Risk Budgeting Using Long/Short Equity

Like a popular diet plan, the term “risk-budgeting” is often discussed, and generally understood, but rarely followed in practice, it seems. In part, like an active “20-something” not needing to think seriously about the consequence of their diet choices, an unprecedented stable and largely upward moving market has made the topic a novel conversation piece among investment academia and in some cases, institutional investors, but not much more.

However, just as Father Time will wield his will on all of our metabolisms, the markets will not be as forgiving at some point in the future…maybe even soon. Which means advisors are possibly entering a period where investment selection, and more importantly, portfolio construction in the pursuit of attractive returns, will once again reign supreme in the battle for client loyalty. As we all know well, if you want to keep your clients—show them returns. The difference is now those returns won’t come free of “risk credits.”

When thinking about the question of risk budgeting we first need to discuss a “risk unit.” There are a few different measurements for risk, so let’s use volatility as a proxy for risk unit. Imagine an investor has $100 to invest and equities have a risk unit cost of 15, while fixed income has a risk unit cost of 4 (both numbers are representative of approximate historical volatilities). For investors who have indicated they are moderate investors, let’s assume they’d be comfortable with a traditional 60/40 equity/bond mix. By extension, they are implying they have 10.6 risk units to spend.

As we know that is only half of the equation though. Like all investors, our imaginary investor wants to maximize return potential for each risk unit spent. So, let’s assume going forward our return for equities is 8% and 3% for fixed income. Without considering the magic of correlation, our investor’s portfolio return expectation is therefore 6%.

For every risk unit spent we expect to receive 0.55% return or in dollar terms, 55 cents per risk unit spent. The goal of portfolio construction, through the lens of risk budgeting, is to try to build a portfolio that can beat this portfolio’s assumed return without increasing the number of risk units spent.

As the title of the paper implies we’re going to explore using long/short equity to do this. First, let’s assume a long/short equity return of 7%, with a cost of 8 risk units invested. If you doubt this combination is possible, I’d suggest you give us a call. Let’s also assume you carry an opinion about a “risky” asset (e.g., a specific sector) and your projection for the “risky” asset is 11%, but it comes at a price of 20 risk units per 100% invested.

If we were to reduce our equity exposure to zero it would free up 9 risk units. In a scenario where we then spent the maximum amount on long/short equity (8 units), our return expectation would be reduced without deploying leverage. Because this might not be desired, let’s explore splitting the allocation between long/short equity and a “risky” asset. In this case, a 50/50 split would cost 8.4 units (14 x 60%) and our equity allocation return projection, without considering correlation, goes from 8% to 9%. Our full portfolio’s expected return goes from 6% to 6.6% with a risk “spend” of 10 units.

This is made possible because the long/short equity allocation is getting a disproportionate return per risk unit relative to a broad market allocation which allows the remaining risk units to be spent on a sector or assets that are projected to outperform, but with more risk. The chart below summarizes the above paragraph.

Market Equity Fixed Income Long/Short Equity “Risky” Asset 60 E / 40 D portfolio 60 L/S / 40 D Portfolio 30 L/S / 30 R / 40 D Portfolio
Projected Return 8.00% 3.00% 7.00% 11.00% 6.00% 5.40% 6.6%
Projected Risk (units) 15 4 8 20 10.6 6.4 10.00

Allocating risk also works when solving for a low return environment in the fixed income space. This thought process would include reducing the fixed income exposure while using long/short equity and the market to optimize your risk spend to maximize return. An example of this is below.

Market Equity Fixed Income Long/Short Equity “Risky” Asset 60 E / 40 D Portfolio 35 L/S / 35 E / 30 D Portfolio
Projected Return 8.00% 3.00% 7.00% 11.00% 6.00% 6.15%
Projected Risk (units) 15 4 8 20 10.6 9.25

Using this concept, one could also look at other types of risk in the portfolio (Drawdown, Credit, Duration for example) and optimize to a lower risk number or higher return.

Like a diet plan that tells us to “spend” our calories any way we’d like as long as we don’t break the budget, risk budgeting allows you to think creatively about solving investment-related problems through holistic portfolio construction with investments that have specific roles in a portfolio. So, after you’ve worked hard building portfolios for the future, feel free to have the cookie instead of that salad!

Read more in the The (Really) Long and the Short of It >