Dividend Discount Model

This is part of a series on valuation techniques.

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.

Suppose I have a constant cost of capital (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.

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.

Perhaps also of interest, we assumed that the first dividend would be distributed the very next day. This reflects the maximum value 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.

Portfolio Update (6 months later)

My portfolio gains versus the S&P, Dow, and NASDAQ.

It's been about 6 months now after I bought my first round 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.

First, let me go over my current portfolio as well as some positions that I've closed since my initial purchase.

Company	Ticker	Status	% Gain
Cisco Systems Inc.	CSCO	Closed	16%
Citigroup Inc.	C	Closed	14%
Hewlett-Packard Company	HPQ	Open	-3%
Intel Corporation	INTC	Open	-8%
JetBlue Airways Corporation	JBLU	Open	21%
JPMorgan Chase & Co.	JPM	Closed	8%
Knight Capital Group Inc.	KCG	Open	24%
NRG Energy Inc.	NRG	Open	17%
Office Depot Inc.	ODP	Closed	14%
Pepco Holdings, Inc.	POM	Open	2%
PG&E Corporation	PCG	Open	-7%
Safeway Inc.	SWY	Open	32%
Staples, Inc.	SPLS	Closed	9%
Xerox Corporation	XRX	Open	16%

As you can see, I closed positions in Cisco, Citigroup, JPMorgan Chase, Office Depot, and Staples.

Valuation Techniques: Liquidation value

This is part of a series on valuation techniques.

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.

I will define the liquidation value of a company as the net worth of a company's tangible assets in event of a bankruptcy.

How it useful?

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?

Neither accuracy nor precision are necessary conditions to make a profit in investing. The only necessary condition to successful investing is arbitrage. 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 lower bounds on the price to determine if it is a worthwhile investment.

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.

Valuation Techniques

Investing 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 algorithmic trading.

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.

Many present models involve looking at one aspect of a business, such as dividends, cash flow, earnings, etc. From these, you can derive dividend discount model, discounted cash flow, 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.

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.

1. Liquidation value
2. Dividend Discount Model

Hewlett-Packard (HPQ) Qualitative Analysis

Over the past week, Hewlett-Packard Company (ticker: HPQ) 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.

The PC isn't going away any time
soon

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.

In fact, it is precisely bear-ish sentiments like these that give investors arbitrage opportunities like this.

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:

Value vs. Growth Investing

If you have done any research on stocks, mutual funds, etc., you have probably heard the terms value stocks and growth stocks. 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.

Benjamin Graham (1894-1976) is hailed as the
father of value investing

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.

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.

Day trading and why you shouldn't do it

Day 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.

Consider the following intraday time series for a stock:

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.

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.

Diversity is Safety

Today, 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.

As you can see from my previous post, 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.

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%.

We can expect a 10% gain on average. However the law of large numbers only holds true over the course of many samples. In this case, there is 34% that you will lose 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.

The probability that you will lose money

Do stock prices matter?

Do stock prices by themselves have any impact on whether or not you should buy it?

TLDR: No.

As an example, consider the two stocks: General Electric and Berkshire Hathaway Class A.

Stock	Ticker	Price	Market Capitalization
General Electric Company	GE	20.99	221.63B
Berkshire Hathaway Inc.	BRK.A	127,380.00	210.91B

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.

Yet from a psychological standpoint, people will drawn more towards low priced shares. However, the raw share price has nothing to do with the market value of the company.

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).

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.

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.

The first stocks

My 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.

Company	Ticker	Bought Price/Share	Current Price/Share	% Gain
Cisco Systems Inc.	CSCO	15.86	17.70	11.60%
Hewlett-Packard Co.	HPQ	17.87	19.41	8.62%
JP Morgan Chase	JPM	36.06	36.92	2.38%
NRG Energy	NRG	19.81	20.88	5.40%
PG&E Corp.	PCG	45.85	45.39	-0.99%
Xerox Corp.	XRX	6.94	7.17	3.31%

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!

Like a boss

Are 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.

But wait, isn't this just an elaborate Ponzi scheme? Let me explain.

Puts Nigerian scammers to shame

Ponzi Schemes

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].

Stocks, bonds, derivatives, oh my!

Today, there are dozens of types of financial instruments employed, ranging from debt securities to derivatives. However, by far the most common are stocks and bonds. These two form the staples of any investor's portfolio, both an individual's and an institution's. By Amdahl's law, 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.

Bonds

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 principal, in return for regular interest payments. When the bond term ends, known as reaching maturity, the principal will be returned to you in full.

U.S. Steel Corporation bond

The interest rate, called the coupon, 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).