Below is a brief look at major asset classes, their forecasted annual return, price volatility, and an application of the Kelly Formula to the Asset Allocation decision. All returns are presented in real terms (net of inflation), in order to show change in investors’ actual capacity to consume.

As of 4/30/16. Source: These expected returns are calculated by Research Affiliates, LLC.

Projected future returns across most major asset classes have been compressed to near the zero bound. Their volatilities lead to near 50% or greater odds of negative returns for many assets. This is not a normal state of affairs. During normal times, US Equities will often offer 10% or greater expected returns. Only Emerging Markets come close to offering a decent investment return.

Below are these expected returns in table format, arranged in relative order of risk. My risk measure is a combination of price volatility and duration.

## Asset Allocation with the Kelly Formula

For stock market investing, the Kelly Formula is:

f = (u – r)/s^2

where f is the Kelly fraction, u is the expected return of the risky asset, r is the opportunity cost, and s is the standard deviation (volatility). Below I take these expected returns and apply them to the Kelly Formula (which gives the optimal bet size). The Kelly Formula, however, assumes we can adjust our allocation instantaneously – and with no trading costs. Obviously we cannot trade so often (I adjust allocations twice a year), thus this version of the formula offers no downside protection. In order to protect against short-term downside moves, in the table below I reduce the projected return by the expected value of a short-term loss. This is taken from the amount of negative volatility (seen in chart above).

The opportunity cost ‘r’ in the Kelly equation is the expected return of the next available safer investment.

Plugging these values into the Kelly Formula leads to an interesting dilemma. * There is no major asset class which currently offers sufficient risk-adjusted return.* Lest you think this is a normal state of affairs, here is a more ‘normal’ situation for the S&P 500:

When the S&P 500 is offering more respectable long-term returns of 11%, this version of the Kelly Formula would allocate 80% of your portfolio to the index.

The conclusion is thus: Currently it is unfortunately best to hold cash until the markets offer us something worth investing in. If you have access to a Stable Value fund, perhaps in a 401(k) plan, many are currently offering a guaranteed 1.5 – 2% return. We’ll revisit the markets in October to see where the world stands.

I’m certainly not the only one suggesting abysmal long-term returns for major asset classes. Fund manager and economist John Hussman is currently suggesting:

We currently estimate that the total return on a conventional portfolio mix of stocks, bonds and Treasury-bills is likely to average scarcely 1.5% annually over the coming decade…..At present, years of relentless quantitative easing by the Federal Reserve have driven equity valuations to the point where prospective 10-12 year S&P 500 total returns are just 0-2% by our estimates, while Treasury yields are also below 2% and Treasury bill yields are only a fraction of a percent. The combination brings the expected return on this portfolio mix to the lowest level in history outside of the valuation extremes of 1929, 1937, and 2000. Yet, because investors and policy-makers seem incapable of distinguishing

realized pastreturns fromexpected futurereturns, they fail to see the danger in this situation.

A history of changes to the Asset Allocation model is shown in Table below and may also be found on the Portfolio page.

One study suggests that more than 91.5% of a portfolio’s return is attributable to its mix of asset classes. Individual stock selection and market timing accounted for less than 7% of a diversified portfolio’s return. William Bernstein says in his book The Four Pillars of Investing, that: “*The ability to estimate the long-term future returns of the major asset classes is perhaps the most important investment skill that an individual can possess.*”

Chris says

How are you calculating your expected volatility and expected return? Those are key inputs. I’d be interested in hearing your methodology.

HWWProject says

These are 10-year projected returns and volatility from Rob Arnott’s group – Research Affiliates. Details and methodology can be found here: http://www.researchaffiliates.com/assetallocation/Pages/Core-Overview.aspx

Chris says

Very interesting, thank you.