and the Financial Crisis
April 20, 2010
Monte Carlo Projections for Yale’s Asset Classes
Overall, the projected risks and returns for the various asset classes from my Monte Carlo simulation agree closely with Yale’s projections.
In the case of private equity, I used PSP, a fund designed to track an index of public private equity firms. The real asset component of the portfolio is somewhat harder to approximate. I have created the real asset sub-portfolio by combining utilities, transport stocks, REIT’s, commodities, and physical gold.
The hardest component of Yale’s projections to reasonably approximate is the Absolute Return (AR) component. While there are funds with this designation, the performance of this ‘asset class’ is so dependent on manager skill that it is inappropriate to rely on them as a proxy for AR performance. AR strategies are supposed to be market-neutral, with near-zero beta. By allocating the 15% that is supposed to go to AR to a short-term bond fund as a conservative proxy, my Monte Carlo projections give this portfolio a projected return of 10% with a volatility of 16.2% (using data through March 2010). If I allocate the 15% targeted to AR to investment-grade corporate bonds (using the LQD ETF), the projected return is 10.5% with volatility of 17%. This seems like a better fit for AR, at least in terms of risk level and impact on the portfolio, because LQD has projected volatility of 9.1% – quite close to the 10% projected by Yale for AR.
Overall, the projected return and risk for our representative portfolio – 10.5% and 17%. respectively – are quite similar to the Yale’s projected return and risk of 10.4% and 13.2%, especially given the challenges in creating a reasonable proxy. A more critical selection of individual investments can certainly add return relative to the market-cap weighted indexes that we have assumed. Further, we have ignored the potential value that active management could add. My own research suggests that it is plausible that an absolute return strategy could generate 10% in return with 10% in annualized volatility (as Yale projects for the AR component of the portfolio). In fact, I have found that this appears to be a fair estimate of what is possible.
Overall, then, our Monte Carlo simulations are broadly in agreement with Yale’s projections, justifying Yale’s estimates of various asset class returns. Our estimates of the portfolio risk and return using index-based asset classes result in a similar projected return, albeit with higher risk than Yale’s estimates. Yale uses derivative instruments to manage risk, and some of the additional return that they expect to receive from their AR strategies could fund the purchase of risk-reducing options and swaps in their portfolio, bringing the risk levels of Yale’s and our Monte Carlo simulations closer into alignment.
Could the magnitude of potential loss in 2008-9 have been anticipated?
One of the largest questions on peoples’ minds with regard to the endowment model is whether the substantial losses in FY 2009 indicate flaws in the underlying model. The almost 25% loss in Yale’s endowment was a shock. Yale’s 2008 report states that the expected real return of the portfolio is 6.4%, which translates to 10.4% in nominal return. The projected risk level was 12.7% in annualized volatility. If we run our Monte Carlo simulation using data through June of 2008 for the proxy portfolio that we created for Yale, we get an expected return of 9.3% with annualized volatility of 11.7%. Note that this is still assuming that Absolute Return is approximated by investment-grade bonds. Based on these estimates, what is the worst than can happen?
The S&P500 lost approximately 26% for the year ending June 2009, so the losses in Yale’s endowment were on track with the market. The risk level that Yale projected for their overall portfolio was 12.7%, however, which is far less volatile than the 20% risk level that they estimated for domestic equities. The losses in FY 2009 to Yale’s portfolio were much more severe relative to their expected risk level than were the losses from domestic equities.
The answer to the question posed at the start of this section, then, is somewhat nuanced. The level of loss suffered by Yale’s portfolio was within the estimated realm of possibility, although it was somewhat higher than was predicted by Yale’s estimate of risk for its portfolio. This situation contrasts starkly, for example, with the events that famously destroyed Long Term Capital Management, which had been estimated as absolutely impossible over the multiple lifetimes of the universe.
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