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1. The return on the index is zero, as is the properly calculated TWR of the portfolio:
1 + TWR = 110 145.46 =1 100 160 TWR = 0%

The MWR, using an Excel spreadsheet, is an internal rate of return of 3.89%: MWR = 3.89% The Dietz method gives an approximation to the MWR of
MWR 2 = Profit 145.46 100 50 4.54 = = = 3.63% Average invested capital 100 + 0.5 50 125

The original Dietz method gives an approximation to the MWR of

MWR 2 = Profit 145.46 100 50 4.54 = = = 3.63% Average invested capital 100 + 0.5 50 125

Note that the original Dietz method gives a poor approximation of the true MWR (the difference is 26 bp). The Dietz method is much closer (a difference of 1 bp). Much more importantly, the MWR is very different from the TWR, which is equal to 0 percent. All three MWRs give the false indication that the manager underperformed the index by more than 300 bp. Indeed, the manager exactly tracked the index. 2. We compute the quarterly return (not annualized): MWR = IRR = 11.51%,with 200 = MWR1 = MWR 2 =
40 180 + 1/ 3 (1 + MWR) (1 + MWR)

180 200 + 40 20 = = 11.54% 200 2 / 3 40 173.33 180 200 + 40 20 = = 11.11% 200 1/ 2 40 180

TWR = 10%, as 1 + TWR = (1 + 10%) (1 + 0%) = 1.1

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3. We compute the monthly return (not annualized): 20 50 145 MWR = IRR = 14.58%,with100 = + 1/ 3 2/3 (1 + MWR) (1 + MWR) (1 + MWR) MWR1 =
15 = 14.52% 100 + kt

30 10 30 20 where kt = 20 + 50 = 3.33 30 30 145 100 + 20 50 15 MWR2 = = 13.04% 100 + 1/ 2 30 115 90 90 145 TWR = 19.85%, as 1 + TWR = = 1.1985 100 70 140

4. For the active manager, a portfolio turnover (sell and buy) of twice a year implies transactions costs of (4)(0.015) = 0.06. Thus, transactions costs and fees amount to 6% + 0.75% = 6.75% For the passive manager, the fees amount to 0.25%. Thus, the active manager must outperform the indexer, gross of costs, by at least 6.75% 0.25% = 6.50% 5. a. The return in dollars is 5% = (1,050,000 1,000,000)/1,000,000 b. The value of the portfolio moves from 1,000,000 = $1,000,000(1/$) to 1,071,000 = $1,050,000 (1.02/$) The return in euros is 7.1% = (1,071,000 1,000,000)/1,000,000 c. The difference is equal to 2.1 percent, while the exchange rate went up by 2 percent. The currency contribution is 2.1 percent because the exchange rate gain applies not only to the initial invested dollar capital (100%), but also to the dollar capital gain (5 percent). So, the currency contribution is equal to 2 percent 1.05 = 2.1 percent The total return on the portfolio, measured in SKr is equal to
1,362,000 1 = 0.135 or 13.5% 1,200,000

6. a.

b. The capital gain amounts to 660,000 600,000 = SKr 60,000 on the Swedish stocks, or 10% 702,000/5.40 600,000/6 = $130,000 $100,000 = $30,000 on the U.S. stocks If we use the SKr 6/$ exchange rate, this is (30,000)(6) = SKr 180,000 The total capital gain is SKr 240,000, or 20% = 240,000/1,200,000 Also note that: The dollar return on U.S. stocks is 30% = 30,000/100,000 The SKr return on U.S. stocks is 17% = 102,000/600,000 The SKr return on Swedish stocks is 10% = 60,000/600,000

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The capital gain is in local currency = (0.5)(0.30) + (0.5)(0.10) = 0.20 = 20% The currency contribution can be calculated as follows: Currency contribution of U.S. investment = SKr return on U.S. stocks dollar return on U.S stocks = 17% 30% = 13% Portfolio currency contribution = portfolio weight U.S. stocks currency contribution = (0.5)( 0.13) = 0.065 = 6.5% The total return can be decomposed as follows: 13.5% = Capital gain + Yield + Currency contribution = 20% + 0% 6.5% c. If the same amounts had been invested respectively in the OMX index and in the S&P index, returns would have been the following: 20% on the Swedish index 25% on the U.S. index Portfolio-weighted market return in local currency = (0.5)(0.20) + (0.5)(0.25) = 0.225 = 22.5% We would have obtained 22.5% in local currency while our realized capital gain was only 20%. Portfolio return in local currency = (0.5)(0.10) + (0.5)(0.30) = 0.20 = 20%. Hence, security selection contributed negatively for 2.5 percent because of a poor selection on the Swedish market: The Swedish portfolio only achieved a 10 percent return, while the OMX index showed a 20 percent growth. On the other hand, our U.S. stocks had a return of 30 percent in dollars, compared with 25 percent on the S&P index. Hence the capital gain itself can be broken down into market (22.5%) and security selection ( 2.5%). 7. Calculations are summarized in the following table: Global Equity Portfolio: Total Return Decomposition
(1) (2) (3) (4) (5) (6) (7) Portfolio Rate of Capital Gain in Currency Market Security Currency Weights Return in $ Local Currency Contribution Index Selection Contribution U.S. stocks Japan stocks Europe stocks Total portfolio 50% 20% 30% 100% 5.000% 4.762% 2.041% 4.065% 5.000% 10.000% 0.000% 4.50% 0.000% 5.238% 2.041% 0.435% 3.000% 5.000% 5.000% 1.00% 2.000% 5.000% 5.000% 3.50% 0.000% 5.238% 2.041% 0.435%

a.

Total return of the portfolio: 4.065% = (0.5)(0.05) + (0.2)(0.04762) + (0.3)(0.02041) Capital gain in local currency on U.S. shares: (52,500 50,000)/50,000 = 5% Currency contribution on U.S. shares: 0% Capital gain in local currency on Japanese shares: (2,200,000 2,000,000)/2,000,000 = 10% Capital gain in U.S. dollars on Japanese shares: (20,952 20,000)/20,000 = 4.76% Currency contribution on Japanese shares: 4.76% 10% = 5.24%

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Capital gain in local currency on European shares: (30,000 30,000)/30,000 = 0% Capital gain in U.S. dollars on European shares: (30,612 30,000)/30,000 = 2.04% Currency contribution on European shares: 2.04% Return in local currency = 4.50% = (0.5)(0.05) + (0.2)(0.10) + (0.3)(0.0) Currency contribution = 0.435% = (0.5)(0.0) + (0.2)( 0.0524) + (0.3)(0.0204) We verify that 4.065% = 4.5% 0.435% b. The return in local currency of 4.50% can be decomposed as the weighted average of the index returns (1%) and the contribution of security selection. Return on the U.S. stock index: (103 100)/100 = 3% Contribution of security selection on the U.S. stock: 5% 3% = 2% Return on the Japanese stock index: (105 100)/100 = 5% Contribution of security selection on the Japanese stock: 10% 5% = 5% Return on the European stock index: (95 100)/100 = 5% Contribution of security selection on the European stock: 0% ( 5%) = 5% Net contribution of security selection: = 3.50% = (0.5)(0.02) + (0.2)(0.05) + (0.3)(0.05) c. We now focus on the performance relative to the benchmark (World index). The portfolio was overweighted in Europe (30 percent instead of 25 percent) and under-weighted in Japan (20 percent instead of 25 percent). This is unfortunate, because Europe went down and Japan up. Using the formula in the text, we can attribute the performance relative to the World index, as done in the following table. The World index had a return of 0.735% in dollars. The performance of the portfolio is good: 4.065 0.735 = 3.33%. It is explained as follows: Benchmark return Market allocation Currency allocation Security selection Portfolio return 0.735% 0.500% 0.330% 3.500% 4.065%

Calculations of benchmark return and security selection have already been explained. The market allocation = (0)(0.03) + ( 0.05)(0.05) + (0.05)( 0.05) = 0.5% The currency allocation = 0.435% ( 0.765%) = 0.33% 0.435% is the currency contribution calculation shown in part (a). 0.765% = (0.25)( 0.05) + (0.25)(0.0194) where 0.25 is the weight of Japan in the World index 0.05 is dollar return on the Japan index minus the yen return on the index 0.25 is the weight of Europe in the World index 0.0194 is the dollar return on the Europe index minus the euro return on the index

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The following table summarizes the solution. Global Equity Portfolio: Performance Attribution Index World Return in World Market Currency Portfolio Index Local Index Allocation Allocation Security Weights Weights Currency Return in $ Contribution Contribution Selection U.S. stocks Japan stocks European stocks Total portfolio 50% 20% 30% 50% 25% 25% 3.00% 5.00% 5.00% 1.500% 0.000% 0.765% 0.735% 2.000% 0.250% 0.250% 0.500% 2.000% 0.202% 0.128% 0.330% 2.000% 5.000% 5.000% 3.500%

8. a. Overall, both managers added value by mitigating the currency effects present in the Index. Both exhibited an ability to pick stocks in the markets they chose to be in (Manager B in particular). Manager B used his opportunities not to be in stocks quite effectively (via the cash/bond contribution to return), but neither of them matched the passive index in picking the country markets in which to be invested (Manager B in particular). Manager A Strengths Currency management Manager B Currency management Stock selection, Use of cash/bond flexibility Country selection

Weaknesses

Country selection (to a limited degree)

b. The column reveals the effect on performance of adjustment for movements in the U.S. dollar relative to local currencies and, therefore, the currency effect on the portfolio. Currency gains/losses arise from translating changes in currency exchange rates versus the U.S. dollar over the measuring period (three years in this case) into U.S. dollars for the U.S. pension plan. The Index mix lost 12.9 percent to the dollar, reducing what would otherwise have been a very favorable return from the various country markets of 19.9 percent to a net return of only 7.0 percent. 9. a. The following briefly describes one strength and one weakness of each manager. 1. Manager A Strength: Although Manager As one-year total return was slightly below the EAFE index return ( 6.0% versus 5.0%, respectively), this manager apparently has some country/ security return expertise. This large local market return advantage of 2.0 percent exceeds the 0.2 percent return for the EAFE index. Weakness: Manager A has an obvious weakness in the currency management area. This manager experienced a marked currency return shortfall compared with the EAFE index of 8.0 percent versus 5.2 percent, respectively.

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2. Manager B Strength: Manager Bs total return slightly exceeded that of the index, with a marked positive increment apparent in the currency return. Manager B had a 1.0 percent currency return versus a 5.2 percent currency return on the EAFE index. Based on this outcome, Manager Bs strength appears to be some expertise in the currency selection area. Weakness: Manager B had a marked shortfall in local market return. Manager Bs country/ security return was 1.0 percent versus 0.2 percent on the EAFE index. Therefore, Manager B appears to be weak in security/market selection ability. b. The following strategies would enable the Fund to take advantage of the strengths of the two managers and simultaneously minimize their weaknesses. i. Recommendation: One strategy would be to direct Manager A to make no currency bets relative to the EAFE Index, and to direct Manager B to make only currency decisions, and no active country or security selection bets. Justification: This strategy would mitigate Manager As weakness by hedging all currency exposures into index-like weights. This would allow capture of Manager As country and stock selection skills while avoiding losses from poor currency management. This strategy would also mitigate Manager Bs weakness, leaving an index-like portfolio construct and capitalizing on the apparent skill in currency management. ii. Recommendation: Another strategy would be to combine the portfolios of Manager A and Manager B, with Manager A making country exposure and security selection decisions, and Manager B managing the currency exposures created by Manager As decisions (providing a type of currency overlay). Justification: This recommendation would capture the strengths of both Manager A and Manager B and would minimize their collective weaknesses. 10. a. The local currency returns are shown in the following table: Country United States United Kingdom France Dec. 31, 2006 $50,000,000 20,000,000 25,000,000 Dec. 31, 2007 $55,000,000 20,500,000 32,000,000 Return (%) 10.0% 2.5% 28.0%

For example, the local currency return for the French portion of the portfolio is
32,000,000 25,000,000 = 0.28 = 28% 25,000,000

The dollar returns and portfolio weights are shown in the following table: Country United States United Kingdom France Total portfolio Dec. 31, 2006 $50,000,000 $30,769,231 $22,727,273 $103,496,504 Dec. 31, 2007 $55,000,000 $33,064,516 $26,666,667 $114,731,183 Return 10.0% 7.46% 17.33% 10.855% Weight 48.31% 29.73% 21.96% 100.0%

To explain the calculations, the United Kingdom will be used as an illustration.

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First the pound values of the U.K. portion of the portfolio must be converted to dollars: For Dec. 31, 2000, dollar value = $30,769,231 = 20,000,000/0.65 per $ For Dec. 31, 2001, dollar value = $33,064,516 = 20,500,000/0.62 per $ The dollar return for the U.K. portion of the portfolio is
33,064,516 30,769,231 = 0.0764 = 7.64% 30,769,231

The portfolio weight for the United Kingdom = 0.2973 = $30,769,231/$103,496,504 The portfolio return = 0.10855 = (0.4831)(0.10) + (0.2973)(0.0746) + (0.2196)(0.1733) b. The total portfolio return decomposition table is shown here: Country U.S. U.K. France Total portfolio Dollar Return 10.0% 7.46% 17.33% 10.855% Capital Gain Currency (local currency) Contribution 10.0% 2.5% 28.0% 11.723% 0.0% 4.96% 10.667% 0.868%

The total portfolio return in U.S. dollars = 10.855%. This can be decomposed into the capital gain of 11.723% in local currency, and the currency contribution of 0.868%. The capital gain in local currency = 0.11723 = (0.4831)(0.10) + (0.2973)(0.025) + (0.2196)(0.28) The currency contribution for the United States is 0% The currency contribution for the United Kingdom = 0.0496 = 0.0746 0.025 = 4.96% The currency contribution for France = 0.10667 = 0.17333 0.28 = 10.667% The overall currency contribution = 0.00868 = (0.4831)(0.0) + (0.2973)(0.0496) + (0.2196)( 0.10667) = 0.868% c. The total portfolio return decomposition table is shown here: Country United States United Kingdom France Total portfolio Dollar Return 10.0% 7.46% 17.33% 10.855% Currency Contribution 0.0% 4.96% 10.667% 0.868% Market Index 9.079% 5.321% 6.211% 7.332% Security Selection 0.92% 2.82% 21.79% 4.391%

The dollar returns and currency contributions are the same as in part (b) above. The total portfolio return in U.S. dollars = 10.855 percent. This can be decomposed into the currency contribution, plus the market return, plus security selection = 0.00868 + 0.07332 + 0.04391 The currency contribution for the United States is 0 percent.

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The currency contribution for the United Kingdom = 0.0496 = 0.0746 0.025 = 4.96% The currency contribution for France = 0.10667 = 0.17333 0.28 = 10.667% The overall currency contribution = 0.00868 = (0.4831)(0.0) + (0.2973)(0.0496) + (0.2196)(0.10667) = 0.868% The market return for the United States = 0.09079 = (829 760)/760 = 9.079% The market return for the United Kingdom = 0.05321 = (1148 1090)/1,090 = 5.321% The market return for France = 0.06211 = (1009 950)/950 = 6.211% The overall market return contribution = 0.07332 = (0.4831)(0.09079) + (0.2973)(0.05321) + (0.2196)(0.06211) = 7.332% The security selection contribution for each country is calculated by subtracting the market return from the local-currency capital gain. Security selection for the United States = 0.0092 = 0.10 0.0908 = 0.92% Security selection for the United Kingdom = 0.0282 = 0.025 0.0532 = 2.82% Security selection for France = 0.2179 = 0.28 0.0621 = 21.79% The overall security selection contribution = 0.04391 = (0.4831)(0.0092) + (0.2973)( 0.0282) + (0.2196)(0.2179) = 4.391%. d. The following table indicates the global performance attribution: Benchmark return Market allocation Currency allocation Security selection Total return
Benchmark return =

7.003% 0.422% 0.117% 4.391% 10.855%

834.622 780 = 0.07003 = 7.003% 780 Market allocation = ( 0.1169)(0.09079) + (0.0973)(0.05321) + (0.0196)(0.06211) = 0.00422 = 0.422% Data are obtained from the following table (Index Return Breakdown).

Index Return Breakdown Country United States index United Kingdom index France index Under/Over Weight* 11.69% 9.73% 1.96% Dollar Return 9.079% 10.417% 2.64% Capital Gain (local currency) 9.079% 5.321% 6.211% Currency Contribution 0.0% 5.096% 8.851%

*The portfolio weight minus the index weight.

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The currency allocation = 0.00868 ( 0.00751) = 0.00117 = 0.117% 0.00868 is the overall currency contribution, the calculation for this is shown above in part c. 0.00751 is the currency contribution for the world market index: 0.007508 = (0.60)(0.0) + (0.20)(0.05096) + (0.20)(0.08851) The security selection contribution is 4.391 percent and has been shown in part (c). 11. Yes. The return on foreign assets looks small relative to its volatility. But the risk that counts is the contribution to the risk of the total portfolio. Here are some return-and-risk characteristics for global portfolios with increasing proportions of foreign assets. %U.S. % Foreign Return (%) Volatility (%) 100 95 90 85 80 75 70 65 60 55 50 0 5 10 15 20 25 30 35 40 45 50 10.00 10.05 10.10 10.15 10.20 10.25 10.30 10.35 10.40 10.45 10.50 12.00 11.64 11.37 11.19 11.11 11.14 11.26 11.48 11.78 12.18 12.65

A portfolio invested 20 percent in foreign fund increases the return from 10.0 percent to 10.2 percent and reduces the volatility from 12.0 percent to 11.1 percent. Portfolio risk is calculated using the following formula:
2 2 p = x 2 d + (1 x )2 2 f + 2 x (1 x ) d f

Portfolio return is calculated using the following formula:

Rp = Rd ( x ) + Rf (1 x )

where p is the risk of the portfolio

d is the risk of domestic stocks f is the risk of foreign stocks

is the correlation between domestic and foreign stocks x is the proportion of the portfolio invested in domestic stocks
12. Yes. The risk that counts is the contribution of the foreign assets to the total risk of the global portfolio. In the proposed example, foreign stocks have a larger standard deviation (20%) than U.S. stocks (15%). However, lets calculate the standard deviation of the diversified portfolio made up of 90 percent domestic stocks and 10 percent foreign stocks. We have
2 2 p = x 2 d + (1 x )2 2 f + 2 x (1 x ) d f

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where p is the risk of the portfolio

d is the risk of domestic stocks f is the risk of foreign stocks is the correlation between domestic and foreign stocks x is the proportion of the portfolio invested in domestic stocks
Here, we will take = 0.10, because the U.S. portfolio is very strongly correlated with the U.S. stock index. 2 p = (0.92)(152) + (0.12)(202) + 2(0.9)(0.1)( 0.1)(15)(20)
2 p = 182.25 + 4 5.4 = 180.85

p = 13.45%
Thus, the addition of foreign equity allows us both to increase the return (here, Rp (0.9)(10) + (0.1)(11) = 10.1% ) and reduce the risk of a domestic portfolio. 13. Year 2008 2009 2010 2011 2012 Portfolio Return 12% 14% 20% 14% 16% Benchmark Return 14% 10% 12% 16% 13% Excess Return 2.0% 4.0% 8.0% 2.0% 3.0% Squared Deviation 0.18% 0.03% 0.34% 0.18% 0.01%

The squared deviation column is the squared deviation of the excess return for each period from the mean excess return of 2.20 percent. Tracking error = 14. Sharpe ratio calculations: Portfolio 1 =
0.135 0.05 = 0.4474 = 44.74%. Rank 3 0.19 0.1625 0.05 = 0.4688 = 46.88%. Rank 2 0.24 0.17 0.05 = 0.5217 = 52.17%. Rank1 0.23 0.0073 = 0.0427, or 4.3% 4

Portfolio 2 =

Portfolio 3 =

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Information ratio calculations: Portfolio 1 =

0.135 0.13 = 0.08. Rank 3 0.065 0.1625 0.13 = 0.41. Rank 2 0.08 0.17 0.13 = 0.57. Rank 1 0.07

Portfolio 2 =

Portfolio 3 =

15. This publicity campaign is misleading because of survivor bias. Only the funds that survive, because of their good performance, are included in the track record. 16. The average performance should be that of the market index minus costs (transaction costs, management fees). If international investors, as a group, beat some national index, it tells us that local investors, as a group, probably underperform the index. Not necessarily. Because of costs, both international and local investors can, as a group, underperform the local index. Note: Solution to problem 17 should be similar to formatting of 5th ed. 17. a. To calculate the indexes, we proceed in four steps: Calculate the return of month t for each market as the difference between the ending and beginning values of the index, divided by the beginning value of the index. Calculate the weights of the country indexes at the start of the month. Calculate the return on the global index. Chain-link the global index value. For the GDP-weighted index in Period 1 IndexGDP = 100 at beginning of period 100 100 = 0.5 = 0.5 WeightGDPB = WeighGDPA = 100 + 100 100 + 100 ReturnA = 5% ReturnB = 10% ReturnGDP = 2.5% IndexGDP = 102.5 at end of period For the capitalization-weighted index: 1.5 100 100 = 0.6 = 0.4 WeightCAPA = WeightCAPB = 1.5 100 + 100 1.5 100 + 100

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The country index returns are given in the following table: Month 0 1 2 3 4 5 IndexA 100 95 100 100 105 110 IndexB 100 110 100 120 125 135 ReturnA 0.05 0.0526 0 0.05 0.0476 ReturnB 0.1 0.0909 0.2 0.0417 0.08

For example, for Month 1: ReturnA = ReturnB =

95 1 = 0.05 100 110 1 = 0.10 100

CAPA = (1 0.05)(150) = 142.5 CAPB = (1 + 0.10)(100) = 110 Months 0 1 2 3 4 5 GDPA 100 100 100 102 102 102 GDPB 100 100 100 101 101 101 CAPA 150 142.5 150 150 157.5 165 CAPB 100 110 100 120 125 135

For example, for Month 1: Month 0 1 2 3 4 5 WeightGDPA WeightGDPB WeightCAPA WeightCAPB 0.5000 0.5000 0.5000 0.5025 0.5025 0.5025 0.5000 0.5000 0.5000 0.4975 0.4975 0.4975 0.6000 0.5644 0.6000 0.5556 0.4975 0.4500 0.4000 0.4356 0.4000 0.4444 0.4425 0.4500

For example, for Month 1: WeightGDPA =

Weight GDPB = Weight CAPA Weight CAPB
100 = 0.50 100 + 100

100 = 0.50 100 + 100 142.5 = = 0.5644 142.5 + 110 110 = = 0.4356 142.5 + 110

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Month ReturnGDP 0 1 2 3 4 5 0.0250 0.0191 0.1 0.0459 0.0637

IndexGDP 100 102.5 100.5383 110.5921 115.6632 123.0344

ReturnCAP IndexCAP 0.01 0.0099 0.08 0.0463 0.0619 100 101 100 108 113 120

For example, for Month 1: ReturnGDP = (0.50)( 0.05) + (0.50)(0.10) = 0.025 IndexGDP = (100)(1 + 0.025) = 102.5 ReturnCAP = (0.6)( 0.05) + (0.4)(0.10) = 0.01 IndexCAP = (100)(1 + 0.01) = 101 b. At the end of each month, we must rebalance the portfolio tracking the GDP-weighted index. For example, at the end of Month 1, the shares of Market B have gone up in value and we must sell some of them to get back to a 5050 breakdown. 18. a. The total risk of a portfolio can be decomposed into absolute risk on each asset class without regard to risk of active managers, and active risk allocation of managers of each asset class. Risk decomposition is complicated by the fact that risks in a global portfolio are correlated. Currency risk is another dimension that adds further complications. b. Risk budgeting refers to the process by which a client allocates the amount of risk it is willing to assign to different asset classes or portfolio managers. Some portfolio managers are allowed to have large tracking errors, because they can provide specific added value for the segment of the portfolios they manage. On the other hand, portfolio managers of some segments may only be allowed to have small tracking errors, because they are judged not to be able to add value relative to the benchmark. 19. The following factors can introduce potential biases in the measurement of portfolio risk and performance: Infrequently traded assets in the portfolio Option-like investment strategies Survivor bias Infrequently traded assets do not have up-to-date market prices; consequently, their prices tend to be smoothed over time. This introduces a downward bias in risk measures for these assets. In addition, the correlations of returns of these infrequently traded assets with conventional asset returns can be very low because of the smoothing effect. In a portfolio context, the net effect is that the calculated risk measure will underestimate true risk. Traditional risk measures, such as standard deviation, assume that returns are normally distributed. The assumption of normality is also usually made when using value at risk (VaR) in asset management. However, some investment strategies, for example, option-like strategies, can result in return distributions that are highly nonnormal. Thus, the validity of such measures of risk as the standard deviation is questionable.

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Survivor bias impacts performance measurement and risk measurement. Survivor bias means that, over time, unsuccessful managers disappear. Thus, taking as an example of hedge funds, the existing or surviving funds will report good track records. However, there is no guarantee that the surviving managers will deliver superior performance in future years. Similarly, from a risk perspective, funds that experienced high levels of risk in the past may have disappeared, leaving behind funds with low volatility. There is no guarantee, however, that funds with low volatility will display low volatility in the future. 20. a. The results are given in the following table: Performance Decomposition (in %), January Total Currency Capital Market Weights Return Yield Gain Gain Index U.S. stocks Japan stocks France stocks Japan bonds Total 29.8 43.0 12.7 14.5 100 1.45 3.45 4.44 4.10 2.21 0.00 0.00 0.00 0.64 0.09 0.00 4.83 8.55 4.86 1.70 1.45 1.38 12.99 1.39 0.42 2.50 2.00 8.00 1.00 0.76 Security Selection 3.95 0.62 4.99 0.39 0.34

The total return is 2.21%, decomposed as Capital gain 0.42% Yield 0.09% Currency gain 1.70% He did better than the World index. The market index returns were, respectively, 2.5%, 2%, 8%, and 1%. If the manager had invested with the same proportions in market indexes, instead of individual securities, he would have obtained + 0.76% in local currency. So, his security selection gave him 0.42 0.76 = 0.34%. He underperformed the indexes for U.S. stocks and yen bonds, but outperformed for French and Japanese stocks. By way of illustration, a set of calculations is shown for Japanese stocks.
64,350 62,205 = 3.45% 62,205 (8,200,00 + 6,100,000) (8,000,000 + 6,500,000) Capital gain in yen (%) = (8,000,000 + 6,500,000) = 1.38% Total return in dollars = Currency contribution = 0.0345 ( 0.0138) = 4.83% The market index return = 98 100 = 2.0% 100

Security selection contribution is equal to the local currency capital gain minus the market index return 0.0138 ( 0.02) = 0.0062 = 0.62%. The totals are calculated by applying portfolio weights to the component returns; for example, the total dollar return is 2.21 percent, calculated as follows:
(0.298)( 0.0145) + (0.43)(0.0345) + (0.127)(0.044) + (0.145)(0.041) = 0.0221

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b. The following table gives the valuation report at the end of February. Number of Securities or Nominal Accrued Accrued Market Interest Amount Interest Subtotal Sub total Description Price in% in $ in $ in $ in% Equity U.S. AMAX 24 Japan Hitachi 880 TDK 6,000 France Club Med 85 Pernod 72 Bonds Yen Govt 6% 92 92% EIB 8.5% 93 98% Cash U.S. dollars Total Market indexes 103 97 110 101 104

1,000 10,000 1,000 200 400 2,000,000 3,000,000

24,000 41,360 28,200 17,850 30,240 1.55% 0.62% 8,648 13,818 72 164,188 146 88 234

24,000 69,560 48,090

14.6% 42.3% 29.2% 29.2%

22,700 72 164,422

13.8% 0.1% 100%

Exchange rates

Yen = 0.0047 dollars U.S. stocks Japanese stocks Euro = 1.05 dollars French stocks Japanese bonds World index

By way of explanation, consider the valuation numbers for the Japanese Government bond: The nominal (face) yen value is 2,000,000. The market price is 92% of face value. The accrued interest is 1.55%. The market price in dollars is (0.92)(2,000,000)(0.0047) = $8,648. The accrued interest in dollars is (0.0155)(2,000,000)(0.0047) = $145.7, or $146. The following table gives the return computations for the account over February. For convenience, we assumed that all cash flows took place at the end of the month.

Chapter 12

Global Performance Evaluation

93

Otherwise, we would have to adjust the mean capital invested and take account of the currency rate at the time of each cash flow. The same calculation would yield slightly different results if the cash flows were assumed to take place at the start of the month or at the middle of the month. Performance Decomposition (in %), February Total Currency Capital Market Weights Return Yield Gain Gain Index U.S. stocks 28.8 Japan stocks 43.5 French stocks 12.9 Japan bonds 14.8 Total 100% 4.37 8.10 9.98 6.59 4.46 0.84 0.00 0.00 0.54 0.32 0.00 4.60 4.29 4.54 2.12 3.53 3.50 5.69 1.51 2.02 0.49 1.02 1.85 2.02 0.23 Security Selection 3.04 4.52 7.54 0.51 1.79