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1、CHAPTER 19 PERFORMANCE EVALUATIONby Andrew Clare,PhDLEARNING OUTCOMESAfter completing this chapter, you should be able to do the following:a Describe a performance evaluation process;b Describe measures of return, including holding- period returns and time- weighted rates of return;c Compare use of

2、arithmetic and geometric mean rates of returns in per-formance evaluation;d Describe measures of risk, including standard deviation and downside deviation;e Describe reward- to- risk ratios, including the Sharpe and Treynor ratios;f Describe uses of benchmarks and explain the selection of a benchmar

3、k;g Explain measures of relative performance, including tracking error and the information ratio;h Explain the concept of alpha;i Explain uses of performance attribution.175INTRODUCTIONInvestors are interested in knowing how their investments have performed. For retail investors, the performance of

4、their investments may determine whether they will enjoy a comfortable retirement, whether they will have enough money to send their children to university, or whether they can afford their dream holiday. Likewise, the pension plans, foundations, and other institutional investors want to monitor the

5、performance of their investments to ensure that the assets will be sufficient to meet their needs. The performance of a fund and its fund manager is also important to an investment management firm; after all, if the output of the car industry is cars, then the output of the investment management ind

6、ustry is, arguably, investment returns. For an investment management company, measuring and understanding fund manager performance is vital to managing and improving the investment process.But knowing the return achieved by an investment management company or fund manager is only part of the process

7、 of performance evaluation. Investment management is a competitive industry. Both investors and investment management companies will want to know how fund managers have performed relative to familiar and relevant financial market benchmarks (e.g., a stock index, such as the S&P 500 Index in the Unit

8、ed States or the Hang Seng Index in Hong Kong SAR) and relative to their peers. In addition, interested parties will want to know how the fund manager achieved the performancefor example, whether the performance was the result of skill or luck or perhaps the result of excessive risk taking.It is onl

9、y through the robust evaluation of investment performance that investment management companies and their investors can make informed decisions about their investments. After reviewing a fund managers performance, investors can decide whether they want to continue to invest with the manager or to mov

10、e their funds to another manager. Similarly, the investment management company can decide whether the manager should be asked to manage additional funds, be supported with more resources in an effort to improve the companys performance, or be replaced.The performance evaluation process includes four

11、 discrete but related components: Measure absolute returnsAdjust returns for riskMeasure relative returnsAttribute performanceThese four components are discussed in the following sections.1Introduction 2014 CFA Institute. All rights reserved.176MEASURE ABSOLUTE RETURNSAbsolute returns are the return

12、s achieved over a certain time period. Absolute returns do not consider the risk of the investment or the returns achieved by similar investments.2.1 Holding- Period ReturnsThe performance of a security, such as an equity (stock) or debt (bond) security, over a specific time periodcalled the holding

13、 periodis referred to as the holding- period return. The holding- period return measures the total gain or loss that an investor own-ing a security achieves over the specified period compared with the investment at the beginning of the period. The return over the holding period usually comes from tw

14、o sources: changes in the price (capital gain or loss) and income (dividends or interest).The holding- period return from owning an ordinary or common share of a company typically comes from a change in the price of the share between the beginning and the end of the period, as well as from the divid

15、ends received over the period. The change in the price of the shares over the period is the capital gain or loss portion of the return. The dividends received over the period are the income portion of the return. Similarly, the holding- period returns from owning bonds result from changes in price (

16、capital gain or loss) and receipt of interest (income).Example1 illustrates how holding- period returns are calculated. As always, you are not responsible for calculations, but the presentation of formulae and calculations may enhance your understanding.EXAMPLE1. HOLDING- PERIOD RETURNSAn investor b

17、uys one ordinary share in Company A on 1 January at a price of 100. On 31 December, Company A pays a dividend per share of 5, and an ordinary share of Company A is selling for 110 on that date.In this case, the holding period is one yearfrom 1 January to 31 December. The return achieved by the inves

18、tor from the increase (appreciation) in the share price over this period is calculated as follows:Capital component of the holding- period return = 110100100101000 1010=.%But the holding- period return should also include the dividend paid to the investor. The return achieved by the investor from th

19、e income received on the share is as follows:Income component of the holding- period return = 51000 055=.%2Chapter 19 Performance Evaluation177The total holding- period return is the sum of the capital and income com-ponents (i.e., 15%). Mathematically, this sum can be shown asTotal holding- period

20、return = 11010051001051000 1515()+=+=.%10010010capital gain5dividendHolding Period ReturnReturn = 15Original Investment = 1001 January31 DecemberHolding-period return = Return Original investment= (10 + 5) 100= .15= 15%The return to an investment fund or portfolio over the course of a given period i

21、s typically made up of the capital gains or losses on all of the assets held over that period plus any income earned on those assets over the same period. This income may include dividend income from equity securities, interest income for portfolios of debt securities, and rental income for portfoli

22、os of commercial real estate.HOLDING- PERIOD RETURNS FOR A VARIETY OF PORTFOLIOSWe can see how capital and income components combine to produce returns by looking at some representative investment portfolios. Exhibits 1A and 1B present the holding- period returns and the split between the capital ga

23、ins and losses portion and the income portion for a range of investment portfolios in 2010. Exhibit1A shows the investment performance of four equity portfolios. The global equity portfolio includes equity securities from around the globe; the US and European equity portfolios include equity securit

24、ies listed in the Measure Absolute Returns178United States and in Europe; the emerging market equity portfolio includes equity securities listed in emerging markets, such as Brazil, Russia, India, and Chinawidely known as the BRIC countries. Exhibit1A Capital Gains, Income, and Total Return for Equi

25、ty Portfolios, 2010Capital GainIncomeTotal ReturnReturn (%)GlobalEmerging MarketUnited StatesEurope201612840Source: Based on data from the Centre for Asset Management Research, Cass Business School, London.Exhibit1B presents the investment performance of three bond portfolios and two commercial prop

26、erty portfolios. The European government bond portfolio includes bonds issued by eurozone governments, such as France, Germany, Greece, Italy, Ireland, and Spain; the European corporate bond portfolio includes bonds issued by companies headquartered in the eurozone; the high- yield bond portfolio in

27、cludes bonds that are rated BB+ or below by Fitch and Standard & Poors and Ba1 or below by Moodys, the credit rating agencies discussed in the Debt Securities chapter; the last two portfolios include US and UK commercial property, respectively.Chapter 19 Performance Evaluation179Exhibit1B Capital Ga

28、ins, Income, and Total Return for Bond and Commercial Property Portfolios, 2010Capital GainIncomeTotal Return201510505Return (%)EuropeanGovernmentUKCommercialEuropeanCorporateEuropeanHigh YieldUSCommercialSource: Based on data from the Centre for Asset Management Research, Cass Business School, Lond

29、on.Exhibit1A shows that the total holding- period return of all the equity port-folios except the European equity portfolio was more than 12% and that the capital gains portion was much larger than the income portion. The European equity portfolios total holding- period return was approximately 4% a

30、nd was made up almost entirely of income return.Exhibit1B indicates that the total holding- period returns of the European government bonds portfolio and the European corporate bonds portfolio were positive. Each of these portfolios experienced a capital loss, but it was more than offset by positive

31、 income returns. The high- yield bond portfolio and the two commercial property portfolios had positive total holding- period returns. Each experienced both a capital gain and a positive income return.Measure Absolute Returns1802.2 Cash Flows and Time- Weighted Rates of ReturnIn the holding- period

32、return calculation in Example1, the income (the dividend) was received at the end of the holding period. This time of receipt, plus the fact that no additional investments were made during the period, makes the calculation of the return relatively easy. In practice, however, calculating a funds hold

33、ing- period return is more complex. In particular,funds may consist of hundreds of individual investments that pay income at different times throughout the holding period.clients may make additional investments (cash inflows) in and withdrawals (cash outflows) from a fund throughout the holding peri

34、od.In other words, there is a constant flow of cash into and out of most investment funds and portfolios. Additional investments and withdrawals by clients will affect the cal-culation of the performance of the fund. Example2 illustrates this point.EXAMPLE2. EFFECT OF A DEPOSIT ON A FUNDS INVESTMENT

35、 PERFORMANCESuppose that an investment fund has a value of $100million on 1 January. By 31 December, the fund has grown in value to $110million. The increase in the value of this fund came from changes in the values of the securities held in the portfolio and from income received and reinvested duri

36、ng the year. The total holding- period return on the fund is 10%, calculated as follows:Fund returnmillionmillionmillion=$.1101001000 101 10%But suppose that one of the funds clients deposited an additional $5million into the fund on 30 June. This deposit means that some of the change in the funds v

37、alue over the year was not from the performance of the securities or from the income on these securities, but attributable to the receipt of additional client money. In other words, a total holding- period return of 10% overstates the funds investment performance.Flows of money into and out of funds

38、 over time can be accounted for by dividing the measurement period into shorter holding periods. A new holding period starts each time a cash flow occursthat is, each time money flows into or out of a fund. If there is only one cash flow during the holding period, the measurement period will be divi

39、ded into two shorter holding periods. If there are two cash flows, there will be three holding periods, and so on. In practice, client cash inflows and outflows may occur on a daily basis, in which case an annual holding- period return is divided into daily holding- period returns.Example3 illustrat

40、es how the total holding- period return is calculated when a cash flow occurs during the holding period. There are two approaches used to combine returns. The first approach is to calculate the arithmetic mean by adding the two six- month returns. This approach, however, does not consider compoundin

41、g; recall from the time Chapter 19 Performance Evaluation181value of money discussion in the Quantitative Concepts chapter that compounding is the process by which interest is reinvested to generate its own interest. The second approach is to calculate the geometric mean, which does consider compoun

42、ding and is usually the preferred approach.EXAMPLE3. CALCULATION OF A FUNDS RETURN WHEN THERE IS A DEPOSITSuppose that the fund in Example2 had received one client cash inflow of $5million at the close of business on 30 June. No other cash inflows or outflows occurred in the period; there was no add

43、itional cash from clients and there was no cash from income on holdings of the fund. The holding period of one year can be divided into two periods of six months. The holding- period return is calculated as follows:First, calculate the six- month holding- period return for the period from 1 January

44、to 30 June, before the additional deposit.Next, calculate the six- month holding- period return for the period from 1 July to 31 December, including the cash inflow of $5million that increased the value of the fund on 30 June.Finally, calculate the annual holding- period return by combining the two

45、six- month holding- period returns.There is one final piece of information that is needed to calculate the return over each of these two six- month periods: the value of the fund on 30 June immediately before the inflow of $5million. Assume that the funds value was as follows (the 30 June value does

46、 not include the $5million deposit):DateFunds Value1 January$100million30 June$98million31 December$110millionThe holding- period return over the first six months (1 January to 30 June) is as follows:Fund returnmillionmillionmillion= $.981001000 020 = = 2 0 . %On 30 June, the fund has fallen in valu

47、e to $98million. But at this point, the fund experiences the positive cash inflow of $5million. This event means that at the start of the second holding period on 1 July, the fund has a value of $103million ($98million + $5million). On 31 December, the fund has a value of $110million. Thus, the hold

48、ing- period return for the second six months (1 July to 31 December) is as follows:Fund returnmillionmillionmillion=$.1101031030 068 = = 6 8 . %Measure Absolute Returns182The clients of the fund may want to know the return achieved by the fund manager over the full calendar year rather than over eac

49、h six- month period. Using our current example, the fund return was 2.0% for the first six months and 6.8% for the last six months. The funds arithmetic return for the year is 4.8% (= 2.0% + 6.8%). Alternatively, the funds compounded return for the year is calculated as follows:Fund return = (1 2.0%

50、) (1+ 6.8%) 1= 0.0466= 4.66%The fund manager achieved an annual holding- period return of 4.66%, which is the return achieved by the fund manager on the funds under management between 1 January and 31 December. Returns calculated in the manner described in Example3 are known as time- weighted rates