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A cost-based optimizer can go further Suppose the system catalog contains three additional pieces of information: (1) that there are 100 rows in Table1, (2) that there are two pages in Table1, and (3) that the value 55 appears 60 times in the index for column2 Those facts change everything The equals operation will match on 60% of the rows, so it's not a narrow search And he whole table can be scanned using two page reads, whereas an index lookup would take three page reads (one to lookup in the index, two more to fetch the data later) Therefore the cost-based optimizer makes a different plan: find matching rows using a table scan Notice that the cost-based optimizer is using volatile data (the row and column values that have been inserted) and an override (that the contents are more important than the fixed assumptions) In other words, a cost-based optimizer is a rule-based optimizer that has additional, volatile information available to it so that it can override the fixed assumptions that would otherwise govern its decisions The terminology causes an impression that one optimizer type is based on rules while the other is based on cost That's unfortunate because both optimizer types use rules and both optimizer types have the goal of calculating cost The reality is that cost-based is an extension of rule-based, and a better term would have been something like "rule-based++" Most vendors claim that their DBMSs have cost-based optimizers, as you can see from Table 17-1 The claims don't mean much by themselves What's important is whether the optimizer estimates cost correctly and how it acts on the estimate In this chapter, we'll look at the actions DBMSs take to fulfill their claims Table 17-1 Cost-Based Optimizers "Explains" the Access "Updates" Statistics for the Plan Optimizer EXPLAIN RUNSTATS SET EXPLAIN UPDATE STATISTICS EXECUTE QEP optimizedb utility SELECT PLAN SET STATISTICS EXPLAIN UPDATE STATISTICS EXPLAIN ANALYZE TABLE EXPLAIN PLAN FOR ANALYZE SET SHOWPLAN ON UPDATE STATISTICS.

illustrating the default initialization of npoints, which occurs when the class Point is prepared ( 1232), and the default initialization of x, y, and root, which occurs when a new Point is instantiated See 12 for a full description of all aspects of loading, linking, and initialization of classes and interfaces, plus a description of the instantiation of classes to make new class nstances 4126 Types, Classes, and Interfaces In the Java programming language, every variable and every expression has a type that can be determined at compile time The type may be a primitive type or a reference type Reference types include class types and interface types Reference types are introduced by type declarations, which include class declarations ( 81) and interface declarations ( 91) We often use the term type to refer to either a class or an interface Every object belongs to some particular class: the class that was mentioned in the creation expression that produced the object, the class whose Class object was used to invoke a re ective method to produce the object, or the String class for objects implicitly created by the string concatenation operator + ( 15181) This class is called the class of the object (Arrays also have a class, as described at the end of this section) An object is said to be an instance of its class and of all superclasses of its class Sometimes a variable or expression is said to have a run-time type This refers to the class of the object referred to by the value of the variable or expression at run time, assuming that the value is not null The compile time type of a variable is always declared, and the compile time type of an expression can be deduced at compile time The compile time type limits the possible values that the variable can hold or the expression can produce at run time If a run-time value is a reference that is not null, it refers to an object or array that has a class, and that class will necessarily be compatible with the compile-time type Even though a variable or expression may have a compile-time type that is an interface type, there are no instances of interfaces A variable or expression whose type is an interface type can reference any object whose class implements ( 815) that interface Here is an example of creating new objects and of the distinction between the type of a variable and the class of an object:.

156 - Investment Planning (4) Because this is a relative measure, the Sharpe index must be used to compare alternative investments Note: In comparing, bigger is better (5) If the portfolio is fully diversi ed (all nonsystematic risk has been eliminated), then the Sharpe index should yield similar results for a comparison of several investments as the Treynor index (6) The Sharpe ratio is calculated as rp rf Si s where rp is the portfolio rate of return, rf is the risk-free rate of return, and is the standard deviation of the portfolio B Treynor ratio (1) Relative measure of the risk-adjusted performance of a portfolio based on the market risk (ie, the systematic risk); therefore, use with diversi ed portfolios (2) Risk is measured by the beta coef cient ( ) (3) If the portfolio is fully diversi ed (all nonsystematic risk has been eliminated), then both indices (Sharpe and Treynor) should yield the same results, because diversi cation will eliminate all unsystematic risk from the portfolio (4) Because this is a relative measure, the Treynor index must be used to compare alternative investments In comparing, if the Ti 0, that is good; if < 0, that is no good (5) The Treynor index should be computed for the market to determine whether a particular portfolio has outperformed the market The results do not indicate by how much each portfolio outperformed the market (6) The Treynor ratio is calculated as beta where rp is the realized return of the portfolio and rf is the risk-free rate of return C Jensen ratio (1) Alpha, , is an absolute measure of performance and measures how well a managed portfolio performed relative to an unmanaged portfolio of equal risk (2) It determines how much the realized return differs from the required return The following formula is used to nd alpha: = rp [rf + (rm rf) beta] (3) In the equation, the (referred to as alpha) value indicates whether a portfolio manager is superior or inferior in market timing and stock selection A positive alpha indicates a superior manager, and a negative alpha indicates an inferior manager (4) Example: Assume a return of 15 percent with a beta of 12 for manager X when the market return is 143 percent and the risk-free rate is 7 ercent The alpha is expressed as (a) = 015 [007 + (0143 007)12] = 00076 (b) This indicates inferior performance because it is negative If portfolio manager Y earns a return of 125 percent with a beta of 07, then the alpha is expressed as = 0125 [007 + (0143 007)07] = 00039 (c) This indicates superior performance because it is positive The absolute return for manager X is higher, but the risk-adjusted return for manager Y is greater, denoting Ti rp rf.

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158 - Investment Planning C In the investment management industry, the time-weighted return is the preferred method of performance measurement because it is not affected by the timing of cash ows If a client adds funds to an investment portfolio at an unfavorable time, the dollar-weighted return will tend to be depressed If funds are added at a favorable time, the dollar-weighted return will tend to be elevated D As indicated in the previous example, the time-weighted rate of return is less than the dollar-weighted rate of return because the stock performed better in the second year when the investor owned more shares If the stock performed better in the rst year rather than the second year when the investor had fewer shares, the time-weighted return would have been more than the dollar-weighted return 7 Probability analysis, including Monte Carlo A Monte Carlo simulation is a mathematical technique for numerically solving differential equations The technique tends to be computer intensive B To understand how the process works, consider an example of how a complex option might be priced Suppose the option s value is dependent on two underliers, a stock index and an exchange rate Monte Carlo simulation might be used to price such an option as follows: (1) Randomly generate 10,000 scenarios for the value, on the option s expiration date, of the two underliers Do so in a manner that is consistent with an assumed (risk neutral) joint probability distribution of the two variables (2) Determine what the option s expiration value would be in each of the 10,000 scenarios (3) Form a histogram of those results This represents a discrete approximation for the probability distribution of the option s expiration value The discounted mean of the histogram is the estimated option price C ote that this solution yields only an approximate price By using more scenarios say 20,000 instead of 10,000 the precision of the result can be improved D A probability distribution is a mathematical function that describes the probabilities of possible events in a sample space The sum probability of all the possible events in the sample space must equal 1.

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