Back in the low-risk area at the left edge of the chart, it turns out, perhaps surprisingly, that investing 10% in stocks and 90% in Treasuries is better than going all-in on Treasuries. Nearly as good is a portfolio that rebalances 15% in stocks against 85% in Treasuries. This finding is robust across all the data-sets in last week's analyses, which covered the most recent 25 years in Germany, Japan, and Australia, and the last century in the U.S. The result is also broad in another sense. It is the aggregate pattern across three types of drawdowns: the maximum drawdowns over 25-year periods, the worst single month in 25-year periods, and the average loss for all months that below the previous peak.
Although the advantage of putting 10% in large-cap stocks may seem small, it was very consistent over time and geography. Perhaps the reason is that the growth potential of equities is needed to counteract how Treasury bonds may lose value down when central banks keep interest rates excessively low or when inflation first erupts.
At this point in the analysis, we have a floor (about 10%) for investors concerned about minimizing drawdowns and a ceiling (near 90%) for those concerned about maximizing gains. What if you care about both? Then, in the jargon of finance, you aim to optimize your risk-adjusted returns. Or, in lay terms, you are willing to expose your portfolio to somewhat more drawdowns, provided that you are paid back, in equal measure, with better returns.
Taking guidance from a method proposed by Franco and Leah Modigliani, I calculated a relative return that adjusted the real return to compensate for the risk of drawdowns. It was calculated as benefit times penalty, where:
- benefit = portfolio's real return minus the real return of 10-year Treasuries
- penalty = average drawdown of 10-year Treasuries divided by the average drawdown of portfolio
That said, even a rebalanced portfolio with a large allocation to stocks would be a winner. In the right hand portion of the chart, the curve remains in positive territory. These portfolios do, therefore, provide an incremental benefit over Treasuries, even after adjusting for their exposure to drawdowns. The risk-adjusted benefit just happens to be rather modest.
My next post will use the same three-step method to analyze the strategy of rotation:
- What is the best floor to minimize drawdowns, 0% or some other value?
- What is the best ceiling to maximize returns, 100% or something else?
- What combination of floor and ceiling values gives the best relative returns?