Slope Divergence

December 1st, 2009

To change an interpretive analysis to one that can be computerized, there are two techniques, one using slopes and the other based on the analysis of peaks. A comparison between the rate at which prices and a momentum indicator are rising or falling will give enough information to automatically identify a divergence. Using a linear regression feature in either a spreadsheet (@S] ope) or a strategy testing program (@Li nea rRegSI ope), the slope of any time interval can be found for both momentum and price over the same period. Because momentum is a detrended series, the period compared should not be too long; otherwise, the slope of the trendline will be zero, a horizontal line.
Divergence can be any combination of conflicting directions between the slope of price and the slope of momentum, including prices rising faster than momentum, momentum rising faster than prices, or the opposite. However, classic analysis has focused on momentum as a leading indicator of a change in the price trend, which limits the combinations to:
1. Prices rising and momentum failing (a bearish divergence)
2. Prices falling and momentum rising (a bullish divergence)
The strength of a bearish divergence, which can be used to select which situations are best for trading, can he determined by the momentum slope provided prices are rising, or the net of the rising slope of prices and the falling slope of momentum. In the second case, the difference between the slopes must be converted to a common denominator. because the angle of price movement can cover a far wider range than the angle of momentum movement.

OSCILLATORS

November 26th, 2009

Because the representation of the momentum index is that of a line fluctuating above and below a zero value, this technique has often been termed an oscillator Even though it does oscillate, the use of that word is confusing. In this presentation, the term oscillator will be restricted to a specific form of momentum, or rate-of-change indicator, which is normalized and expressed in terms of values that are limited to the ranges between +1 and -1, +1 and 0, or 100 and 0, as in percent.
To transform a standard momentum calculation into the normalized form (maximum value of +1, minimum value of -1), divide the momentum calculation by the maximum attainable value of the momentum index. A 5-day index for silver with a 20-limit move could be divided by $1.00 to find the normalized value. If silver were to move its limit up for 5 days, the oscillator would have the value of +1 rather than the momentum value of 100. If the limits were to expand, the divisor would change as well, giving the technique a means of adjusting for varying volatility Using the normalized momentum, or oscillator, the top and bottom zones become volatility-adjusted at any level.
Erratic movements in the simple momentum and oscillator make it a very difficult tool to apply without additional work. Some of these problems can be eliminated by making the buying and selling zones more extreme or by smoothing the indicator values.

The Risk/Return Tradeoff

November 23rd, 2009

At one extreme, if we are unwilling to bear any risk at all, but we are willing to forego the use of our money for a while, then we can earn the risk-free rate. Because the risk-free rate represents compensation for just waiting, it is often called the time value of money.
If we are willing to bear risk, then we can expect to earn a risk premium, at least on average. Further, the more risk we are willing to bear, the greater is that risk premium. Investment advisors like to say that an investment has a “wait” component and a “worry” component. The time value of money is the compensation for waiting, and the risk premium is the compensation for worrying. There are two important caveats to this discussion. First, risky investments do not always pay
more than risk-free investments. Indeed, that’s precisely what makes them risky. In other words, there is a risk premium on average, but, over any particular time interval, there is no guarantee. Second, we’ve intentionally been a little imprecise about what we mean exactly by risk. As we will discuss in the chapters ahead, not all risks are compensated. Some risks are cheaply and easily avoidable, and there is no expected reward for bearing them. It is only those risks that cannot be easily avoided that are compensated (on average).

EXAMPLE OF PAYMENT STRUCTURE FOR FIXED RATE MORTGAGE

November 20th, 2009

Mortgages are among the longest-term loans that banks provide. In most countries the normal term at the onset is between 20 and 30 years. In the case of a fixed rate mortgage both the actual rate and the monthly payment are fixed. In each month a proportion of the payment goes towards repaying the principal and the remainder towards paying interest on the remaining outstanding balance.
We will base most of our analysis using a simplified example of a 20-year, fixed rate mortgage. We have simplified the payments to assume that they are done on an annual basis, rather than a monthly basis. We still need to input the basic variables in order to determine the pricing structure necessary to meet our 24% required rate of return.
The result of this payment structure is that in early years the bulk of the monthly payment goes towards interest payments. In our example of a 20-year mortgage, in the early years less than 30% of the payments go towards principal repayment. A borrower who pays off the loan after five years will find that while they have made $192 100 in total payments the outstanding balance has only fallen by $54 993 from $400 000 to $345 007.
As the principal starts to reduce, however, the proportion that goes to principal repayment starts to rise. Principal repayments account for more than half of the monthly payments from the twelfth year onward in this example.
These characteristics mean that the shorter the average remaining term of a portfolio of mortgages the greater the level of capital repayments and the lower the level of outstanding mortgage loans and interest income. This has implications for both Treasury and the capital management division. As a portfolio of mortgages ages the outstanding principal falls and less capital is required to be set aside and more and more capital is released to the capital management group. It must find an alternative use for this capital to continue to generate the required 24% pre-tax return.
For a bank to simply maintain its mortgage portfolio at a particular absolute level it must continuously write more new mortgages. This takes no account of the new mortgages that have to be written to replace loans that have been repaid as a result of a mortgagor selling her. property or paying off the loan by getting refinancing at a lower rate from another lender. This brings us to the subject of mortgage prepayment risk.
Fixed rate mortgages are more attractive to borrowers than floating rate mortgages because borrowers hold an embedded call option, allowing them to repay their loan before the formal term. This can be represented as follows:
Value of mortgage loan = Value of equivalent straight loan – Value of embedded call option
If interest rates fall borrowers can repay their outstanding mortgage and take out a new mortgage at the then lower prevailing rates. This exposes the lending bank to prepayment risk.

Online brokers

November 18th, 2009

The most important recent change in the brokerage industry is the rapid growth of online brokers, also known as e-brokers or cyberbrokers. With an online broker, you place buy and sell orders over the internet using a web browser. If you are currently participating in a portfolio simulation such as Stock-Trak, then you already have a very good idea of how an online account looks and feels.
Before 1995, online accounts essentially did not exist; by 1998, millions of investors were buying and selling securities on-line. Projections suggest that by 2000, more than 10 million online accounts will be active. The industry is growing so rapidly that it is difficult to even count the number of online brokers. By late 1998, the number was approaching 100, but the final tally will surely be much larger.
Online investing has fundamentally changed the discount and deep-discount brokerage industry by slashing costs dramatically. In a typical online trade, no human intervention is needed by the broker as the entire process is handled electronically, so operating costs are held to a minimum. As costs have fallen, so have commissions. Even for relatively large trades, online brokers typically charge less than $15 per trade. For budget-minded investors and active stock traders, the attraction is clear.
Who are the online brokers? As the industry evolves, this information changes, so check our web site (www.mhhe.com/cj) for more up-to-date information. You might notice that at least some of these online brokers are actually just branches of large discount brokers. Charles Schwab, for example, is both the largest discount broker and the largest online broker.
Competition among online brokers is fierce. Some take a no-frills approach, offering only basic services and very low commission rates. Others, particularly the larger ones, charge a little more, but offer a variety of services, including research and various banking services including check writing privileges, credit cards, debit cards, and even mortgages. As technology continues to improve and investors become more comfortable using it, online brokerages will almost surely become the dominant form because of their enormous convenience and the low commission rates.

Real Estate Price Indices

November 14th, 2009

In markets where the residential property market has been through a boom–bust cycle one of the most common requirements for analysts is to estimate the level of negative equity within the system.
Estimating system-level negative equity is only really possible if a representative property index exists. In many emerging markets that is rarely the case but it is usually possible to find some proxy or failing that actually goes to the land registry (if there is one) and check a select number of transaction prices on comparable properties.
The following example shows how to go about estimating the level of negative equity in a market. We will assume that all of the mortgages had an original term of 20 years and that banks lent on an 80% loan-to-price basis.
The starting point is to estimate how much prices have fallen over time. We will assume that the bubble took place in the late 1990s and that we are at the end of December 2000. The value of properties bought in 2Q96 is 50% lower now than when bought. All of the properties bought between 3Q95 and 3Q97 are worth less now than when bought.

Slope

November 8th, 2009

The one-day-ahead forecast suggested in “Following the Trend,” a few paragraphs earlier. is essentially a projection of the slope of the trendline. Because of the frequent erratic price movement, also called noise, the purpose of directional analysis, whether regression or moving averages, is to uncover the true direction of prices. Therefore, the slope of the trendline, or the direction of the regression forecast, is the logical answer.
The popular alternate for triggering a new directional signal is a price penetration of an envelope or band value. Using regression analysis that band can be replaced by a confidence level. While it is true that the number of random, or false, penetrations declines as the confidence band gets farther away from the trendline, so does the total number of penetrations. At any band distance there are still a large number of erroneous signals. The slope itself should be viewed as the best approximation of direction.

Types of Real Options

November 6th, 2009

The word option is a synonym for choice—the ability to do something or not do something in the future, at your discretion. Financial options are common. The most familiar are stock options, which are traded, e.g., on the Chicago Board Options Exchange (CBOE). The prices of these options can be looked up on Yahoo!Finance. Some options are traded over the counter: if you want to purchase a 10-year option on the Sony, chances are that you would have to ask someone—typically an investment bank—to manufacture such an option for you. Other financial options are embedded in contracts and securities. For example, your mortgage contract more than likely gives you the option to pay off the mortgage at your discretion, which you should do (and refinance) if interest rates drop enough. Your car insurance liability may have a deductible, which de facto means that the insurance is only an option that gives you the right to exercise it if the damage exceeds the deductible.
But this series of posts is not so much interested in financial options as it is in real options. What is the difference? A real option differs from a financial option in that the exercise of the real option requires a change in the physical, “real” project. Such real option projects can be factories, buildings, R&D activities, and so on. The most prominent real options are
Timing Your ability to start or stop a project at a time of your discretion. Abandoning Your ability to abandon a project at a time of your discretion. Accelerating Your ability to speed up a project at a time of your discretion. Expansion Your ability to expand a project at a time of your discretion. Switching Your ability to switch to a different technology.
Real options are difficult to value, but no one would argue that this means that you can ignore them. In fact, valuing real options is often more important than getting the discount rate right. You have no alternative but to give it your best shot.

Bias in Data

October 28th, 2009

When sampling is used to obtain data, it is common to divide entire subsets of data into discrete parts and attempt a representative sampling of each portion- These samples are then weighted to reflect the perceived impact of each part on the whole. Such a weighting will magnify or reduce the errors in each of the discrete sections. The result of such weighting may cause an error in bias. Even large numbers within a sample cannot overcome intentional bias introduced by weighting one or more parts
Price analysis and trading techniques often introduce bias in both implicit and explicit ways. A weighted average is an overt way of adding a positive bias (positive because it is intentional). On the other hand, the use of two analytic methods acting together may unknowingly rely doubly on one statistical aspect of the data; at the same time, other data may he used only once or may be eliminated by offsetting use. The daily high and low used in one part of a program and the daily range (high to low) in another section would introduce bias.