In order to diversify the risks of the LTP, the Partners Investment Committee introduced a new type of assets, real assets, into the original LTP during the past years. Both of the assets performance turned to be excellent during 2004. As a result, the Investment Committee was considering expanding the real-asset segment of the LTP. Michael Manning, the deputy treasurer of Partners Healthcare System, was asked to recommend the size and the composition for the real-asset portfolio contributed to the $2.4 billion long-term pool (LTP) in the Partners. Facts and Analysis
Due to the fact that different Partners Healthcare hospitals might have different acceptable risk levels for their investment portfolio then the most reasonable solution would be to invest both in risk-free STP and risky LTP. By choosing different mixes each hospital could achieve their acceptable risk level.
Since the STP has a nearly fixed rate of return considered to be risk free for each hospitals own portfolio, the variation from LTP would ultimately determine the risk and return level of individual portfolio. Using long-term historical data, Manning and his staff calculated average annual returns, volatilities, and correlations for each of the asset classes (exhibit 3). Since real assets belong to LTP, there is no direct impact on the STP returns from investing in this category. Given the current mix of Domestic Equities (55%), Foreign Equities (30%) and LT Bonds (15%) and our expected return for each category (exhibit 3), the expected return of the LTP is calculated from the following formula: e.g. E(Rp)= 0.55(0.1294)+0.30(0.1242)+0.15(0.054) = 10.8%
In order to find the optimal portfolio allocation, the group needs to find the portfolio structured with lowest risk under a given return. This can be achieved by applying Mean-Variance Theory and Markowitz model find the efficient frontier, which yields the most optimal portfolio under given returns. It can be expressed in mathematical terms and solved by quadratic programming. [Appendix A]
In this case, the Partners Treasury Department has computed all the portfolios for minimum level of risk with different types of assets, more specifically, adding Real Estate Investment Trusts (REITs), Commodities or both, from an undefined approach. Since the results are identical as calculated from Mean-Variance Theory, they should be the optimal portfolios for each target level of return. Therefore a graph with efficient frontier, which represents the optimal portfolios with different assets, is constructed based on Exhibit 5 to 8 for comparison. [Appendix B] Technically, any portfolio on the efficient frontier is an optimized portfolio and is indifferent from each other in terms of risk/return trade off.
From the Risk VS Return graph, we can see that for any given return, the portfolio with both REITs and commodities would yield the lowest risk. Also, the portfolio with only commodities would outperform the portfolio with only REITs. For instance, if we invest in both REITs and Commodities, in order to obtain a return of 10%, the new proportion of the LTP will be portfolio 4 with approximately US Equity 14.3%, Foreign Equity 27.5%, Bonds 22.2%, REITs 13.8%, and Commodities 22.3%. It produces the lowest risk of 8.49%, comparing to original portfolio of 9.94%, REITs only portfolio of 9.69% and Commodities only portfolio of 8.49%. This is the basic concept of diversification, which means that the more assets with less correlation are introduced to the portfolio; the less risky the portfolio will be for any achievable rate of return. 
For the overall portfolio, each hospital can allocate between the STP and the LTP. In fact, they can always construct the most efficient portfolio for their acceptable risk level with combination of LTP, which holds the risky assets, and STP, which holds the risk-free asset according to The One-Fund Theorem.  For example, if the shareholders want a total return of X, with a 3.2% return of STP and a 10% return of LTP, the proportion of STP and LTP can be obtained through X= w(0.032) + (1-w)(0.10)
And it is guaranteed to be the optimal portfolio.
Even though Mean-Variance theory can allocate the most optimal portfolio, there are several flaws with its assumptions. First of all, it assumes that assets returns are normally distributed. However, often times, its observed that asset returns are more like to be fat-tailed distribution,  instead of having thin tails like normal distribution. Second of all, it assumes there is a constant correlation between different assets.
However, under certain conditions, for example, severe financial crisis like 2008, all assets tend to be positively correlated with decreasing rate of return. Depending on the total time period used for historical data, it can place an impact on the long term correlation. Aside from the assumptions, the time period of data can also affect each variable. In this case, the client uses data started from 1970 for the new asset classes, which might not be as representative as using long term historical data from 1926 as they did with the US equities and US long-term bonds. This can have some impacts on the returns, standard deviations, and correlations depending on the movement of assets from 1926 to 1970. Recommendation
By comparing the data in the table of Exhibit 5a with the numerical results shown in Exhibit 6 and Exhibit 7, as well as the efficient frontier constructed, we can derive the conclusion that with the same expected returns, the most optimal portfolio is to add both REITs and commodities. In other words, we can control the risk of LTP by expanding the portion of real assets. If only one asset is allowed to be added to the real asset category, its more efficient to add the commodities than the REITs based on the position of the efficient frontier. Therefore, with a combination of risk free STP and the improved LTP, each individual hospital is able to construct the most optimized portfolio under any given risk level.