1. Suppose different hospitals within Partners system choose different mixes of the risk-free STP and baseline LTP, whose future expected returns and risks are shown in Exhibit 3. (Provided Picture below) Not sure how to graph in part 8 so if you could do a step by step thank you!
   1. On Exhibit 3, plot the returns and risks of the various potential portfolios that can be formed by allocating funds between the STP and baseline LTP. What shape does a line drawn through these portfolios take? Why?
   2. In contrast, what would the risk-return opportunities available to the hospitals be if they could invest only in STP and US Equities?
   3. 

Exhibit 2 Selected Operating and Income Statement Data of Partners for Fiscal Years 19952004 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 1,660 2,820 1,511 327 1,571 339 181 443 Gross Patient Revenue Operating: Net Patient Service Revenue Academic and Research Revenue Other Revenue Total Operating Revenue Total Operating Expenses Income from Operations 1,998 448 213 2,287 505 242 3,678 915 617 3,137 718 363 141 2,487 548 291 3,326 3,325 106 335 3,361 824 367 4,552 4,520 397 1,979 1,965 14 2,091 2,104 2,209 2,221 2,659 2,679 -20 3,034 3,091 -57 3,772 3,724 4,218 4,148 70 4,990 4,885 105 -13 -12 1 48 32 Long-Term Pool: Assets at Year-End: Total Return during Year (%) Total Return (in $) 636 15.0 43 716 13.3 85 887 28.2 202 891 -4.7 -42 1.235 25.2 225 1,398 18.1 224 1,365 -7.3 -102 1,399 -3.3 -45 1,839 21.1 295 2,253 16.7 307 Source: Company documents. Notes: Long-term pool inception was April 1, 1995 (1995 reflects return from April though September). Total returns on endowment funds, all of which are invested in the long-term pool, are included in the operating and income statements only when distributed. Exhibit 3 Summary of the Assumptions To Be Used in the Portfolio Analyses REITS Commodities Annual Expected Returns Standard Deviations, and Correlations Correlation with Asset Class Expected Ret. Stdev US Equity Foreign Equity Bonds US Equity 12.94% 15.21% 1.00 Foreign Equity 12.42% 14.44% 0.62 1.00 Bonds 5.40% 11.10% 0.25 0.06 1.00 REITS 9.44% 13.54% 0.56 0.40 0.16 Commodities 10.06% 18.43% (0.02) 0.01 (0.07) 1.00 (0.01) 1.00 14.00% US Equity Foreign Equity Baseline LTP 12.00% 10.00% Commodities REITS 8.00% Expected Return 6.00% Bonds 4.00% STP 2.00% 0.00% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.09% 16.0% 18.0% 20.0% Risk: Standard Deviation Source: Author's estimates using historical data from CRSP and Thomson Financial Datastream. Standard deviations and correlations are calculated using monthly returns from 1970 to 2004 (except REITs, which use monthly data from 1990 to 2004). Expected returres are calculated using a risk-free rate of 3.2% (the current yield of the STP) and a bond excess return estimated from 1970 to 2004. The U.S. equity risk premium (U.S. equity expected return minus bond expected return) is set to 7.2%, the difference in average return from 1926 to 2004. Foreign expected return is set so that the ratio of its risk premium to standard deviation i.e., its Sharpe ratio) matches that of the U.S. Commodity excess returns are estimated from 1970 to 2004. The REIT excess return is estimated using data from 1995 to 2004 and then scaled by the ratio of the U.S. excess return to the U.S. excess return from 1995 to 2004. The Analysis To begin with, Manning needed some assumptions about future expected returns, risks, and correlations of the various asset classes in order to compare and evaluate different potential portfolios. He had his staff collect and analyze information on each of the five asset classes. Using very long-term historical data from 1926 to 2004, they calculated the average realized returns from U.S.equities relative to U.S. long-term bonds in order to estimate the risk premium that equities had paid on average relative to bonds over this very long-term time horizon. Unfortunately, such very long-term data were not available for most asset classes. Using data on realized returns from 1970 onward, they calculated average annual returns, volatilities, and correlations for each of the asset classes. These historical data drove the assumptions about future returns, risks, and correlations that would be used in the analysis, which are displayed in Exhibit 3. Exhibit 3 also includes a "risk- return" plot of these assumptions for the five asset classes, with the future expected returns on the vertical axis and the annualized future standard deviation of retums on the horizontal axis. The plot also displays the calculated future risk (12.02%) and expected return (11.65%) of the baseline 55/30/15 LTP given these assumptions (see the Appendix for the formulas used to calculate the future risks and returns of a multi-asset portfolio) and the current yield of the STP (3.2%). At first glance, REITs seemed attractive with their low risk and reasonable expected returns Commodities appeared as though they might be less attractive because of their much higher risk, notwithstanding their slightly higher expected returns. But how much these opportunities would increase the LTP's return or lower its risk clearly depended on how much capital Partners was willing to allocate to these investments and their correlations with assets in the baseline portfolio. Solving this problem would require portfolio analysis: calculating the expected return and risk of portfolios with different levels of investment in each of the asset classes and then asking which combination(s) offered the lowest risks and/or greatest expected returns. Manning began by asking whether the baseline LTP allocation of domestic equities, foreign equities, and bonds had offered the best risk-return trade-off for investors relative to all other portfolio mixes that invested in just these same three asset classes. He first considered sets of different portfolio weights that deviated arbitrarily from the baseline allocations in the LTP, but where the 3 w weights were constrained to be positive and to add to 100%. Exhibit 4a reports the calculated future expected returns and standard deviations for 16 of these arbitrary alternative three-asset-class portfolios. Exhibit 4b presents a risk-return scatterplot of these 16 portfolios. Similarly, Exhibit 4 displays a risk-return scatterplot for a much larger sample of several hundred arbitrarily chosen three-asset portfolios. Manning was not really sure whether any of these alternative portfolios were clearly better or worse than the baseline LTP. Some of the Partners hospitals might prefer some of the portfolios with lower risks, but others would probably prefer some of the portfolios with higher retums. Indeed, he wondered whether any of the portfolios could be considered superior or inferior to the others given that the hospitals and physician organizations all had somewhat different tolerances for risk. He hoped, though, that at least some of these potential portfolios could be eliminated from consideration on the grounds that they offered lower expected returns but higher risks relative to others. To better understand what the interests of particular hospitals might imply for the optimal mix of assets in the LTP, Manning considered the perspective of a hospital targeting 10% future expected returns. It was clear that many different combinations of U.S. equities, foreign equities, and bonds could achieve this goal. However, not all such combinations would offer identical risks. Therefore, Manning asked his staff to search across all combinations to identify the one that would deliver the 10% expected return but with the least amount of risk. They reported back to him that an investment of 23.4% in U.S. stocks, 40.4% in foreign stocks, and 36.2% in bonds could deliver the targeted 10% expected returns at 994% riska lower level of risk than any other possible set of allocations producing the 10% expected returns. Manning concluded that this combination must be optimal for any hospital wishing to achieve 10% expected returns. He then asked them to repeat their search procedure to identify the minimum level of risk required to achieve several other different target- return levels. These portfolios are reported in Exhibit sa along with a plot in Exhibit 5b of their future expected returns and standard deviations. Now, Manning thought that they were ready to analyze how much the introduction of REITs and/or commodities might improve the risk-return opportunities available for the LTP. Manning wondered whether REITs or commodities would be more helpful. Commodities had higher expected returns than REITs, but they also carried far greater risk. To analyze the problem, he again asked his staff to determine the minimum attainable risk level (standard deviation) for different target-return levels when REITs were added to the set of investable assets (see Exhibits 6), and similarly when commodities were added to the set of investable assets (see Exhibit 7). Because Partners could easily maintain investments in both of these new asset classes at relatively low setup and transaction costs, Manning knew that he should consider investing in both simultaneously. Exhibit 8 reports the results of the same analysis when all five assets were available for investment. Stepping back from the numbers, Manning wondered whether the addition of real assets would really make the hospitals better off. Their needs and preferences were quite varied. Some wished to keep the future risks of their overall financial assets quite limited; others were willing to take more risk in pursuit of substantially higher future retums. How would real assets in the LTP help them, if at all? Could a "one-size-fits-all" solution for the LTP reasonably meet the needs of the Partners hospitals? Exhibit 2 Selected Operating and Income Statement Data of Partners for Fiscal Years 19952004 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 1,660 2,820 1,511 327 1,571 339 181 443 Gross Patient Revenue Operating: Net Patient Service Revenue Academic and Research Revenue Other Revenue Total Operating Revenue Total Operating Expenses Income from Operations 1,998 448 213 2,287 505 242 3,678 915 617 3,137 718 363 141 2,487 548 291 3,326 3,325 106 335 3,361 824 367 4,552 4,520 397 1,979 1,965 14 2,091 2,104 2,209 2,221 2,659 2,679 -20 3,034 3,091 -57 3,772 3,724 4,218 4,148 70 4,990 4,885 105 -13 -12 1 48 32 Long-Term Pool: Assets at Year-End: Total Return during Year (%) Total Return (in $) 636 15.0 43 716 13.3 85 887 28.2 202 891 -4.7 -42 1.235 25.2 225 1,398 18.1 224 1,365 -7.3 -102 1,399 -3.3 -45 1,839 21.1 295 2,253 16.7 307 Source: Company documents. Notes: Long-term pool inception was April 1, 1995 (1995 reflects return from April though September). Total returns on endowment funds, all of which are invested in the long-term pool, are included in the operating and income statements only when distributed. Exhibit 3 Summary of the Assumptions To Be Used in the Portfolio Analyses REITS Commodities Annual Expected Returns Standard Deviations, and Correlations Correlation with Asset Class Expected Ret. Stdev US Equity Foreign Equity Bonds US Equity 12.94% 15.21% 1.00 Foreign Equity 12.42% 14.44% 0.62 1.00 Bonds 5.40% 11.10% 0.25 0.06 1.00 REITS 9.44% 13.54% 0.56 0.40 0.16 Commodities 10.06% 18.43% (0.02) 0.01 (0.07) 1.00 (0.01) 1.00 14.00% US Equity Foreign Equity Baseline LTP 12.00% 10.00% Commodities REITS 8.00% Expected Return 6.00% Bonds 4.00% STP 2.00% 0.00% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.09% 16.0% 18.0% 20.0% Risk: Standard Deviation Source: Author's estimates using historical data from CRSP and Thomson Financial Datastream. Standard deviations and correlations are calculated using monthly returns from 1970 to 2004 (except REITs, which use monthly data from 1990 to 2004). Expected returres are calculated using a risk-free rate of 3.2% (the current yield of the STP) and a bond excess return estimated from 1970 to 2004. The U.S. equity risk premium (U.S. equity expected return minus bond expected return) is set to 7.2%, the difference in average return from 1926 to 2004. Foreign expected return is set so that the ratio of its risk premium to standard deviation i.e., its Sharpe ratio) matches that of the U.S. Commodity excess returns are estimated from 1970 to 2004. The REIT excess return is estimated using data from 1995 to 2004 and then scaled by the ratio of the U.S. excess return to the U.S. excess return from 1995 to 2004. The Analysis To begin with, Manning needed some assumptions about future expected returns, risks, and correlations of the various asset classes in order to compare and evaluate different potential portfolios. He had his staff collect and analyze information on each of the five asset classes. Using very long-term historical data from 1926 to 2004, they calculated the average realized returns from U.S.equities relative to U.S. long-term bonds in order to estimate the risk premium that equities had paid on average relative to bonds over this very long-term time horizon. Unfortunately, such very long-term data were not available for most asset classes. Using data on realized returns from 1970 onward, they calculated average annual returns, volatilities, and correlations for each of the asset classes. These historical data drove the assumptions about future returns, risks, and correlations that would be used in the analysis, which are displayed in Exhibit 3. Exhibit 3 also includes a "risk- return" plot of these assumptions for the five asset classes, with the future expected returns on the vertical axis and the annualized future standard deviation of retums on the horizontal axis. The plot also displays the calculated future risk (12.02%) and expected return (11.65%) of the baseline 55/30/15 LTP given these assumptions (see the Appendix for the formulas used to calculate the future risks and returns of a multi-asset portfolio) and the current yield of the STP (3.2%). At first glance, REITs seemed attractive with their low risk and reasonable expected returns Commodities appeared as though they might be less attractive because of their much higher risk, notwithstanding their slightly higher expected returns. But how much these opportunities would increase the LTP's return or lower its risk clearly depended on how much capital Partners was willing to allocate to these investments and their correlations with assets in the baseline portfolio. Solving this problem would require portfolio analysis: calculating the expected return and risk of portfolios with different levels of investment in each of the asset classes and then asking which combination(s) offered the lowest risks and/or greatest expected returns. Manning began by asking whether the baseline LTP allocation of domestic equities, foreign equities, and bonds had offered the best risk-return trade-off for investors relative to all other portfolio mixes that invested in just these same three asset classes. He first considered sets of different portfolio weights that deviated arbitrarily from the baseline allocations in the LTP, but where the 3 w weights were constrained to be positive and to add to 100%. Exhibit 4a reports the calculated future expected returns and standard deviations for 16 of these arbitrary alternative three-asset-class portfolios. Exhibit 4b presents a risk-return scatterplot of these 16 portfolios. Similarly, Exhibit 4 displays a risk-return scatterplot for a much larger sample of several hundred arbitrarily chosen three-asset portfolios. Manning was not really sure whether any of these alternative portfolios were clearly better or worse than the baseline LTP. Some of the Partners hospitals might prefer some of the portfolios with lower risks, but others would probably prefer some of the portfolios with higher retums. Indeed, he wondered whether any of the portfolios could be considered superior or inferior to the others given that the hospitals and physician organizations all had somewhat different tolerances for risk. He hoped, though, that at least some of these potential portfolios could be eliminated from consideration on the grounds that they offered lower expected returns but higher risks relative to others. To better understand what the interests of particular hospitals might imply for the optimal mix of assets in the LTP, Manning considered the perspective of a hospital targeting 10% future expected returns. It was clear that many different combinations of U.S. equities, foreign equities, and bonds could achieve this goal. However, not all such combinations would offer identical risks. Therefore, Manning asked his staff to search across all combinations to identify the one that would deliver the 10% expected return but with the least amount of risk. They reported back to him that an investment of 23.4% in U.S. stocks, 40.4% in foreign stocks, and 36.2% in bonds could deliver the targeted 10% expected returns at 994% riska lower level of risk than any other possible set of allocations producing the 10% expected returns. Manning concluded that this combination must be optimal for any hospital wishing to achieve 10% expected returns. He then asked them to repeat their search procedure to identify the minimum level of risk required to achieve several other different target- return levels. These portfolios are reported in Exhibit sa along with a plot in Exhibit 5b of their future expected returns and standard deviations. Now, Manning thought that they were ready to analyze how much the introduction of REITs and/or commodities might improve the risk-return opportunities available for the LTP. Manning wondered whether REITs or commodities would be more helpful. Commodities had higher expected returns than REITs, but they also carried far greater risk. To analyze the problem, he again asked his staff to determine the minimum attainable risk level (standard deviation) for different target-return levels when REITs were added to the set of investable assets (see Exhibits 6), and similarly when commodities were added to the set of investable assets (see Exhibit 7). Because Partners could easily maintain investments in both of these new asset classes at relatively low setup and transaction costs, Manning knew that he should consider investing in both simultaneously. Exhibit 8 reports the results of the same analysis when all five assets were available for investment. Stepping back from the numbers, Manning wondered whether the addition of real assets would really make the hospitals better off. Their needs and preferences were quite varied. Some wished to keep the future risks of their overall financial assets quite limited; others were willing to take more risk in pursuit of substantially higher future retums. How would real assets in the LTP help them, if at all? Could a "one-size-fits-all" solution for the LTP reasonably meet the needs of the Partners hospitals