</a> was forged around the basis that the Internet was an infinite source of wealth. Investors believed that each up and coming dot com company would be the next best thing and was worth putting money into at any price. This only fueled the delusions even further until finally the bubble popped in March of 2000.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-BqtEKm4Mtq4/UCVVywLte-I/AAAAAAAAALE/gbjuJxAmGng/s1600/dotcom_bubble.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="197" src="http://3.bp.blogspot.com/-BqtEKm4Mtq4/UCVVywLte-I/AAAAAAAAALE/gbjuJxAmGng/s320/dotcom_bubble.gif" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Aaand the bubble pops</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"></div>When this happened, even the largest and most successful companies suffered catastrophic losses in value. The online retail giant Amazon.com fell almost 95% from $106 per share to just under $6 per share. Other companies hardly fared any better and many did not survive.<br /><br />The recent <a href="http://en.wikipedia.org/wiki/Subprime_mortgage_crisis">subprime mortgage crisis</a> occurred in a similar fashion as houses became the new investment fad. Reckless investment behavior led to unreasonably high housing prices. Houses were being bought on the basis that the "price can only go up" and not because the physical properties themselves were worth the amount paid. The end result was a national depression and bankruptcy of previously well-respected firms like <a href="http://en.wikipedia.org/wiki/Lehman_Brothers">Lehman Brothers</a>.<br /><br />In these respects, the stock market can still act like a global scale Ponzi scheme. The lesson to be taken away is that no amount of news or hype can substitute for cold hard facts. A stock is a part of a company, nothing more and nothing less. Valuing as anything else can only be a recipe for disater.<br /><br /><h3>References</h3>[1] <a href="http://www.sec.gov/answers/ponzi.htm">http://www.sec.gov/answers/ponzi.htm</a>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-48606143647990490192012-08-09T01:15:00.001-07:002012-08-09T01:27:58.837-07:00Stocks, bonds, derivatives, oh my!<div>Today, there are dozens of types of financial instruments employed, ranging from debt securities to derivatives. However, by far the most common are <a href="http://www.investopedia.com/terms/s/stock.asp">stocks</a> and <a href="http://www.investopedia.com/terms/b/bond.asp"><span id="goog_1435553525"></span>bonds<span id="goog_1435553526"></span></a>. These two form the staples of any investor's portfolio, both an individual's and an institution's. By <a href="http://en.wikipedia.org/wiki/Amdahl's_law">Amdahl's law</a>, the bulk of one's time should be spent understanding how these two securities operate and studying how to maximize returns in these two areas.<br /><br /></div><h3>Bonds</h3><div>Bonds are essentially loans given to a company as a way for them to raise both short term and long term funds. You pay a certain amount of money up front, called the <b>principal</b>, in return for regular interest payments. When the bond term ends, known as reaching <b>maturity</b>, the principal will be returned to you in full.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-uNOT5zHq5UM/UCNw15rDSBI/AAAAAAAAAKc/AH4I_db5ujE/s1600/corporate_bond.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="143" src="http://4.bp.blogspot.com/-uNOT5zHq5UM/UCNw15rDSBI/AAAAAAAAAKc/AH4I_db5ujE/s200/corporate_bond.jpg" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">U.S. Steel Corporation bond</td></tr></tbody></table></div><div>The interest rate, called the <b>coupon</b>, is fixed throughout the lifetime of the bond and is typically paid either annually or semi-annually (every 6 months). Short-term maturities (1-5 years) are safer and thus have lower coupon rates than longer-term maturities (10-30 years).</div><div><br /><a name='more'></a></div><div>The terms of the bond generally lead people to believe that they are a safe investment, as the company promises a positive return on your money. However, promises are not always honored. You must realize that the principal amount you give them will not be idling in a savings account. Instead it will be used to fund their own business, and as with any business, it can be prone to failure. In the event of a bankruptcy, bondholders may end up losing some or all of the principal amount (and all future interest payments).<br /><br /></div><h3>Stocks</h3><div>Stocks are fundamentally very different from bonds. Typically when you buy company stock on the stock market, you are not funding the company directly. Instead, you are buying a stake in the company in hopes that the share prices will go up in the future, at which point you can sell at a profit.</div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-woBxqgJ9214/UCNruNEZoWI/AAAAAAAAAKE/HtjjTtvI1U8/s1600/walmart_stock.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="125" src="http://1.bp.blogspot.com/-woBxqgJ9214/UCNruNEZoWI/AAAAAAAAAKE/HtjjTtvI1U8/s400/walmart_stock.PNG" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Stock price of Wal-Mart (ticker: WMT) the past year</td></tr></tbody></table><div>Owning shares of a company's stock is owning a part of that company, in an amount proportional to the number of shares. The total number of shares in the market represents how coarse or fine a company is divided into. If a company X is valued at $1,000,000 with a total of 100,000 shares, each share will cost $10 on the stock market. If I buy 10,000 shares for $100,000, I can claim a 10% ownership of that company.</div><div><br /></div><div>So why do people buy stock? The reason is fundamentally the same as why people invest money into companies: they believe that the business will grow and will be worth more in the future than what it's worth now. If in 5 years, company X grows to a $1,500,000 business, each share will be worth $15 and any shareholders can sell their shares for a 50% profit.</div><div><br /></div><div>Many companies also let you partake in part of their profits as a shareholder through <b>dividends</b>. If company X made $100,000 this year, the board of directors may elect to distribute the earnings to it's shareholders. In that case, each shareholder would receive $1 per share owned. However, more likely the company will reinvest the $100,000 back into the business in hopes of generating even greater profits the next year. This would raise the value of the company, causing stock prices to increase, and thus indirectly benefiting shareholders.<br /><br /></div><h3>The Rest of the Iceberg</h3><div>If you go beyond the tip, you start entering the world of futures, options, forex, swaps, and more. Even within stocks and bonds, you have preferred stock, mutual funds, floating rate notes, treasury inflation protected securities (TIPS), etc.</div><div><br /></div><div>There are a lot of possibilities and choices, but thankfully the individual investor need only concern himself with a select few. Future posts will be dedicated to giving a more in-depth analysis of how the bond market and stock market work, how money can be lost and made in these markets, and what you should do to minimize losses and maximize gains.</div><div><br /></div>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-32183386300317471072012-08-08T14:24:00.000-07:002012-08-08T15:18:18.043-07:00From zero to 401kOk so as you probably know, a <a href="http://en.wikipedia.org/wiki/401%28k%29">401k</a> doesn't actually stand for $401,000. It's a type of retirement savings account named after subsection 401(k) of some U.S. legalese [1]. So what's all the buzz behind it and why does it matter?<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-YSRKDgkjFk0/UCLerLcFG7I/AAAAAAAAAJ0/4kPhLAwh2GY/s1600/401k_sign.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://3.bp.blogspot.com/-YSRKDgkjFk0/UCLerLcFG7I/AAAAAAAAAJ0/4kPhLAwh2GY/s200/401k_sign.jpg" width="131" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Road to retirement</td></tr></tbody></table><br />A 401(k) account is provided through your employer. The idea behind it is that you put some money in every year and lock the sum away until you retire. By imposing some rather strict guidelines and fees on early withdrawals, a 401(k) account offers two very worthwhile benefits.<br /><br /><a name='more'></a><h3>Employer match</h3>Many employers will often match your contribution to your 401(k). This means if you put \( X \) amount of dollars into the account, your employer will contribute an additional \( cX \) dollars, where \( c \) is some pre-agreed upon percentage in your benefits contract. Some companies will provide a dollar for dollar match while others will match 50% or some other percentage. In addition, there is typically some additional fine print that limits the amount they contribute to some percentage of your total pay (e.g. up to 6% of your total salary).<br /><br />However, in spite of the limitations, it is ultimately free money. No matter what additional investment options you may consider, you cannot hope to compete with a 50-100% return.<br /><br /><h3>Tax Benefits</h3>Not all employers will match your contribution, but that doesn't necessarily mean you shouldn't invest in a 401(k). The second benefit is saving money on your taxes. There are two kinds of 401(k) accounts: a traditional account and a Roth account, the difference being when taxes are collected.<br /><br /><h4>Traditional 401(k)</h4>In a traditional 401(k), contributions are made on a pre-tax basis. This means that contributions are made before income taxes are collected, and you are only taxed on the <i>remaining</i> income.<br /><br />Suppose you are single and made $100,000 this year, putting yourself in the 28% tax bracket [2]. Normally, you would be paying $28,000 in taxes that year. However, if you had contributed $10,000 towards your 401(k), your <i>taxable income</i> for that year becomes $90,000, or only $25,200 in taxes. The catch is that you must pay taxes on the $10,000 when you withdraw the money in retirement.<br /><br />Why is this potentially beneficial? The key assumption is that when you retire, your retirement income (amount of money you receive through such withdrawals, pensions, etc) might be less than what you are making currently. If your income in retirement is only $35,000 per year, that will put you in the 15% tax bracket and the money you withdraw will be taxed at the <i>15%</i> rate, not the 28%. This means you pay $1,500 upon withdrawal, a net gain of 13%.<br /><h4>Roth 401(k) </h4>In a Roth 401(k), everything works in reverse: your contributions are made on a post-tax basis. You pay your income taxes as usual, and then you put money into your retirement account. The benefit of this approach is that you won't ever have to pay taxes on that money ever again. As you can see, the Roth 401(k) benefits those who are already in a low income tax bracket and will likely be a higher bracket in retirement.<br /><br />Let's consider another case study. Suppose you made $35,000 this year, taxed at a rate of 15%, leaving you with $29,750. If you put $5,000 towards your Roth 401(k), this will give you with $5,000 in retirement, regardless of what tax bracket you may be in the future.<br /><br /><h3>Other Benefits</h3>Money put into retirement is also money invested. The money is typically put into various investments like stocks, bonds, and mutual funds, where it will grow over time. You do not have to choose between putting money into a retirement account and investing it.<br /><br /><h3>So What?</h3>If you compound the tax benefits, employer match, and overall market return, you end up with a sizable gain on your retirement cash. The only cost is that you cannot withdraw the money until you retire (or else pay a hefty fee). If you have income to spare, it is almost universally worth it to put it into a retirement account.<br /><br />In the first case study, your $10,000 will be matched by your employer, giving $20,000. Over 30 years at a 10% yearly market return, this yields \( 20000(1+0.10)^{30}=348988 \). At a 15% retirement tax rate, this leaves you with <b>$296,640</b>. If you had invested this money in the stock market yourself, you would first pay a 28% tax, no employer match, subject yourself to much greater market risk, and end up with an expectation of $125,635, less than half of our previous result.<br /><br />The Roth 401(k) tells a similar story. <br /><br />On the issue of choosing between a traditional 401(k) and a Roth 401(k), optimizing your expected returns can be rather complicated. But as a simple rule, if you're in a low tax bracket (e.g. students, recent graduates, etc), go with the Roth. If you're in a high bracket, go with the traditional account. If you're somewhere in the middle, the difference is negligible compared to the big picture (I will work through the math in a future post).<br /><br /><h3>The Fine Print</h3>A few important points:<br /><ul><li>You can only withdraw without penalty after the age of 59 1/2</li><li>Withdrawing early will incur a 10% fee</li><li>In certain cases like buying a house, you can take funds from your retirement account without fees</li><li>There is a yearly contribution limit (inflation adjusted and depends on age)</li></ul><br /><h3>References</h3>[1] http://www.law.cornell.edu/uscode/text/26/401#k<br />[2] http://en.wikipedia.org/wiki/Income_tax_in_the_United_States#Year_2012_income_brackets_and_tax_ratesChenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0tag:blogger.com,1999:blog-3395163988550322009.post-56403591798073261462012-08-08T09:29:00.001-07:002012-08-08T14:27:43.977-07:00The blog takes flight<br />As the saying goes, "time is money"; and if you look at the interest rates on today's bank accounts, it is certainly not time well spent. Currently, <a href="http://en.wikipedia.org/wiki/Citibank">Citibank</a> offers a 0.01% annual percentage yield (APY), which means if I keep $1000 in my checking account, at the end of the year it will have yielded a paltry 10 cents. In 10 years time, I will have finally made my first dollar.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="http://3.bp.blogspot.com/-PWuhZ5aVysc/UCIZpD7nQWI/AAAAAAAAAJg/yYrY3t_pryU/s1600/citibank_interest.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-PWuhZ5aVysc/UCIZpD7nQWI/AAAAAAAAAJg/yYrY3t_pryU/s1600/citibank_interest.PNG" /></a></td></tr><tr><td class="tr-caption" style="font-size: 13px;">Thanks, but no thanks</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"></div>In contrast, if that same $1000 had been invested in the stock market, the story is much different. Despite the <a href="http://en.wikipedia.org/wiki/Dot-com_bubble">dot-com bust</a> in 2000-2002 and the more recent <a href="http://en.wikipedia.org/wiki/Subprime_mortgage_crisis">subprime mortgage crisis</a> of 2008, the <a href="http://en.wikipedia.org/wiki/S%26P_500">S&P 500</a> index has averaged a 9.2% annual growth over the past 45 years [1]. This means if all I did was invest in the top 500 publicly trade companies, in 10 years time my portfolio would grow a whopping 241%. That same $1000 I put in my checking account for a $1 return would have netted me $1410. And this is with almost <i>zero work</i> on my part: no stock research whatsoever.<br /><br /><a name='more'></a>So what happens when you put some effort into it? <a href="http://en.wikipedia.org/wiki/Warren_Buffett">Warren Buffett</a> is one of the most successful investors of all time, and with him at the reins of <a href="http://en.wikipedia.org/wiki/Berkshire_Hathaway">Berkshire Hathaway</a>, the company has enjoyed an average annual return of <b>19.8%</b>. This means over the last 45 years, he has increased his wealth over <b>5000 fold</b>. Sure beats leaving it with Citibank.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="http://3.bp.blogspot.com/-ZKJxW_TlALo/UCIAx8BBEOI/AAAAAAAAAJQ/1EZHZkTQAJg/s1600/exponential_growth.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-ZKJxW_TlALo/UCIAx8BBEOI/AAAAAAAAAJQ/1EZHZkTQAJg/s1600/exponential_growth.gif" /></a></td></tr><tr><td class="tr-caption" style="font-size: 13px;">The power of exponential growth</td></tr></tbody></table>In the words of Albert Einstein, "Compound interest is the most powerful force in the universe" (some discussion about this claim [2]).<br /><br />So somewhere between the decent 9.2% returns of the S&P 500 and the astronomical 19.8% returns of Mr. Buffett should lie the expectations of an intelligent investor.<br /><br />That is the purpose of this blog: to document my own discoveries, triumphs, and failures as I begin my foray into the investing world in an attempt to "beat the market." It is my intention to keep my ideas and impulses open and transparent. The purpose being two-fold: to simultaneously educate others about how to invest their money and to keep myself under constant scrutiny in my ventures.<br /><br />It is worth noting that I have no prior financial or investing experience nor education. But I shall treat this not as a liability, but as an asset. I will discuss and test the theoretical foundations behind investing, taking nothing for granted. Ultimately, my goal is to gain a comprehensive understanding of how the markets behave and develop a series of investment strategies to maximize my returns.<br /><br />On a more personal level, I will treat this as a fun, interesting, and worthwhile endeavor. Fun in the sense that there's some degree of speculation (read: gambling) involved. Interesting in that there will be mathematics and statistics in the process. And worthwhile in that I will (if I do my job right) be making a decent amount of money.<br /><br /><h3>References</h3>[1] <a href="http://www.berkshirehathaway.com/2011ar/2011ar.pdf">http://www.berkshirehathaway.com/2011ar/2011ar.pdf</a><br />[2] <a href="http://quoteinvestigator.com/2011/10/31/compound-interest/">http://quoteinvestigator.com/2011/10/31/compound-interest/</a>Chenyu Zhaohttps://plus.google.com/100370260701246453420noreply@blogger.com0