CFA 2018 level 3 schweser practice exam CFA 2018 level 3 question bank CFA 2018 CFA 2018 r33 evaluating portfolio performance IFT notes

It can be divided into the following three components:  Performance measurement  Performance attribution  Performance appraisal The focus of this reading is on how fund sponsors owner

Evaluating Portfolio Performance

1 Introduction 3

2 The Importance of Performance Evaluation 3

2.1 The Fund Sponsor’s Perspective 3

2.2 The Investment Manager’s Perspective 3

3 The Three Components of Performance Evaluation 3

4 Performance Measurement 4

4.1 Performance Measurement without Intraperiod External Cash Flows 4

4.2 Total Rate of Return 4

4.3 The Time-Weighted Rate of Return 4

4.4 The Money-Weighted Rate of Return 5

4.5 TWR versus MWR 5

4.6 The Linked Internal Rate of Return 5

4.7 Annualized Return 6

4.8 Data Quality Issues 6

5 Benchmarks 6

5.1 Concept of a Benchmark 6

5.2 Properties of a Valid Benchmark 7

5.3 Types of Benchmarks 7

5.4 Building Custom Security-Based Benchmarks 8

5.5 Critique of Manager Universes as Benchmarks 9

5.6 Tests of Benchmark Quality 9

5.7 Hedge Funds and Hedge Fund Benchmarks 10

6 Performance Attribution 10

6.1 Impact Equals Weight Times Return 10

6.2 Macro Attribution Overview 11

6.3 Macro Attribution Inputs 11

6.4 Conducting a Macro Attribution Analysis 12

6.5 Micro Attribution Overview 13

6.6 Sector Weighting/Stock Selection Micro Attribution 14

6.7 Fundamental Factor Model Micro Attribution 15

6.8 Fixed-Income Attribution 15

7 Performance Appraisal 18

7.1 Risk-Adjusted Performance Appraisal Measures 18

7.2 Quality Control Charts 19

7.3 Interpreting the Quality Control Chart 20

8 The Practice of Performance Evaluation 21

8.1 Noisiness of Performance Data 21

8.2 Manager Continuation Policy 22

8.3 Manager Continuation Policy as a Filter 22

Summary 23

Examples from the Curriculum 32

Example 1 Rate-of-Return Calculations When There Are No External Cash Flows 32

Example 2 Rate-of-Return Calculations When External Cash Flows Occur at the Beginning or End of an Evaluation Period 32

Example 3 Calculating Subperiod Rates of Return 33

Example 4 Calculating the TWR 34

Example 5 Calculating the MWR 34

Example 6 When TWR and MWR Differ 34

Example 7 An Example of LIRR 35

Example 8 Annualized Return 35

Example 9 Returns Due to Style and Active Management 35

Example 10 Returns from a Market Model 36

Example 11 An Analogy to the Expression for Revenue 36

Example 12 Active Return Relative to a One-Factor Model 37

Example 13 The Pure Sector Allocation Return for Consumer Nondurables 37

Example 14 The Within-Sector Allocation Return for Technology 38

Example 15 The Allocation/Selection Interaction Return for Technology 38

Example 16 Fundamental Factor Model Micro Attribution 38

Example 17 The Influence of Noise on Performance Appraisal 39

This document should be read in conjunction with the corresponding reading in the 2018 Level III CFA®

Program curriculum Some of the graphs, charts, tables, examples, and figures are copyright

2017, CFA Institute Reproduced and republished with permission from CFA Institute All rights reserved

Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of the

products or services offered by IFT CFA Institute, CFA®, and Chartered Financial Analyst® are

trademarks owned by CFA Institute

1 Introduction

Performance evaluation is the ex post analysis of investment performance It can be divided into the

following three components:

 Performance measurement

 Performance attribution

 Performance appraisal

The focus of this reading is on how fund sponsors (owners of large pool of investable assets) and

investment managers conduct performance evaluation

2 The Importance of Performance Evaluation

LO.a: Demonstrate the importance of performance evaluation from the perspective of fund

sponsors and the perspective of investment managers

2.1 The Fund Sponsor’s Perspective

Form a fund sponsor’s perspective, performance evaluation acts as a feedback and control mechanism

It helps answer the following questions:

 What is the fund’s performance relative to investment objectives?

 What are the investment program’s strengths and weaknesses?

 What are the successful and unsuccessful strategies?

2.2 The Investment Manager’s Perspective

From an investment manager perspective, performance evaluation is important because:

 Virtually all fund sponsors will insist on performance evaluation

 It helps determine the effectiveness of various elements of investment process and examine

relative contributions of those elements

3 The Three Components of Performance Evaluation

LO.b: Explain the following components of portfolio evaluation: performance measurement,

performance attribution, and performance appraisal

Performance evaluation is measured for an account An account is defined as ‘one or more portfolios

managed by one or more investment managers’ Thus an account could be a single portfolio invested by

a single manager or numerous portfolios invested by many different managers across multiple asset

categories

The three questions related to investment performance of an account are:

1 What was the account’s performance? – Measurement (Section 4)

2 Why did the account produce the observed performance? – Attribution (Section 6)

3 Is the account’s performance due to luck or skill? – Appraisal (Section 7)

4 Performance Measurement

4.1 Performance Measurement without Intraperiod External Cash Flows

If there are no intraperiod external cash flows, then the account’s rate of return during the evaluation

period can be calculated as:

𝑟𝑡 =𝑀𝑉1− 𝑀𝑉0

𝑀𝑉0

Example 1 illustrates the use of this formula

Refer to Example 1 from the curriculum

If there is an external cash flow at the beginning of the evaluation period, then the account’s rate of

return can be calculated as:

𝑟𝑡 =𝑀𝑉1− (𝑀𝑉0+ 𝐶𝐹)

𝑀𝑉0+ 𝐶𝐹

If there is an external cash flow at the end of the evaluation period, then the account’s rate of return

can be calculated as:

𝑟𝑡 =(𝑀𝑉1− 𝐶𝐹) − 𝑀𝑉0

𝑀𝑉0

Example 2 illustrates the use of these formulae

Refer to Example 2 from the curriculum

4.2 Total Rate of Return

Prior to 1960s performance measurement focused on income Since then the focus has shifted to total

rate of return which measures increase in wealth due to income and capital gains

In our discussions henceforth, it is assumed that the rate of return refers to the total rate of return

LO.c: Explain the following components of portfolio evaluation: performance measurement,

performance attribution, and performance appraisal

This LO is covered in sections 4.3, 4.4 and 4.5

4.3 The Time-Weighted Rate of Return

Time-weighted rate of return (TWR) reflects the compound rate of growth of $1 invested at T = 0

To calculate TWR, the account must be valued every time an external cash flow occurs These sub period

returns must then be linked together to compute the TWR for the entire evaluation period

A process called ‘chain-linking’ is used to combine the sub period returns In this method we first add 1

to the decimal rate of return for each sub period to create a set of ‘wealth relatives’ Wealth relatives

are simply the ending value of one unit of currency invested at each sub period’s rate of return Then

the wealth relatives are multiplied together to produce a cumulative wealth relative for the full period,

and 1 is subtracted from the result to obtain the TWR

rtwr = (1 + r t,1 ) × (1 + r t,2 ) × … × (1 + r t,n) – 1  

Refer to Example 3 from the curriculum

Refer to Example 4 from the curriculum

4.4 The Money-Weighted Rate of Return

Money-weighted rate of return (MWR) measures compound growth rate of all funds invested in the

account over the evaluation period Put simply, it is the IRR of the portfolio

Refer to Example 5 from the curriculum

Note: The curriculum uses a long formula to calculate the MWR, however, we recommend using the CF

register and IRR function to compute the MWR

4.5 TWR versus MWR

Represents growth of a single unit of currency

invested

Represents average growth of all money invested

Unaffected by external cash flows Sensitive to size and timing of external cash

flows

Appropriate measure if investment manager has

little or no control over external cash flows

Appropriate measure if investment manager has control over timing of external cash flows (for example with private equity)

Requires valuation on every day that an external

cash flow takes place This is a major

disadvantage of TWR

Requires valuation at start and end of period

Under normal conditions TWR and MWR will produce similar results However, when large external cash

flows occur and the account’s performance fluctuates significantly during the measurement period, then

the MWR and the TWR can differ materially

Refer to Example 6 from the curriculum

4.6 The Linked Internal Rate of Return

TWR requires valuation on every day that an external cash flow takes place To overcome this drawback

and make calculations simpler, we use the Linked Internal Rate of Return (LIRR) method

In this method, TWR is approximated by calculating the MWR over reasonably frequent time intervals

and then chain linking those returns

Refer to Example 7 from the curriculum.

4.7 Annualized Return

For comparison purposes we often need to annualize returns To annualize the returns, we first chain

link sub period returns for each year Then we calculate the geometric mean of the annual returns

Refer to Example 8 from the curriculum

4.8 Data Quality Issues

LO.d: Identify and explain potential data quality issues as they relate to calculating rates of return

Quality of performance management process depends on quality of input data For accounts invested in

liquid and transparently priced securities, reported rates are likely to be reliable However, for accounts

invested in illiquid and infrequently priced assets, the underlying valuations may be suspect The

estimated prices may have been derived based on dealer-quoted prices for similar assets (matrix

pricing)

We should have appropriate data collection procedure and the stated account value should:

 Reflect impact of unsettled trades

 Reflect income owed to or by the account

5 Benchmarks

5.1 Concept of a Benchmark

LO.e: Demonstrate the decomposition of portfolio returns into components attributable to the

market, to style, and to active management

A benchmark can be thought of as:

 Collection of securities or risk factors and associated weights that represent the persistent and

prominent investment characteristics of an asset category or a manager’s investment process

 Passive representation of manager’s investment style

 Opportunity set that represent the manager’s area of expertise

The difference between the manager’s benchmark portfolio and the market index (B – M) can be

defined as the manager’s investment style S

P = M + S + A

This equation states that a portfolio return has three components: market, style, and active

management

Refer to Example 9 from the curriculum

LO.f: Discuss the properties of a valid performance benchmark and explain advantages and

disadvantages of alternative types of benchmarks

This LO is covered in sections 5.2 and 5.3

5.2 Properties of a Valid Benchmark

A valid benchmark should have the following properties:

 Unambiguous The identities and weights of securities or factor exposures constituting the

benchmark are clearly defined

 Investable It is possible to forgo active management and simply hold the benchmark

 Measurable The benchmark’s return is readily calculable on a reasonably frequent basis

 Appropriate The benchmark is consistent with the manager’s investment style or area of

expertise

 Reflective of current investment opinions The manager has current investment knowledge (be

it positive, negative, or neutral) of the securities or factor exposures within the benchmark

 Specified in advance The benchmark is specified prior to the start of an evaluation period and

known to all interested parties

 Owned The investment manager should be aware of and accept accountability for the

constituents and performance of the benchmark It is encouraged that the benchmark be

embedded in and integral to the investment process and procedures of the investment

manager

5.3 Types of Benchmarks

The following table summarizes the various types of benchmarks and the advantages and disadvantages

of each type

Absolute - An absolute return is

the return objective

satisfy benchmark validity criteria

Manager Universes – Median

manager or fund from a broad

Benchmark Advantages Disadvantages

understand, widely available and satisfies most properties of

a valid benchmark

At times manager’s style might differ from style reflected in a market index

Style Indexes - Represent

specific portions of an asset

Factor-Model-Based - Use a set

of factor exposures as a

benchmark

Captures systematic sources of return; easy to see manager’s investment style

Not intuitive: very few think in terms of factor exposures when designing a portfolio; not easily investable

Returns-Based - Benchmark

constructed using 1) series of

manager’s account returns and

2) series of returns on several

investment style indexes over

the same period Then identify

combination that most closely

tracks the account’s returns

Easy to use and intuitive

Useful when only information is account return information

Might hold positions that manager finds unacceptable

Requires many months of data

Custom Security Based -

Represents manager’s research

The simplest form of a factor model is a one-factor model Example: the market model In a market

model the return on a security is expressed as a linear function of the return on a broad market index

Rp = a p + βpRI + εp  

Refer to Example 10 from the curriculum

In a multi factor model, we include more than one factors, for example: company’s size, industry,

growth characteristics, financial strength The general form of a multi-factor model is given below:

Rp = a p + b1F1 + b2F2 + … + b KFK + εp

A normal portfolio is a portfolio with exposures to sources of systematic risk that are typical for a

particular manager, i.e it has a normal beta exposure to the various systematic risk factors

5.4 Building Custom Security-Based Benchmarks

LO.g: Explain the steps involved in constructing a custom security-based benchmark

To build a custom security benchmark we need to follow these steps:

 Identify prominent aspects of the manager’s investment process

 Select securities consistent with that investment process

 Devise a weighting scheme for the benchmark securities, including a cash position

 Review the preliminary benchmark and make modifications

 Rebalance the benchmark portfolio on a predetermined schedule

5.5 Critique of Manager Universes as Benchmarks

LO.h: Discuss the validity of using manager universes as benchmarks

Performing better than the median of a universe of investment managers is a reasonable objective, but

it is not a suitable performance benchmark because:

 It cannot be specified in advance

 It is not investable

 It is not unambiguous (who’s the median manager? Is style appropriate?)

Also manager universes are subject to survivorship bias, because fund sponsors terminate poor

performing managers

5.6 Tests of Benchmark Quality

LO.i: Evaluate benchmark quality by applying tests of quality to a variety of possible benchmarks

The following table summarizes the various criteria to test benchmark quality

Systematic Biases Minimal systematic biases or risks in the benchmark relative to the account

Historical beta of account relative to benchmark ≈ 1 on average Manager’s ability to identify attractive and unattractive investment opportunities should be uncorrelated with whether the manager’s style is in or out of favor relative to overall market

Correlation between A = (P – B) and S = (B – M) ≈ 0 on average Tracking Error Benchmark should capture important aspects of manager’s investment style

Volatility of active returns (P – B) should be low relative to volatility of (P – M) Risk

Turnover Benchmark turnover = proportion of benchmark’s market value allocated to

purchases during periodic rebalancing of benchmark Low turnover is better; otherwise investability is impacted

Largely negative active positions implies that benchmark is a poor representation

of manager’s investment approach (this shows that manager has no investment opinion on many securities)

5.7 Hedge Funds and Hedge Fund Benchmarks

LO.j: Discuss issues that arise when assigning benchmarks to hedge funds

In a long-short hedge funds the net value of the portfolio is very small Hence, standard return measures

don’t work with hedge funds Therefore, we need another performance measure One method is to

measure the value added with respect to a benchmark

The hedge fund definition is vague which makes it difficult to identify suitable benchmarks This has led

to a widespread use of the Sharpe ratio It is often used and compared with Sharpe ratio of other hedge

funds However, comparing with median performance has issues (Similar to the manager universe

benchmark.) Also the use of standard deviation as measure of risk is problematic because of high

skewness of returns in case of hedge funds

6 Performance Attribution

LO.k: Distinguish between macro and micro performance attribution and discuss the inputs typically

required for each

Performance attribution is the comparison of an account’s performance with that of a designated

benchmark and the identification and qualification of sources of differential returns

The two basic forms of performance attribution are:

 Macro attribution: performance attribution at the fund sponsor level

 Micro attribution: performance attribution at the investment manager level

6.1 Impact Equals Weight Times Return

There can be two possible reasons for a positive active return:

1 Selecting superior performing assets

2 Owning superior performing assets in greater proportion relative to the benchmark

The assets themselves can be divided or combined into all sorts of categories: economic sectors,

financial factors, investment strategies, etc

Impact = active weight x return (Similar to Revenue = Price × Quantity sold)

Refer to Example 11 from the curriculum

LO.l: Demonstrate and contrast the use of macro and micro performance attribution methodologies

to identify the sources of investment performance

This LO is covered in sections 6.2 to 6.6

6.2 Macro Attribution Overview

For a fund sponsor, ‘Account’ refers to total fund consisting of investments in various asset categories

For each category we can have multiple investment managers

Performance attribution can be carried out based on a rate of return metric Also, it is useful to think

about performance attribution in monetary terms We will look at examples of both approaches

6.3 Macro Attribution Inputs

In the macro attribution approach, we use the following sets of inputs

1 Policy allocations: asset categories and weights

2 Benchmark portfolio returns; and

3 Fund returns, valuations, and external cash flows

With these inputs in hand we can decompose a fund’s performance from a macro perspective

Exhibit 3 shows the policy allocations of a fund sponsor

Exhibit 4 shows the benchmarks that the fund sponsor has selected for its managers

Domestic equities S&P 500

Asset Category Benchmark

Equity Manager #1 Large-Cap Growth Index

Equity Manager #2 Large-Cap Value Index

Domestic fixed income Lehman Govt./Credit Index

Fixed-Income Manager #1 Lehman Int Govt./Credit Index

Fixed-Income Manager #2 Lehman Treasury Index

Exhibit 5 shows the beginning and ending values, external cash flows, and the actual and benchmark

returns for the total fund, asset categories, and investment managers

Asset Category

Beginning

Net Cash Flows

Actual Return

Benchmark Return

With the help of these inputs we can conduct a macro performance attribution (covered in next section)

6.4 Conducting a Macro Attribution Analysis

Macro attribution starts with the fund’s beginning market value and ends with it ending market value

We consider six levels and changes in these levels can increase or decrease the market value The levels

are:

1 Net Contributions: Net sum of contributions and/or withdrawals

2 Risk-Free Asset: Assumes that everything is invested in the risk-free asset

3 Asset Categories: Assumes funds are invested in asset categories per policy allocation

4 Benchmarks: Measures impact of the managers’ investment styles

5 Investment Managers: Returns actually produced by the managers

6 Allocation Effects: It is a reconciliation factor (plug)

Exhibit 6 summarizes the results for macro attribution analysis conducted using the inputs from the

previous section

Decision-Making Level

(Investment Alternative) Fund Value

Incremental Return Contribution

Incremental Value Contribution

6.5 Micro Attribution Overview

Micro attribution based on sector weighting/stock selection

Here we calculate the Investment returns of individual portfolios relative to designated benchmarks The

portfolio can be thought of as a collection of sectors which in turn are a collection of securities The

manager’s value-added can be seen to come from two sources: the weights assigned to securities in the

Portfolio relative to their weights in the benchmark and the returns on the securities relative to the

overall return on the benchmark

There are four cases of relative-to-benchmark weights and returns for security i to consider Exhibit 7

shows these cases and their impact versus the benchmark

w pi – w Bi r i – r B Performance Impact versus Benchmark

1 Positive Positive Positive

2 Negative Positive Negative

3 Positive Negative Negative

4 Negative Negative Positive

Micro attribution based on fundamental factor model

Security-by-security micro attribution is difficult if you have a large number of securities The alternative

is to use a factor model

Factors represent common elements with which security returns are correlated and can be defined in

many ways

 Sector or industry membership variables

 Financial variables such as balance sheet or income statement items

 Macroeconomic variables such as changes in interest rates, inflation or economic growth

 Movement of a broad market index

Refer to Example 12 from the curriculum

6.6 Sector Weighting/Stock Selection Micro Attribution

The value added by a manager can be broken down into three components:

1 Pure sector allocation: Decision to overweight/ underweight a sector

2 Within sector selection: Decision to overweight/underweight a security

3 Allocation/selection interaction: Combined effect of 1 and 2

The value added by a manager can be expressed as:

where S is the number of sectors and r B is the return on the Portfolio’s benchmark

Exhibit 8 shows the results of a micro attribution analysis

Portfolio Return (%)

Sector Benchmark Return (%)

Performance Attribution

Total Value- Added

Pure Sector Allocation

Allocation/

Selection Interaction

Within- Sector Selection

Examples 13, 14 and 15 demonstrate how to analyze this results

Refer to Example 13 from the curriculum

Refer to Example 14 from the curriculum

Refer to Example 15 from the curriculum

6.7 Fundamental Factor Model Micro Attribution

LO.m: Discuss the use of fundamental factor models in micro performance attribution

We first decide which factor model to use At start of evaluation period, we then determine exposure of

the portfolio and the benchmark to the factors of the fundamental factor model At end of evaluation

period, we determine performance of each factor

Refer to Example 16 from the curriculum

The normal portfolio returns represent a manager’s investment style The manager’ skill is measured by:

Actual portfolio returns – Normal portfolio returns

6.8 Fixed-Income Attribution

LO.n: Evaluate the effects of the external interest rate environment and active management on

fixed-income portfolio returns

Some concepts from sector weighting/stock selection can be applied to fixed income However, the

model needs to be enhanced to consider the major determinants of fixed income returns such as

changes in:

 General level of interest rates (represented by shifts in the treasury yield curve)

 Sector spreads

 Credit quality

As a general rule, fixed-income security prices move in the opposite direction of interest rates: If interest

rates fall, bond prices rise, and vice versa In consequence, fixed-income portfolios tend to have higher

rates of return in periods of falling interest rates and, conversely, lower rates of return in periods of

rising interest rates

Exhibit 10 demonstrates the effect of interest rate term structure

Consider the example displayed in Exhibit 10, where the US Treasury spot rate yield curve shifted

upward across all maturities during the nine-month period ending 30 June 2004, and where the return

for the Lehman Brothers US Government Index for the nine-month period was – 0.56% Comparing the

yield curves for 30 September 2004 and 30 June 2004, we see that in the third quarter of 2004 the

change in the US Treasury yield curve was more complex: short-term rates rose, while the yields on

government securities with terms to maturity longer than two years fell Reflecting the decline in

intermediate and long-term yields, the return on the Lehman Brothers US Government Index for the

three-month period was 3.11%

LO.o: Explain the management factors that contribute to a fixed-income portfolio’s total return and

interpret the results of a fixed-income performance attribution analysis

Exhibit 13 shows the sources of total return of a fixed-income portfolio

The contribution due to skills of the manager can be broken down into the following components:

 Interest rate management effect: Measures how well the manager predicts interest rate

changes

 Sector/quality effect: Measures the manager’s ability to select the right issuing sector and

quality group

 Security selection effect: Measures the manager’s ability to select the right securities within

each sector

 Trading activity: Captures the effect of sales and purchases of bonds over a given period and is

the total portfolio return minus all the other components

Exhibit 14 shows the performance attribution analysis of two fixed-income managers

Evaluation Period Returns (%) Broughton Asset

Management

Matthews Advisors

Bond Portfolio Benchmark

I Interest Rate Effect

III Other Management Effects

V Total return (sum of I, II, III,

Broughton asset management claims expertise in:

1 Interest rate management

2 Security selection

Mathews Advisors claims expertise in:

1 Identifying undervalued sectors

Data from the table validates their claims

7 Performance Appraisal

7.1 Risk-Adjusted Performance Appraisal Measures

LO.p: Calculate, interpret, and contrast alternative risk-adjusted performance measures, including

(in their ex post forms) alpha, information ratio, Treynor measure, Sharpe ratio, and M2

LO.q: Explain how a portfolio’s alpha and beta are incorporated into the information ratio, Treynor

measure, and Sharpe ratio

The most commonly used measure are:

Ex Post Alpha (also called Jensen’s alpha)

Sharpe ratio can be generalized to use the manager’s benchmark rather than the risk free asset: this

gives us the information ratio: active return/active risk

𝐼𝑅𝐴=𝑅̅𝐴 ⎯ 𝑅̅𝐵

𝜎̂𝐴−𝐵

Important points to note are:

 M2

and Sharpe ratio will evaluate manager skill in the same way Treynor Measure and ExPost

Alpha will evaluate manager skill in the same way

 It is possible that M2/Sharpe and Treynor/Ex Post Alpha give us a different conclusion when

manager takes a large amount of non-systematic risk

LO.r: Demonstrate the use of performance quality control charts in performance appraisal

This LO is covered in sections 7.2 and 7.3

7.2 Quality Control Charts

Quality control charts help us evaluate an active manager’s performance relative to his benchmark

The three assumptions underlying quality control charts are:

 Null hypothesis: manager has no investment skill

 Manger’s value-added returns are independent from period to period and are normally

distributed around expected value of 0

 Manager’s investment process does not change from period to period

If the standard deviation of value added returns is 4.1%, then based on the properties of a normal

distribution, we know that 1.28 standard deviations around the mean will capture ex ante 80 percent of

the possible outcomes associated with a normally distributed random variable 4.1 x 1.28 = 5.2 Hence

80% of possible outcomes will be +/- 5.2 around the manager’s expected value-added return of zero

This is shown in Exhibit 16

This range however only corresponds to one time period To create confidence bands for other time

periods, we transform this range into a funnel shaped lines as shown in Exhibit 15 below

7.3 Interpreting the Quality Control Chart

If the manager fails to breach the upper edge of the confidence band consistently, then we can say that

the manager performance is meeting expectations Exhibit 15 illustrates this scenario

If a manager breaches the upper edge of the confidence band consistently then we can say that the

manager performance is significantly greater than the benchmark Exhibit 17 illustrates this scenario