# Near Zero Interest Rates and Diversification

There is an interesting relationship between the “risk-free” rate (t-bill rate) and the benefits of diversification. When rates are close to zero, the risk reduction benefits from low or anti-correlated assets can offset the requirement for those assets to have a sufficient expected return to make diversification practical for enhancing risk adjusted returns. This extends to all assets– including those that do not have a theoretical risk premium such as certain commodities and currencies. Conversely when the risk-free rate is high, it is nearly impossible to justify diversification with the exception of those assets that can be assured of producing a risk premium. In this case, only stocks, bonds and real estate would qualify as assets that should produce a return in excess of the risk-free rate since their pricing is inherently tied to the cost of borrowing/lending.

It is conventional wisdom that gold should not have a risk premium, and historically this has been true though this is a separate debate. What is more important is that gold carries a negative correlation to other assets, and thus in a low or zero interest rate environment it does not need to have much of an expected return in order to improve portfolio risk-adjusted returns. Consider that holding standard deviation constant, an asset with a -.5 correlation reduces portfolio risk by 50%. That means that gold returns can be up to 50% lower than all other asset returns and still improve the portfolio sharpe. The same principle holds true for all assets that have low or negative correlations to equities. This substantially increases the pool of assets that would qualify for inclusion in a properly diversified portfolio. The lower the correlation, and the lower the expected return of equities, the lower the expected return hurdle for assets without risk premiums need to be to improve risk-adjusted performance. This means that expected returns that are zero or even negative can potentially qualify such assets for an efficient portfolio. Of course, this is a “special situation” that occurs in the rare circumstances where interest rates are near zero. Thus the conventional approach of focusing only on assets that have a risk premium in all environments is a flawed approach. A superior approach would consider the dynamics of interest rates and all asset correlations along with a possible range of expected returns.

It also relies upon investors being able to satisfy the other conditions for CAPM (around unconstrained borrowing in other asset classes, about standard deviation being the best risk measure, etc) as well as being subject to the biggest risk that most investors forget about – model risk (i.e. the risk that your assumptions are wrong, badly wrong).

An alternative way to think about this is engineered diversification – i.e. embracing ways that will materially and definitely reduce the risk of alll your assets falling in value at the same time, without needing to forecast return distributions.

Optionality fits very much into this category for example – with the extra benefit that the explicit and implicit costs of the diversification are taken into account as part of the risk-return trade-off. Compare that to, for example, to investors who hold sovereign bonds for diversification purposes: they are explicitly surrendering the potential extra returns that they would get from holding higher expected return assets for the diversification benefit, but I see little suggesting they have evaluated just how valuaable the diversification is, how much they are explicitly relying on that diversification, and whether those benefits could be obtained in a more efficient fashion.

I guess what I am saying is that the vast majority of retail and institutional investors use incredibley naive and unsophisticated portfolio construction techniques on the 95% of their investment risk associated with asset class selection, compared to what they (and the managers that they hire) do on the other 5% of the risk (i.e. active management).

It really should be the other way around.

Just one person’s opinion.

I’m having trouble understanding you. I think a critical point is here: “When rates are close to zero, the risk reduction benefits from low or anti-correlated assets can offset the requirement for those assets to have a sufficient expected return to make diversification practical for enhancing risk adjusted returns.”

Consider an investor who invests relative to a benchmark that is a 100% allocation to the risk-free asset. Assuming the covariance of the risk-free asset with every other asset is zero, you could rewrite this as maximizing (r-rf) for a given volatility (and adjust volatility to generate the efficient frontier). Assuming the covariance matrix is unchanged, basically you’re talking about how the optimal allocation changes as rf changes. However, rf is a constant. It doesn’t impact anything, you could drop it and get the same result. On the other hand, if you make implicit assumptions that r=a*rf+B*rm, where a is equal to 1 for some assets and 0 for others, then it may not be the case.