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LO 70.4: Determine the statistical significance of a performance measure using standard error and the t-statistic.
Alpha (a) plays a critical role in determining portfolio performance. A positive alpha produces an indication of superior performance; a negative alpha produces an indication of inferior performance; and zero alpha produces an indication of normal performance matching the benchmark. The performance indicated by alpha, however, could be a result of luck and not skill. In order to assess a managers ability to generate alpha, we conduct a r-test under the following hypotheses:
Null (i70): True alpha is zero.
Alternative ( N f : True alpha is not zero.
_ a 0 ~~ ct/V n
where: i = alpha estimate O o = alpha estimate volatility N = sample number of observations standard error of alpha estimate = a / Vn
In order to compute the r-statistic, we will need to know the alpha estimate, the sample number of observations, and the alpha estimate of volatility. From the volatility and sample size estimates, we can compute the standard error of the alpha estimate, which is shown in the denominator of the r-statistic calculation.
At a 95% confidence level (5% significance level) we reject the null hypothesis if we estimate a r-value of 2 or larger. That is, the probability of observing such a large estimated alpha by chance is only 5%, assuming returns are normally distributed.
Professors Note: Using a t-value o f 2 is a general test o f statistical significance. >From the F R M Part I curriculum, we know that the actual t-value with a 95% confidence level given a large sample size is 1.96.
If we assume an excess (alpha) return of 0.09% and a standard error of the alpha of 0.093%, the r-statistic would be equal to 0.97 (t = 0.09% / 0.093%); therefore, we fail to reject H Q and conclude that there is no evidence of superior (or inferior) performance.
Professors Note: Using statistical inference when evaluating performance is extremely challenging in practice. By the tim e you are reasonably confident that a managers returns are in fa ct due to skill, the manager may have moved elsewhere.
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
M e a s u r in g H e d g e Fu n d P e r f o r m a n c e

LO 70.3: Describe the uses for the Modigliani-squared and Treynor s measure in comparing two portfolios, and the graphical representation of these measures.
Universe Comparisons
Portfolio rankings based merely on returns ignore differences in risk across portfolios. A popular alternative is to use a comparison universe. This approach classifies portfolios according to investment style (e.g., small cap growth, small cap value, large cap growth, large cap value) and, then, ranks portfolios based on rate of return within the appropriate style universe. The rankings are now more meaningful because they have been standardized on the investment style of the funds. This method will fail, however, if risk differences remain across the funds within a given style.
The Sharpe Ratio
The Sharpe ratio uses standard deviation (total risk) as the relevant measure of risk. It shows the amount of excess return (over the risk-free rate) earned per unit of total risk. Hence, the Sharpe ratio evaluates the performance of the portfolio in terms of both overall return and diversification.
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
The Sharpe ratio is defined as:
c _ R a – R f —————
A
where: RA = average account return R f = average risk-free return ctA = standard deviation of account returns
Professors Note: Again, the risk measure, standard deviation, should ideally he the actual standard deviation during the measurement period.
The Treynor Measure
The Treynor measure is very similar to the Sharpe ratio except that it uses beta (systematic risk) as the measure of risk. It shows the excess return (over the risk-free rate) earned per unit of systematic risk.
The Treynor measure is defined as: – p _ R a – R f < - where: R a = average account return R f = average risk-free return PA = average beta Professors Note: Ideally, the Treynor measure should be calculated using the actual beta for the portfolio over the measurement period. Since beta is subject to change due to varying covariance with the market, using the premeasurement period beta may not yield reliable results. The beta for the measurement period is estimated by regressing the portfolios returns against the market returns. For a well-diversified portfolio, the difference in risk measurement between the Sharpe ratio and the Treynor measure becomes irrelevant as the total risk and systematic risk will be very close. For a less than well-diversified portfolio, however, the difference in rankings based on the two measures is likely due to the amount of diversification in the portfolio. Used along with the Treynor measure, the Sharpe ratio provides additional information about the degree of diversification in a portfolio. Sharpe vs. Treynor. If a portfolio was not well-diversified over the measurement period, it may be ranked relatively higher using Treynor than using Sharpe because Treynor considers only the beta (i.e., systematic risk) of the portfolio over the period. When the Sharpe ratio is calculated for the portfolio, the excess total risk (standard deviation) due to diversifiable risk will cause rankings to be lower. Although we do not get an absolute measure of the lack of 2018 Kaplan, Inc. Page 121 Topic 70 Cross Reference to GARP Assigned Reading - Bodie, Kane, and Marcus, Chapter 24 diversification, the change in the rankings shows the presence of unsystematic risk, and the greater the difference in rankings, the less diversified the portfolio. Jensens Alpha Jensens alpha, also known as Jensens measure, is the difference between the actual return and the return required to compensate for systematic risk. To calculate the measure, we subtract the return calculated by the capital asset pricing model (CAPM) from the account return. Jensens alpha is a direct measure of performance (i.e., it yields the performance measure without being compared to other portfolios). A = RA - E (Ra ) where: a A Ra E(RA) = RF +pA[E(RM) - RF] = alpha = alpha = the return on the account A superior manager would have a statistically significant and positive alpha. Jensens alpha uses the portfolio return, market return, and risk-free rate for each time period separately. The Sharpe and Treynor measures use only the average of portfolio return and risk-free rate. Furthermore, like the Treynor measure, Jensens alpha only takes into account the systematic risk of the portfolio and, hence, gives no indication of the diversification in the portfolio. Information Ratio The Sharpe ratio can be changed to incorporate an appropriate benchmark instead of the risk-free rate. This form is known as the information ratio or appraisal ratio: i r a = where: R a = R b = cta - b = R a - R b cta - b average account returnstandard deviation of excess returns measured as the difference : average account return = average benchmark return = standard deviation of excess returns measured as the difference between account and benchmark returns The information ratio is the ratio of the surplus return (in a particular period) to its standard deviation. It indicates the amount of risk undertaken (denominator) to achieve a certain level of return above the benchmark (numerator). An active manager makes specific cognitive bets to achieve a positive surplus return. The variability in the surplus return is a measure of the risk taken to achieve the surplus. The ratio computes the surplus return relative to the risk taken. A higher information ratio indicates better performance. Page 122 2018 Kaplan, Inc. Topic 70 Cross Reference to GARP Assigned Reading - Bodie, Kane, and Marcus, Chapter 24 Professor's Note: The version o f the information ratio presented here is the most common. However, you should he aware that an alternative calculation o f this ratio exists that uses alpha over the expected level o f unsystematic risk over the time period, a A ct(a ) M-Squared (M2) Measure A relatively new measure of portfolio performance developed by Leah Modigliani and her grandfather, 1985 Nobel Prize recipient Franco Modigliani, has become quite popular. The M 2 measure compares the return earned on the managed portfolio against the market return, after adjusting for differences in standard deviations between the two portfolios. Professor's Note: There are no squared terms in the M -squared calculation. The term M -squared" merely refers to the last names o f its originators (Leah and Franco Modigliani). The M 2 measure can be illustrated with a graph comparing the capital market line for the market index and the capital allocation line for managed Portfolio P. In Figure 2, notice that Portfolio P has a higher standard deviation than the market index. But, we can easily create a Portfolio P that has standard deviation equal to the market standard deviation by investing appropriate percentages in both the risk-free asset and Portfolio P. The difference in return between Portfolio P and the market portfolio, equals the M 2 measure for Portfolio P. Figure 2: The M2 Measure of Portfolio Performance Return 2018 Kaplan, Inc. Page 123 Topic 70 Cross Reference to GARP Assigned Reading - Bodie, Kane, and Marcus, Chapter 24 Example: Calculating the M2 performance measure Calculate the M2 measure for Portfolio P: Portfolio P mean return Portfolio P standard deviation Market portfolio mean return Market portfolio standard deviation Risk-free rate 10% 40% 12% 20% 4% Answer: To answer the question, first note that a portfolio, P, can be created that allocates 50/50 to the risk-free asset and to Portfolio P such that the standard deviation of Portfolio P equals the standard deviation of the market portfolio: cjp, = WpCTp = 0.50(0.40) = 0.20 Therefore, a 50/50 allocation between Portfolio P and the risk-free asset provides risk identical to the market portfolio. What is the difference in return between Portfolio P and the market portfolio? To answer this question, first we must derive the mean return on Portfolio P: Rp, = WpRp + WpRp = 0.50(0.04) + 0.50(0.10) = 0.07 Alternatively, the mean return for Portfolio P can be derived by using the equation of the capital allocation line for Portfolio P: Rp> Rp + R d R e
\
CTp
CTp R p +
/
R d Re V dp
/
ctm
Therefore, we now have created a portfolio, P, that matches the risk of the market portfolio (standard deviation equals 20%). All that remains is to calculate the difference in returns between Portfolio P and the market portfolio:
0.20 = 0.04 + (0.15)0.20 = 0.07
.10-0.04
0.40
\
/
V0
/
0.04 +
M2 = Rp, – RM = 0.07 – 0.12 = -0.05
Clearly, Portfolio P is a poorly performing portfolio. After controlling for risk, Portfolio P provides a return that is 5 percentage points below the market portfolio.
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
Professors Note: Unfortunately, a consistent definition ofM 2 does not exist. Sometimes M 2 is defined as equal to the return on the risk-adjusted Portfolio P rather than equal to the difference in returns between P and M. However, portfolio rankings based on the return on P or on the difference in returns between P and M will be identical. Therefore, both definitions provide identical portfolio performance rankings.
M2 will produce the same conclusions as the Sharpe ratio. As stated earlier, Jensens alpha will produce the same conclusions as the Treynor measure. However, M2 and Sharpe may not give the same conclusion as Jensens alpha and Treynor. A discrepancy could occur if the manager takes on a large proportion of unsystematic risk relative to systematic risk. This would lower the Sharpe ratio but leave the Treynor measure unaffected.
Example: Risk-adjusted performance appraisal measures
The data in Figure 3 has been collected to appraise the performance of four asset management firms:
Figure 3: Performance Appraisal Data
Return Beta
Standard deviation Standard deviation of excess returns
Fund 1 6.45% 0.88 2.74%
5.6%
Fund 2 8.96% 1.02 4.54%
6.1%
Fund 3 9.44% 1.36 3.72%
12.5%
Fund 4 5.82% 0.80 2.64%
5.3%
Market Index
6% 1.00 2.80%
N/A
The market index return and risk-free rate of return for the relevant period were 6% and 3%, respectively. Calculate and rank the funds using Jensens alpha, the Treynor measure, the Sharpe ratio, the information ratio, and M2.
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
Answer:
Evaluation Tool
Fund 1
Jensens Alpha
Rank
6.45 – 5.64 =
0.81%
3
Fund 2
8.96-6.06 =
2.90%
1
Fund 3
9.44 – 7.08 =
2.36%
2
Fund 4
5.82-5.40 =
0.42%
4
Treynor
Rank
Sharpe
Rank
6-45 3 – 3 S P
0.88
8-9 6 -3 _
9.0^
1.02
3
1
9-44 – 3 _ i 7/
1.36
2
5’82 3 – 3 53
0.80
4
6-45-3 2.74 O J L O
8-96-3 _
4.54
9-44 – 3
3.72 / X /
5-82 2.64
3 _
i .u/
3
2
1
4
Information
Ratio
6-45 -6
5.6 u.uo _ n n s
u.uo
8 -9 6 -6
6.1
U.rry
9.44 6
12.5
_ PI ^8 U jLi O
5 .8 2 -6
5.3
PI 03
U V /
Rank
M2
Rank
3
1
2
4 6.53% – 6% 3 + (1.26) x (2.8) = 6.53% – 6%
=0.53%
3 + (1.31) x (2.8) = 6.67% 6%
=0.67% 7.84% – 6% 3 + (1.73) x (2.8) = 7.84% – 6%
1.84%
3 + (1.07) x (2.8) = 6% 6% =0
3
2
1
4
Note that Jensens alpha and the Treynor measures give the same rankings, and the Sharpe and M2 measures give the same rankings. However, when comparing the alpha/Treynor rankings to the Sharpe/M2 measures, Funds 2 and 3 trade places.
Fund 2 has a much higher total risk (standard deviation) than Fund 3 but has a much lower beta. Relatively speaking, a smaller proportion of Fund 2s total risk relates to systematic risk, which is reflected in the low beta. Compared to Fund 3, it must have a bigger proportion of risk relating to non-systematic risk factors.
Hence, Fund 2 does better in the alpha/Treynor measures, as those measures only look at systematic risk (beta). It fares less well when it comes to the Sharpe/M2 measures that look at total risk.
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
St a t is t ic a l Sig n if ic a n c e o f Al p h a Re t u r n s

LO 70.2: Describe and distinguish between risk-adjusted performance measures, such as Sharpes measure, Treynor s measure, Jensens measure (Jensens alpha), and information ratio.

LO 70.1: Differentiate between time-weighted and dollar-weighted returns of a portfolio and describe their appropriate uses.
The dollar-weighted rate of return is defined as the internal rate of return (IRR) on a portfolio, taking into account all cash inflows and outflows. The beginning value of the account is an inflow as are all deposits into the account. All withdrawals from the account are outflows, as is the ending value.
Example: Dollar-weighted rate of return
Assume an investor buys a share of stock for $100 at t = 0, and at the end of the next year (t = 1), she buys an additional share for $120. At the end of year 2, the investor sells both shares for $130 each. At the end of each year in the holding period, the stock paid a $2.00 per share dividend. What is the investors dollar-weighted rate of return?
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
Answer:
Step 1: Determine the timing of each cash flow and whether the cash flow is an inflow
(+) or an outflow (). t = 0:
purchase of first share
= $100
= +$2 = $120
$118
dividend from first share purchase of second share subtotal, t = 1
t = 1:
t = 2:
dividend from two shares proceeds from selling shares = +$260 +$264 subtotal, t = 2
= +$4
Step 2: Net the cash flows for each time period, and set the PV of cash inflows equal to
the present value of cash outflows.
PV:inflows = PVoutflow s
$100 + $120 U + r)
$2
(1 + r)
$264 (1 + r)2
Step 3: Solve for r to find the dollar-weighted rate of return. This can be done using trial
and error or by using the IRR function on a financial calculator or spreadsheet. The intuition here is that we deposited $100 into the account at t = 0, then added $118 to the account at t = 1 (which, with the $2 dividend, funded the purchase of one more share at $120), and ended with a total value of $264.
To compute this value with a financial calculator, use these net cash flows and follow the procedure described in Figure 1 to calculate the IRR.
Net cash flows: CFQ = 100; CFj = 120 + 2 = 118; CF2 = 260 + 4 = 264
Figure 1: Calculating Dollar-Weighted Return With the TI Business Analyst II Plus
Calculator
Key Strokes
Explanation
[CF] [2nd] [CLR WORK] Clear cash flow registers
100 [+/-] [ENTER] [4-] 118 [+/-] [ENTER] [4] [4] 264 [ENTER] [IRR] [CPT] Initial cash outlay Period 1 cash flow Period 2 cash flow
Calculate IRR
Display
CFO = 0.00000
CFO = -100.00000 C01 =-118.00000 C02 = 264.00000 IRR = 13.86122
The dollar-weighted rate of return for this problem is 13.86%.
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
Time-weighted rate of return measures compound growth. It is the rate at which $1.00 compounds over a specified time horizon. Time-weighting is the process of averaging a set of values over time. The annual time-weighted return for an investment may be computed by performing the following steps: Step 1: Value the portfolio immediately preceding significant addition or withdrawals.
Form subperiods over the evaluation period that correspond to the dates of deposits and withdrawals.
Step 2: Compute the holding period return (HPR) of the portfolio for each subperiod. Step 3: Compute the product of (1 + HPRt) for each subperiod t to obtain a total return
for the entire measurement period [i.e., (1 + HPRt) x (1 + HPR2) … (1 + HPRn)]. If the total investment period is greater than one year, you must take the geometric mean of the measurement period return to find the annual time-weighted rate of return.
Example: Time-weighted rate of return
A share of stock is purchased at t = 0 for $100. At the end of the next year, t = 1, another share is purchased for $120. At the end of year 2, both shares are sold for $130 each. At the end of years 1 and 2, the stock paid a $2.00 per share dividend. What is the time- weighted rate of return for this investment? (This is the same data as presented in the dollar-weighted rate-of-return example.)
Answer:
Step 1: Break the evaluation period into two subperiods based on timing of cash flows.
Holding period 1:
Holding period 2:
beginning price =$100.00 dividends paid = $2.00 ending price
=$120.00
beginning price = $240.00 (2 shares) dividends paid = $4.00 ($2 per share) ending price
= $260.00 (2 shares)
Step 2: Calculate the HPR for each holding period.
HPRj = [($120 + 2) / $100] – 1 = 22%
HPR2 = [($260 + 4) / $240] – 1 = 10%
Step 3: Take the geometric mean of the annual returns to find the annualized time-
weighted rate of return over the measurement period.
(1 + time-weighted rate of return) = (1.22) (1.10)
time-weighted rate of return = y/( 1.22)(1.10) – 1 = 15.84%
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
In the investment management industry, the time-weighted rate of return is the preferred method of performance measurement for a portfolio manager because it is not affected by the timing of cash inflows and outflows, which may be beyond the managers control.
In the preceding examples, the time-weighted rate of return for the portfolio was 15.84%, while the dollar-weighted rate of return for the same portfolio was 13.86%. The difference in the results is attributable to the fact that the procedure for determining the dollar- weighted rate of return gave a larger weight to the year 2 HPR, which was 10% versus the 22% HPR for year 1.
If funds are contributed to an investment portfolio just before a period of relatively poor portfolio performance, the dollar-weighted rate of return will tend to be depressed. Conversely, if funds are contributed to a portfolio at a favorable time, the dollar-weighted rate of return will increase. The use of the time-weighted return removes these distortions, providing a better measure of a managers ability to select investments over the period. If a private investor has complete control over money flows into and out of an account, the dollar-weighted rate of return may be the more appropriate performance measure.
Therefore, the dollar-weighted return will exceed the time-weighted return for a manager who has superior market timing ability.
Ris k -Ad j u s t e d Pe r f o r m a n c e M e a s u r e s

LO 69.9: Describe the use of alpha, benchmark, and peer group as inputs in performance measurement tools.
One could use linear regression analysis to regress the excess returns of the investment against the excess returns of the benchmark. One of the outputs from this regression is alpha, and it could be tested for statistical significance to determine whether the excess returns are attributable to manager skill or just pure luck. The other output is beta, and it relates to the amount of leverage used or underweigh ting/overweighting in the market compared to the benchmark.
The regression also allows a comparison of the absolute amount of excess returns compared to the benchmark. Furthermore, there is the ability to separate excess returns due to leverage and excess returns due to skill. One limitation to consider is that there may not be enough data available to make a reasonable conclusion as to the managers skill.
One could also regress the excess returns of the manager against the excess returns of the managers peer group. The features of this regression are generally similar to that for the benchmark, except that the returns of the peer group suffer from survivorship bias, and there is usually a wide range of funds under management amongst the peers (that reduces the comparability).
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Topic 69 Cross Reference to GARP Assigned Reading – Litterman, Chapter 17
Ke y Co n c e pt s
LO 69.1 VaR and tracking error are both measures of risk. VaR is defined to be the largest loss possible for a certain level of confidence over a specific period of time. Tracking error is defined as the standard deviation of excess returns.
LO 69.2 There are five risk planning objectives to consider.
Setting expected return and expected volatility goals. Defining quantitative measures of success or failure. Generalizing how risk capital will be utilized to meet the entitys objectives. Defining the difference between events that cause ordinary damage versus serious

damage. Identifying mission critical resources inside and outside the entity and discussing what should be done in case those resources are jeopardized.
The risk planning process frequently requires the input and approval of the entitys owners and its management team.
LO 69.3 The risk budget quantifies the risk plan. There needs to be a structured budgeting process to allocate risk capital to meet the corporate objectives and minimize deviations from plan.
Quantitative methods may be used in risk budgeting. Activities include: setting the minimum acceptable levels of RORC and ROE, applying mean-variance optimization, simulating portfolio performance, and applying sensitivity analysis.
LO 69.4 Within an entitys internal control environment, risk monitoring attempts to seek and investigate any significant variances from budget.
LO 69.3 Sources of risk consciousness include: (1) banks, (2) boards of investment clients, senior management, and plan sponsors, and (3) investors.
LO 69.6 A risk management unit (RMU) monitors an investment management entitys portfolio risk exposure and ascertains that the exposures are authorized and consistent with the risk budgets previously set. To ensure proper segregation of duties, it is crucial that the risk management function be independent and not report to senior management.
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Topic 69 Cross Reference to GARP Assigned Reading – Litterman, Chapter 17
LO 69.7 The risk monitoring process attempts to confirm that investment activities are consistent with expectations. Specifically, is the manager generating a forecasted level of tracking error that is consistent with the target? And is risk capital allocated to the expected areas?
LO 69.8 Liquidity considerations are important because a portfolios liquidity profile could change significantly in the midst of a volatile market environment or an economic downturn, for instance.
LO 69.9 The excess returns of an investment can be regressed against the excess returns of its benchmark (e.g., S&P 500 Index). An output from this regression is alpha, which determines whether the investments excess returns are due to skill or luck.
The excess returns of a manager can be regressed against the excess returns of the managers peer group. This is similar to the liner regression with a benchmark portfolio, but differs since it suffers from survivorship bias.
LO 69.10 Performance measurement looks at a portfolio managers actual results and compares them to relevant comparables such as benchmarks and peer groups.
A performance measurement framework includes: (1) comparison of performance with expectations, (2) return attribution, (3) calculation of metrics such as the Sharpe ratio and the information ratio, and (4) comparisons with benchmark portfolios and peer groups.
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Topic 69 Cross Reference to GARP Assigned Reading – Litterman, Chapter 17
Co n c e pt Ch e c k e r s
1.
2.
3.
4.
3.
Which of the following statements about tracking error and value at risk (VaR) is least accurate? A. Tracking error and VaR are complementary measures of risk. B. Both tracking error and VaR may assume a normal distribution of returns. C. Tracking error is the standard deviation of the excess of portfolio returns over
the return of the peer group.
D. VaR can be defined as the maximum loss over a given time period.
Which of the following statements about the use of quantitative methods in risk budgeting is least accurate? They may be used: to simulate the performance of portfolios. A. to set levels of return on equity (ROE) and return on risk capital (RORC). B. C. in a scenario analysis context to determine the weights for each asset class. D. in a sensitivity analysis context to consider changes in estimates of returns and
covariances.
A risk management unit (RMU) is most likely to be active in which of the following contexts? A. Risk monitoring. B. Risk measurement. C. Risk budgeting. D. Risk planning.
Which of the following statements does not help explain the purpose of risk decomposition? A. To ensure that there is no style drift. B. To detect large concentrations of risk. C. To detect excessive amounts of tracking risk. D. To ensure that investment activities are consistent with expectations.
Which of the following statements regarding alphas and betas is incorrect? A. Alpha is the excess return attributable to pure luck. B. Alpha is the excess return attributable to managerial skill. C. Beta suggests the relative amount of leverage used. D. Beta suggests whether some of the returns are attributable to over or under
weighting the market.
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Topic 69 Cross Reference to GARP Assigned Reading – Litterman, Chapter 17
Co n c e pt Ch e c k e r An s w e r s
1. C All of the statements are accurate with the exception of the one relating to the peer group.
Tracking error is the standard deviation of the excess of portfolio returns over the return of an appropriate benchmark, not peer group.
2. C All of the statements are accurate with the exception of the one relating to scenario analysis. One should apply mean-variance optimization (and not scenario analysis) to determine the weights for each asset class.
3. A A RMU monitors an investment management firms portfolio risk exposure and ascertains
that the exposures are authorized and consistent with the risk budgets previously set.
4. C Risk decomposition is not designed to detect excessive amounts of tracking risk. In fact, it is the forecasted tracking error amount that should be compared to budget to ensure that there is not excessive tracking risk. All the other reasons are consistent with the purpose of risk decomposition.
5. A Alpha is a measure of the excess return of a manager over the peer group/benchmark that relates to skill as opposed to pure luck. Beta is a measure of the amount of leverage used compared to the peer group or a measure of the underweighting or overweighting of the market compared to the benchmark.
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The following is a review of the Risk Management and Investment Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
Po r t f o l i o Pe r f o r m a n c e Ev a l u a t io n
Topic 70
Ex a m Fo c u s
Professional money managers are routinely evaluated using a wide array of metrics. In this topic, alternative methods of computing portfolio returns will be presented, and contrasts will be made between time-weighted and dollar-weighted returns for portfolios experiencing cash redemptions and contributions. For the exam, be sure to understand differences in the risk-adjusted performance measures, including the Sharpe ratio, Treynor ratio, Jensens alpha, information ratio, and M2, and how the trading practices of hedge funds complicates the evaluation process. Be able to apply Sharpes regression-based style analysis to conduct performance attributions.
Tim e -We ig h t e d a n d D o l l a r -We ig h t e d Re t u r n s

LO 69.10: Describe the objectives of performance measurement.
Performance measurement looks at a portfolio managers actual results and compares them to relevant comparables such as benchmarks and peer groups. Therefore, performance measurement seeks to determine whether a manager can consistently outperform (through excess returns) the benchmark on a risk-adjusted basis. Similarly, it seeks to determine whether a manager consistently outperforms its peer group on a risk-adjusted basis.
Furthermore, performance measurement may help to determine whether the returns achieved are commensurate with the risk taken. Finally, performance measurement provides a basis for identifying managers who are able to generate consistent excess risk-adjusted returns. Such superior processes and performance could be replicated on an on-going basis, thereby maximizing the entitys long-run returns and profitability.
Comparison of Performance with Expectations
>From a risk perspective (e.g., tracking error), portfolio managers should be assessed on the basis of being able to produce a portfolio with risk characteristics that are expected to approximate the target. In addition, they should also be assessed on their ability to actually achieve risk levels that are close to target.
>From a returns perspective (e.g., performance), portfolio managers could be assessed on their ability to earn excess returns.
Goldman Sachs Asset Management utilizes a so-called green zone to identify instances of actual tracking error or performance that are outside of normal expectations. An acceptable amount of deviation (from a statistical perspective) is determined, and any deviations up to that amount are considered a green zone event. Unusual events that are expected to occur with some regularity are considered yellow zone events. Truly unusual events that require immediate investigation are considered red zone events. In using this simple color-coded system, the various zones are predefined and provide clear expectations for the portfolio managers. The movements of portfolios into yellow or red zones are triggering events that require further investigation and discussion.
Return Attribution
The source of returns can be attributed to specific factors or securities. For example, it is important to ensure that returns result from decisions where the manager intended to take risk and not simply from sheer luck.
Variance analysis is used to illustrate the contribution to overall portfolio performance by each security. The securities can be regrouped in various ways to conduct analysis by industry, sector, and country, for example.
In performing return attribution, factor risk analysis and factor attribution could be used. Alternatively, risk forecasting and attribution at the security level could also be used.
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Topic 69 Cross Reference to GARP Assigned Reading – Litterman, Chapter 17
Sharpe and Information Ratio
The Sharpe ratio is calculated by taking the portfolios actual return and subtracting the risk-free rate in the numerator. The denominator is the portfolios standard deviation. The information ratio is calculated by taking the portfolios excess returns and subtracting the benchmarks excess returns (if applicable) in the numerator. The denominator is the portfolios tracking error. These two measures are both considered risk-adj usted return measures.
Strengths of these metrics include the following: (1) easy to use as a measure of relative performance compared to a benchmark or peer group; (2) easy to determine if the manager has generated sufficient excess returns in relation to the amount of risk taken; and (3) easy to apply to industrial sectors and countries.
Weaknesses of these metrics include the following: (1) insufficient data available to perform calculations; and (2) the use of realized risk (instead of potential risk) may result in overstated performance calculations.
Comparisons with Benchmark Portfolios and Peer Groups

LO 69.8: Explain the importance of liquidity considerations for a portfolio.
Liquidity considerations are important because a portfolios liquidity profile could change significantly in the midst of a volatile market environment or an economic downturn, for instance. Therefore, measuring portfolio liquidity is a priority in stress testing.
One potential measure is liquidity duration. It is an approximation of the number of days necessary to dispose of a portfolios holdings without a significant market impact. For a given security, the liquidity duration could be calculated as follows:
(O.lOxV)
where: LD = liquidity duration for the security on the assumption that the desired maximum
daily volume of any security is 10%
Q = number of shares of the security V = daily volume of the security
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Pe r f o r m a n c e M e a s u r e m e n t

LO 69.7: Describe how risk monitoring can confirm that investment activities are consistent with expectations.
Is the manager generating a forecasted level o f tracking error that is consistent with the target?
The forecasted tracking error is an approximation of the potential risk of a portfolio using statistical methods. For each portfolio, the forecast should be compared to budget using predetermined guidelines as to how much variance is acceptable, how much variance requires further investigation, and how much variance requires immediate action. Presumably, the budget was formulated taking into account client expectations.
Tracking error forecast reports should be produced for all accounts that are managed similarly in order to gauge the consistency in risk levels taken by the portfolio manager.
Is risk capital allocated to the expected areas?
Overall tracking risk is not sufficient as a measure on its own; it is important to break down the tracking risk into subsections. If the analysis of the risk taken per subsection does not suggest that risk is being incurred in accordance with expectations, then there may be style drift. Style drift may manifest itself in a value portfolio manager who attains the overall tracking error target but allocates most of the risk (and invests) in growth investments.
Therefore, by engaging in risk decomposition, the RMU may ensure that a portfolio managers investment activities are consistent with the predetermined expectations (i.e., stated policies and manager philosophy). Also, by running the report at various levels, unreasonably large concentrations of risk (that may jeopardize the portfolio) may be detected.
Liq u id it y C o n s id e r a t io n s

LO 69.6: Describe the objectives and actions of a risk management unit in an investment management firm.
A risk management unit (RMU) monitors an investment management entitys portfolio risk exposure and ascertains that the exposures are authorized and consistent with the risk budgets previously set. To ensure proper segregation of duties, it is crucial that the risk management function has an independent reporting line to senior management.
The objectives of a RMU include: Gathering, monitoring, analyzing, and distributing risk data to managers, clients,
and senior management. Accurate and relevant information must be provided to the appropriate person(s) at the appropriate time(s). .Assisting the entity in formulating a systematic and rigorous method as to how risks are identified and dealt with. Promotion of the entitys risk culture and best risk practices is crucial here.
Going beyond merely providing information by taking the initiative to research relevant

risk topics that will affect the firm.
Monitoring trends in risk on a continual basis and promptly reporting unusual events to
management before they become significant problems. Promoting discussion throughout the entity and developing a process as to how risk data and issues are discussed and implemented within the entity. Promoting a greater sense of risk awareness (culture) within the entity.
Ensuring that transactions that are authorized are consistent with guidance provided to
management and with client expectations. Identifying and developing risk measurement and performance attribution analytical tools.
Gathering risk data to be analyzed in making portfolio manager assessments and market
environment assessments. Providing the management team with information to better comprehend risk in individual portfolios as well as the source of performance.
Measuring risk within an entity. In other words, measuring how consistent portfolio
managers are with respect to product objectives, management expectations, and client objectives. Significant deviations are brought to the attention of appropriate management to provide a basis for correction.
Professors Note: You may see references elsewhere to an Independent Risk Oversight Unit. This is the same concept as RMU. Both measure and manage risk exposure and operate as an independent business unit.
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LO 69.3: Identify sources of risk consciousness within an organization.
The increasing sense of risk consciousness within and among organizations is mainly derived from the following three sources: 1. Banks who lend funds to investors are concerned with where those funds are invested.
2 . Boards of investment clients, senior management, and plan sponsors have generally become
more versed in risk management issues and more aware of the need for effective oversight over asset management activities.
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3.
Investors have become more knowledgeable about their investment choices. For example, beneficiaries of a defined contribution plan are responsible for selecting their individual pension investments.