CFA level 1 Quantitative s Part考试复习资料.pdf

2012 PASSMAX All Rights Reserved PASSMAX 2012 CFA LEVEL I STUDY GUIDE STUDY SESSION 2 QUANTITATIVE METHODS 2012 PASSMAX All Rights Reserved SS2 2 HOW TO USE THIS BOOK This book only has one objective to maximize your chances of passing the CFA Exam To achieve this objective we have incorporated a number of features into this book First of all the CFA Institute has made it very clear that every examination question will be based on one or more Learning Outcome Statement LOS Consequently these notes are a direct response to each LOS nothing more and nothing less Instead of re stating the LOSs word for word we have simply titled each one based on the core concept that underlies it Furthermore when we found an LOS to be incorporating multiple concepts we broke down the LOS into its separate components and explained each one individually For example LOS 3 11 c asks the candidate to define and interpret a decision rule and the power of a test and explain the relation between confidence intervals and hypothesis tests In this study guide you will find this LOS explained in the following components 3 11 c i DECISION RULE 3 11 c ii POWER OF THE TEST 3 11 c iii CONFIDENCE INTERVALS AND HYPOTHESIS TESTS Therefore mastery of each of these components will ensure that the candidate is well prepared to handle any examination question related to this LOS This study guide will explain each concept from the ground up thus minimizing the need for candidates to memorize formulas Each study session is summarized into a separate booklet This serves a number of benefits i Convenience Since you will be studying the sessions one at a time it would be very inconvenient to be logging along an entire book comprised of multiple study sessions ii Psychological With each booklet only containing one study session you can see the quantity of material that needs to be covered in order to master that study session Having a thick book with multiple study session to go through can seem overwhelming and discouraging Therefore with our study guides you ll be able to measure your progress in 18 small manageable steps as opposed to taking 5 or 6 giant leaps We have deliberately not included any practice questions with these study guides because we believe that it is imperative for the candidate to attempt all the practice questions found in the CFA readings as well as the sample tests and mocks provided by the CFA Institute For any kind of support related to your exam preparation you may contact The Exam Coach at coach passmax org Good luck and best wishes in your pursuit of the CFA charter PASSMAX 2012 PASSMAX All Rights Reserved SS2 3 2 5 THE TIME VALUE OF MONEY 2 5 a INTERPRETING INTEREST RATES Suppose that Bank M is offering 6 per annum on its deposit accounts Across the street Bank Q is also inviting savers to deposit with them We may interpret the 6 in a number of ways 1 It s the return that savers require in order to deposit their funds with Bank M 2 If savers instead deposit with Bank Q they would forgo making 6 with Bank M Thus the 6 may be viewed as the opportunity cost of depositing funds with Bank Q In other words 6 is the yield on the best available investment alternative that s of equal risk 3 If one were to deposit 100 today the account would be worth 106 in one year Alternatively we can view the 100 today as being the present value of 106 discounted at 6 over one year Thus the 6 may also be regarded as the discount rate 2 5 b COMPONENTS OF INTEREST RATE FOR AN INVESTMENT No matter how it s interpreted a nominal value for interest rate may be found by summing the values of the following components 1 The real risk free rate RFR reflects investor s willingness to forego current consumption in order to invest today and thus have a greater consumption potential in the future The more resistant investors are to sacrificing current consumption the higher the real return must be in order to induce them to do otherwise 2 The inflation premium reflects the expected price appreciation of goods and services during the life of the investment An investment must yield enough to cover inflation so that the purchasing power of the investor s capital would not diminish For example if an investment were to yield 3 while the prices of goods were to increase by 5 then an investor would be able to purchase less number of goods a year from now As a result an investor would demand that the investment must yield more than the expected inflation The sum of the real risk free rate and the inflation premium yields us the nominal risk free rate NRFR This would be the yield that s observed on Treasuries Consequently all other investments must yield a return that s higher than the NRFR in order to compensate for the risks that they may have in relation to default risk free Treasuries 3 The default risk premium compensates the investor for any uncertainties associated with the timing and magnitude of the underlying asset s returns The more uncertain the future returns the higher will be the default risk premium demanded by investors 2012 PASSMAX All Rights Reserved SS2 4 4 The liquidity risk premium compensates investors for any loss in value that may arise as a result of a time lag that may arise between the time the decision is made to trade the security and the time that it is actually traded The more illiquid the asset the greater will be the potential time lag and thus the greater will be the divergence in price between the time of the decision and the timing of the trade Illiquid assets may force investors to make greater price concessions in order to facilitate a trade For example if buying an illiquid asset the investor may have to bid a higher price therefore costing more and if selling an illiquid asset the investor may have to ask for a lower price receiving less Thus to compensate for this risk investors would command a higher liquidity premium from illiquid assets The less liquid the asset the higher the premium 5 The maturity premium compensates investors for having to hold assets with maturities that exceed their investment horizons Holding all other variables constant a longer term maturity bond would generally provide a higher maturity premium than a corresponding shorter maturity bond In reality maturity premium is unobservable it is not simply the difference in yield between a long term Treasury bond and a short term Treasury bill as this spread would also be affected by the different inflation expectations built in to each respective security 2 5 c THE EFFECTIVE ANNUAL RATE Suppose that a bank charges 1 interest each month In practice the bank would quote its interest rate on an annualized basis but with reference to the number of times in the year that interest is charged In our example the bank s quoted rate would appear as 12 compounded monthly The 1 charged each month is referred to as the periodic rate while the 12 is referred to as the stated annual interest rate SAIR or the annual percentage rate APR Therefore the relation between the APR and the periodic rate may be stated as follows It s important to note however that the periodic rate is applied on the outstanding balance not just the original amount The difference is that the outstanding balance includes interest amounts computed from previous periods Therefore interest is being charged not only on the original principal amount but also on the accumulated interest For example had we borrowed 1 from the bank the outstanding balance would have accumulated to as follows 1 1 01 12 1 1268 By having to repay 1 1268 on a 1 loan the effective annual rate EAR was 12 68 even though the SAIR was 12 For those who prefer the formula approach 2012 PASSMAX All Rights Reserved SS2 5 Note that we subtract the 1 because that accounts for the principal repayment thus leaving us with only the interest component If interest was compounded daily At the extreme if we were to compound interest continuously the EAR would be computed as follows Notice that for the same stated annual interest rate as we increased the compounding frequency the EAR increased as well 2 5 d TIME VALUE OF MONEY PROBLEMS Now let s look at an example that incorporates compounding frequencies Suppose that you deposit 286 000 in Bank K today If the bank quotes a SAIR of 5 8 compounded quarterly what would your balance be at the end of 6 5 years Since we are measuring time in quarters we would enter the following values for the respective time value variables found on a financial calculator Enter PV 286 000 N 6 5 x 4 26 I 5 8 4 1 45 Compute FV 415 833 2012 PASSMAX All Rights Reserved SS2 6 In other words by placing 286 000 with Bank K today a cash outflow and earning 1 45 per quarter for 26 quarters we would have accumulated 415 833 by the end of 6 5 years Note that of this total amount 286 000 was principal so the dollar interest earned must have been 415 833 286 000 129 833 2 5 e i FUTURE VALUE OF A SINGLE SUM Suppose that a bank has a savings product with an APR of 8 compounded quarterly If you were to deposit 5 000 and leave the money invested for eight years how much would you have at the end of the term Notice how we express N and I in quarterly terms When dealing with time value problems it is very important that you enter these variables in the time denomination that is appropriate for the exercise In the extreme case when compounding is continuous we use the following formula to solve for PV or FV Therefore if the same bank had been offering an APR of 8 compounded continuously the future value of the 5 000 at the end of eight years would be found as follows FV 5 000 e 08 8 9 482 2 5 e ii PRESENT VALUE OF A SINGLE SUM Suppose that an investment is expected to pay off 10 000 at the end of six years How much would you be willing to pay for this investment today if your required rate of return was 7 2 Using a financial calculator 2012 PASSMAX All Rights Reserved SS2 7 2 5 e iii ORDINARY ANNUITIES AND ANNUITY DUE An annuity describes a series of equal cash flows that continues over a finite period There are two types of annuities distinguished by the time in the period when the payments are made For instance an ordinary annuity assumes that the payments are made at the end of each period whereas an annuity due assumes that the payments are made at the beginning of each period Suppose that you plan to start a savings program in which you would invest 3 000 at the end of each year at an annual interest rate of 8 How much will you have by the end of 13 years Now suppose that you planned to invest the 3000 at the beginning of each year How much would you have at the end of the same horizon Notice that for the same annual savings the annuity due resulted it in a higher future value This makes intuitive sense since with an annuity due the savings program began to earn interest one period sooner CAUTION After completing an annuity due problem you must reset your calculator back to its default mode otherwise all subsequent annuity problems will be solved as if the payments were made in the beginning To compute the PV of an annuity the process is just a simple Suppose that an investment is expected to yield 800 at the end of each month for the next two years If you require a monthly yield of 0 7 how much would you be willing to pay for this investment today Now suppose that this investment paid 800 at the beginning of each month How much would it be worth now 2012 PASSMAX All Rights Reserved SS2 8 Notice again that for the same set of values an annuity due resulted in a much higher present value than its corresponding ordinary annuity Therefore it is always the case then that the PV and FV of an annuity due will always exceed that of a corresponding ordinary annuity 2 5 e iv PERPETUITY A perpetuity describes a stream of constant cash flows that continues into infinity The present value of a perpetuity may be found as follows Therefore assuming that there is a preferred stock which pays an annual dividend of 2 32 how much would you be willing to pay for the stock if your required rate of return was 10 2 Since a perpetuity runs into infinity one cannot find its future value In other word if it has no end then how can we find its ending value 2 5 e v PV that is when the investment is yielding more than its opportunity cost NPV may also be interpreted as the present value of cash flows that are in excess of the principal repayment and capital charge for each period In our case the annual principal repayment and capital charge may be computed as follows When a company embarks on a zero NPV project value is neither added nor is it destroyed The company would simply become larger but without adding any benefits For example if a company raises 1 000 and buys an asset which will generate cash flows that have a present value of 1 000 today then there is no value added Instead the company would now simply have 1 000 more in assets There are a number of points to keep in mind when computing NPV 1 Focus only on the marginal cash flows arising as a result of the specific project Therefore expenditures that would exist irrespective of whether we undertake the project or not should be ignored 2 All cash flows incurred before the evaluation date of the project must be ignored when computing NPV These are commonly referred to as sunk costs 3 All cash flows must be on an after tax basis 4 If there are a number of mutually exclusive projects choose the one with the highest NPV 2012 PASSMAX All Rights Reserved SS2 13 2 6 a ii CALCULATING AND INTERPRETING IRR The internal rate of return IRR may be interpreted in a couple of ways 1 It s the project s expected rate of return In other words given its current cost what average rate of return would the project s cash flows translate into 2 It s the discount rate that will make the PV of the project s cash flows equal to its cost In other words IRR is the rate at which NPV will equal to zero Suppose that an investment is expected to generate annual cash flows of 12 000 over the next 7 years Your required rate of return is 9 If this investment is priced at 43 000 what is its IRR PMT 12 000 N 7 PV 43 000 Compute I 20 22 Therefore the project is expected to yield 20 22 or alternatively 20 22 is the rate that would equate NPV to zero There are a number of points to keep in mind when interpreting IRR 1 IRR will only be realized if the project s interim cash flows are also reinvested at the initial IRR Should these cash flows be reinvested at rates below the initial IRR then the realized return will be less than the initial IRR On the other hand if the interim cash flows are reinvested at rates above the initial IRR then the realized return will be greater than the initial IRR 2 IRR simply measures the project s cash flows relative to the initial investment it does not take into consideration the investor s required rate of return 3 It is possible for a given project to yield multiple IRRs This generally occurs when some of the interim cash flows are negative The decision rule with respect to IRR is as follows 1 If the IRR exceeds the required rate of return the project should be accepted In our case the project IRR of 20 22 well exceeded the required rate of return of 9 Therefore we would accept such a project 2 If the IRR is less than the required rate of return the project should be rejected 3 If the IRR is equal to the required rate of return then we would be indifferent between accepting and rejecting the project 2012 PASSMAX All Rights Reserved SS2 14 2 6 b i NPV RULE vs IRR RULE The NPV rule and the IRR rule are conceptually linked since both measure benefit relative to cost For example if on a stand alone basis the project s benefits exceed its cost then it must be true that 1 IRR exceeds required return and 2 PV exceeds the initial investment i e NPV 0 Therefore both the NPV rule and the IRR rule would lead to the acceptance of this project It follows then that for a given required rate of return the IRR and the NPV rule will result in the same decision The exception to this rule arises if there are multiple projects available and they are mutually exclusive i e only one may be chosen even if they all have positive NPVs 2 6 b ii PROBLEMS WITH THE IRR METHOD When the projects are independent the IRR rule and the NPV rule will always lead to the same Accept Reject decision In other words if an independent project were to be accepted under the IRR rule then it would also be accepted under the NPV rule However if the projects are mutually exclusive the IRR rule and the NPV rule may lead to different decisions These conflicts typically arise when 1 The initial investment amounts differ among the projects i e differences in project size 2 The timing of the cash flows differ For example when one project has a greater proportion of its cash flows in the beginning relative to the other project then the rankings will differ based on the IRR and NPV method Whenever there is a conflict between the two decision rules the proper course of action is to abide by the NPV rule We say this for number of reasons 1 Between NPV and IRR only NPV incorporates our required rate of return and therefore our opportunity cost of capital 2 The IRR method assumes that the interim cash flows are reinvested at the initial IRR whereas the NPV method assumes that the cash flows are reinvested at our required rate of return In financial theory the latter assumption is more plausible 3 Since shareholders objective is to maximize share value we like to employ measures which indicate the amount of value that s added Once again NPV better serves this purpose 2012 PASSMAX All Rights Reserved SS2 15 2 6 c HOLDING PERIOD RETURN HPR HPR is an un annualized measure of return which includes not only the capital appreciation of the asset but the accumulated cash flows as well For a single period i e with no opportunity to invest any income HPR may be computed as follows Suppose that at the beginning of the