A two-dimensional, return-and-volatility view of investments may not allow you to see important risks.

Today’s CIO Weekly Perspectives comes from guest contributors Peter von Lehe and Stephen Smith.

If you’ve been reading the financial press lately, you may have seen how investors can get caught out if they think only in terms of return and volatility, while ignoring illiquidity—especially when they invest in private markets, where illiquidity is one of the key risks.

Illiquidity shouldn’t come as a nasty surprise, but all too often it does. Why is this, and how might we go about integrating liquidity risk into our investment thinking?


Back in the 1880s, an English schoolmaster named Edwin Abbot published an eccentric little satirical novel, Flatland.

In Flatland, everyone is a two-dimensional shape, like the Square who narrates the novel. The Square has a dream about Lineland, a one-dimensional land where everyone is a line. The Square is unable to convince the Linelanders that he is anything more than a collection of four lines.

But the Square’s understanding is just as limited. Visited by a Sphere from Spaceland, a land of three dimensions, he is unable to see anything other than a disk. A third dimension is incomprehensible to him.

We believe something similar happens when investors and asset allocators who invest mostly in liquid markets try to account for illiquid assets in their asset allocation models.

Theirs is a world where risk is quantified as the annualized volatility of an investment’s market value. When they see private assets, which are generally bought and sold only once every few years and receive a (non-market) valuation once a quarter, they tend to impute annualized volatility values to them in order to squeeze them into their black boxes.

When they do this, it tends to result in higher imputed volatility than that observed in equivalent liquid assets—which could penalize illiquid assets in the allocation process and does not tie to an investor’s actual experience.


But volatility is not the relevant measure of risk for illiquid assets, in our view. We believe what matters to illiquid-asset investors is the quarterly valuation that shows up in their capital accounts and, most importantly, the cash they receive when assets are sold.

Moreover, the focus on creating a volatility number often distracts from what we regard as the real risks associated with private assets, which are illiquidity (being unable to get your hands on your money when you need it) and the final return outcome (how much you realize when you ultimately sell the asset).

Just as the Square misses the essential characteristic of the Sphere, so the mean-variance optimizer misses these essential characteristics of a private asset.

We think there are solutions, however. They involve integrating illiquidity and the profile of an investor’s liabilities into asset allocation analysis. That enables us to calculate the probability of not having access to enough cash to meet liabilities as they come due—either because you have the value in your portfolio (but not the liquidity), or because you have the liquidity (but not the value).

The Third Dimension

Let’s imagine you set aside $100 today and need $200 in cash in 10 years’ time. An asset mix that has generated a long-term average annual return above 10% with average annualized volatility of 6% might appear suitable. But we believe this two-dimensional view is incomplete.

First, we expand the second dimension, volatility, to include the left tails, or extreme drawdowns, in the return distribution. An unusually big drawdown could bring the average annual return for any discrete 10-year period below 10%, leaving you with less than $200. What probability of that outcome are you prepared to tolerate?

Then we introduce the third dimension, liquidity. Diversifying your asset mix can help to get left-tail risk down to a tolerable level, but it can also reduce estimated return. Adding illiquid assets has the potential to raise that estimated return back to the required level without adding volatility or tail risk—but that’s when you have to consider the risk of illiquidity. What do you think the cash realizations from your illiquid investments might be before 10 years are up?

While it is demanding, this is why we believe it is worth making the intellectual effort to escape from the two-dimensional world view of Flatland. If you don’t, like the Square puzzling himself about the visiting disk, or the investor unable to redeem from a fund, you may fail to see a more comprehensive view of your risk—and may not meet your investment objective.

In Case You Missed It

  • U.S. Consumer Price Index: +0.1% month-over-month, +7.1% year-over-year (core CPI +0.2% month-over-month, +6.0% year-over-year)
  • December FOMC Meeting: The Federal Reserve raised interest rates by 50bps
  • U.S. Retail Sales: -0.6% in November
  • Japan Manufacturing Purchasing Managers’ Index: -0.2 to 48.8 in December
  • European Central Bank Policy Meeting: The ECB raised interest rates by 50bps
  • Eurozone Manufacturing Purchasing Managers’ Index: +0.7 to 47.8 in December

What to Watch For

  • Monday, December 19:
    • NAHB Housing Market Index
    • Bank of Japan Policy Meeting
  • Tuesday, December 20:
    • U.S. Housing Starts and Building Permits
  • Wednesday, December 21:
    • U.S. Consumer Confidence
    • U.S. Existing Home Sales
  • Thursday, December 22:
    • U.S. 3Q GDP (Final)
    • Japan Consumer Price Index
  • Friday, December 23:
    • U.S. Personal Income and Outlays
    • U.S. Durable Goods Orders
    • U.S. New Home Sales

    Investment Strategy Group