Since the development of modern portfolio theory, many institutional investors have used mean-variance optimization techniques to help identify their appropriate asset mix. This quantitative approach allows an investor to assess various allocations by considering the trade off between risk and return, and the relationship between the assets.

The inputs to this approach include expected asset return, volatility (risk) and correlation (behaviour of asset returns relative to each other). With this type of exercise, it’s important to remember that your output is only as valid as your input.

**Determining the appropriate asset classes**

The goal for all investors is an asset mix that puts your assets to work in the most efficient way possible. The classic approach is to create an efficient frontier, which represents a combination of asset classes that would, in theory, deliver the maximum unit of return per unit of risk. The use of an efficient frontier, although quite theoretical in nature, can also help to illustrate the benefits of adding imperfectly correlated asset classes to your portfolio.

Correlation measures the movement of an asset relative to another asset. Correlation coefficients range from being perfectly negatively correlated -1 (assets are moving in opposite direction) to perfectly positively correlated +1 (assets are moving in lockstep). A coefficient of zero would imply the assets move completely independently of each other.

**Read: The implied volatility of your investment policy**

By combining imperfectly correlated assets (anything with a coefficient between -1 and +1) to a traditional 60/40 strategy and expanding the opportunity set, the entire efficient frontier moves up and to the left, which means more expected return at any level of risk; a portfolio’s expected volatility may be reduced, often without a significant effect on returns. With everything else equal, the closer the coefficient is to -1, the larger the benefit of diversification will be on reducing volatility. As the theory goes, this move is a good thing for investors.

But is correlation constant over time? No. The culprit is volatility. Volatility is typically associated with asset returns. However, correlation can also be influenced by the volatility of the asset classes it measures, often to the detriment of portfolios believed to be adequately diversified. Challenges to portfolio construction arise when the correlations among assets do not remain constant.

First, let’s look at volatility over time.

When thinking about portfolio diversification, investors instinctively focus on correlation and its impact on portfolio volatility. It’s the right approach, but an incomplete one. Combining assets with low historical correlation will reduce volatility but it doesn’t eliminate risk or the possibility of adverse co-movement in times of crisis.

**Read: A real-life stress test**

Next, let’s have a look at the correlation coefficients for the core equity classes over time. As you can see, it’s very unstable.

For simplicity purposes, we have isolated the correlation of the S&P/TSX Composite (Canadian equities) with the S&P 500 (U.S. equities) to plot against the volatility of the TSX.

While not a perfect indicator, the chart indicates that higher volatility regimes result in higher correlation.

**Constructing your portfolio**

Once you have determined which asset classes are appropriate for you, the next step is to supplement the analytical framework with your projected outcomes. The horizon of your projections must be in line with the investment horizons of institutional investors; limiting projections to the short-term and more immediate market behaviour causes uncertainty and is not very helpful for strategic decision making.

**Read: Sovereign pension plans investing heavily in real estate: study**

A building-block approach is often used for the return assumption, which studies have shown is the most important input when it comes to producing a valid output. We start with inflation expectations, add the expected real risk-free interest rate and then a risk premium for each asset class. Clearly, there is a mix of historical perspective and future expectations influencing each block.

The most dynamic, and tricky to handle, block due to changes in implied volatility is the risk premium. All investors expect to be compensated for taking on risk. The risk premium measures that level of additional compensation for riskier assets, which is the difference in returns of the asset class versus the nominal risk-free rate.

When we allocate capital toward equities over bonds, we do so because we expect the equities to produce a higher return. However, the premium that investors demand for investing in the asset class is not static. Determinants include dynamic and ever-changing aspects, such as the level of investor risk aversion, information uncertainty and simple perceptions of macroeconomic risk. The challenge, in both theoretical and practical terms, is how to measure the risk in an investment and how to convert the risk measure into an expected return that compensates for risk.

**Read: Brexit vote incites volatile market, stunning global investors**

That is, because the risk premium reflects fundamental views about volatility – and risk in general – and the return we demand for taking that risk, the premium will change at different points in time as volatility changes and the economic and financial context evolve.

Thus, the implied risk premium of the assets in your portfolio is in constant flux while your internal required rate of return for your portfolio is more static. This is a disconnect that should be managed dynamically. Indeed, a tightly constrained portfolio with rigid rebalancing guidelines ignores this fact and will expose you to an overall level of risk that is either materially above or below what is necessary to meet your required return.

In times of high implied volatility where risk premiums rise, plan sponsors can afford to move down the efficient frontier and protect the assets from the higher volatility. Likewise, when risk is perceived as low and volatility subdued, investors should be well served in moving out on the efficient frontier to maintain the desired risk exposure.

**Read: Is it time for pension funds to rethink their fixed-income allocations?**

The goal of portfolio construction is to minimize risk while maximizing the probability of achieving the required return. To do so, committees and decision makers need a core understanding of how different assets react to different market environments, along with the knowledge that constructing an asset mix with low average portfolio variance mitigates only one dimension of risk.