The Harvard Management Company and Inflation-Protected Bonds
The Harvard Management Company (HMC) is the organization that actively manages the assets of Harvard University. Overseeing a total of $19 billion in assets, HMC had managed to achieve an average real return of 11.3% during the 90’s, 9.1% above the average return of US T-Bills and 3.6% below US equities. With a target of 6%-7% average real return, HMC’s goals are to correctly measure Harvard University’s financial requirements and to provide investment opportunities that will accurately meet or exceed them with the lowest amount of risk assumed by the institution. In order to determine the relevance of each asset on its diversified portfolio, HMC is considering three factors: expected future returns, volatility of real returns and correlation of real returns on each asset class with those on all other asset classes. In Exhibit 1 of the report we observe the portfolio composition of Harvard’s portfolio from 1984 until 2010.
Through the use of historical data and mean-variance analysis, HMC was in a position to identify the portfolio that best suits its needs and considers making changes to it only in response to (1) changes in the goals or risk tolerance of the university as an institution, (2) changes in capital market assumptions, or (3) the appearance of a new asset class in the market. The 1997 introduction of TIPS in the US market seemed to satisfy both conditions 2 and 3, as described next.
Treasury Inflation-Protected Securities (TIPS)
TIPS are inflation indexed bonds issued by the US treasury. While such bonds had been issued before 1990 in other countries (Exhibit 2), they made their first appearance in the US in 1997. They are designed to approximate real bonds with payouts that are constant despite inflation surprises. They are quoted in terms of a real interest rate and are issued mostly at long maturities greater than 10 years. The principal on these bonds grows with a pre-specified price index, which in the U.S. is the Consumer Price Index (CPI-U), while the coupons are equal to the inflation-adjusted principal on the bond times a fixed coupon rate. Thus the coupons on these bonds also fluctuate with inflation.
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In general, TIPS have a low correlation with other asset classes and a very low default risk. In times of high inflation, they protect investors from loss on their real returns, whereas in the US the final payment of their principal is protected against deflation. However, their coupons are not, and therefore, the inflation-adjusted value of the principal for coupon computation purposes can fall below the initial value at issuance1. It is clear that in periods of substantial inflation uncertainty, TIPS are an attractive bet. In Exhibit 3 we can observe the values of inflation from 1914 until 2011.
In addition, it is worth noting that in the US inflation-adjustments of principal are considered ordinary income for tax purposes. As a result, the tax obligations associated with holding a TIPS increase when inflation is high so that on an after-tax basis U.S. TIPS are not fully indexed to inflation2. , 
Comparing the Current with the Proposed Policy Portfolio
The proposed portfolio has an estimated Sharpe Ratio of 0.32, 0.04 higher than the Sharpe Ratio of the current portfolio. Therefore, the proposed portfolio will offer a better return/risk ratio. The four important facts that characterize the proposed Policy Portfolio are:
- US equities decreased from 32% to 22%
- US bonds decreased from 11% to 7%
- Elimination of shorting cash from -5% to 0%
- TIPS are introduced, representing 7% of the portfolio
In the following graph we depict the efficient frontiers according to the portfolio optimization calculations presented in exhibits 5 and 6 of the case, under different sets of constraints.
It is graphically confirmed that the proposed policy portfolio is superior to the current one, since it approaches the efficient frontiers. However, the fact that it does not lie on them suggests that there exist different asset allocations that can further improve the Policy Portfolio.
Potential problems with the analysis
In mean-variance analysis, the accuracy of estimates for the means and covariance matrix of assets is an important prerequisite. The HMC team only had three-year data for the performance of TIPS, so they relied on the real yield on TIPS (about 4%) within that period (1997-2000) to derive the expected real return on TIPS as well as covariance of TIPS with other asset classes. However, whether the performance of TIPS in this particular period is representative enough can be seriously doubted. As we can see from the graph of U.S. Annual Inflation Rate, there was a clear upward trend in inflation rate from 1997 to 2000, which probably contributed to the outperformance of TIPS to a large extent. When inflation rate does not keep increasing, TIPS will not necessarily provide investors with a superior real yield. If the estimates for mean real return and covariance of TIPS are biased themselves, the mean-variance analysis conducted by HMC could be meaningless.
The Proposed Portfolio is indeed an attractive portfolio in relation to the current one. It does not manage to reach the efficient frontiers, but this could be due to the fact that the portfolio composition on the frontiers is based on some unrealistic situations that do not meet HMC’s goals, such as very high TIPS dependence (almost 55% on average), very high cash shortage (almost -40% on average) and 0 investments in Domestic Equity.
At the same time, the importance of market and economic conditions should not be underestimated. In the early 00’s recession made TIPS an excellent investment choice, since times of recession are followed by high inflation and unemployment rates.
However, we should also point out that the proposed portfolio calculated by HMC in 2000 was based - as far as TIPS were concerned - on assumed values and not historical observation, since TIPS were first introduced in the US in 1997. This shortage of information makes it hard to come to accurate conclusions and solid decisions.
- Harvard University: Portfolio Composition
- Introduction of Inflation-Indexed Bonds
* In 1975 the United Kingdom issued non- marketable index-linked national savings retirement bonds ("granny bonds"). Marketable index-linked debt was first issued in 1981.
- Historical Inflation
1 In contrast, neither the principal nor the coupons on inflation-linked gilts are protected from deflation in the UK.
2 In the UK principal adjustments of inflation-linked gilts are not taxed. This gives inflation-linked gilts a tax advantage over nominal gilts, a larger share of whose cash flows come in the form of taxable nominal coupon payments.
Markowitz Mean-Variance Analysis—Basic Model
The underlying idea of the model:
to minimize the variances of the portfolio given a target rate of return:
(σij: covariance between asset i and asset j;
rbari: expected rate of return of asset i;
rbar: target rate of return for the whole portfolio;
αi: portfolio weight of asset i)
Using Lagrange Method to solve this problem:
Setting the first-order derivatives of L with respect to each of the n weight variables α to be 0 yields n equations, from which the optimal solutions to the problem can be derived:
Suppose (rmin,σmin) is the minimum variance point without any constraint on the portfolio rate of return. Then we can go ahead and graph all pairs (rbar, σ) in the minimum-variance set satisfying rbar >= rmin. This set of pairs is called the “Efficient Frontier”. All portfolios on the efficient frontier are “efficient”, in the sense that they all have the minimum portfolio variance given a certain target rate of return.
 A Scorecard for Indexed Government Debt
 John Y. Campbell, Robert J. Shiller : “A Scorecard for Indexed Government Debt”
 Carolin E. Pflueger and Luis M. Viceira : “Inflation-Indexed Bonds and the Expectations
 Campbell, JY and RJ Shiller. 1996. A Scorecard for Indexed Government Debt.