Risk-Based Asset Allocation: Worth the Effort

by: Ioulia Tretiakova posted on: June 15, 2008 | about stocks: SPY    

Everybody knows the importance of asset allocation. But what exactly does it mean to get asset allocation right? The best asset allocation is the one that provides the highest return, but hindsight is 20/20. We know how difficult successful tactical asset allocation is for an individual investor. Holding a little bit of everything, relying on diversification and engaging in strategic asset allocation with the goal to control risk rather than chase returns (a notoriously fruitless exercise) is an alternative.

One aspect is often overlooked in the context of strategic asset allocation. Say an investor is deciding between 60% equities: 40% bonds, and 70% equities: 30% bonds. Investors know that equities are more risky than bonds and that the first asset mix will allow them to sleep better. But here comes the rub: the risk of asset classes themselves changes.

Rebalancing to a fixed asset mix

Let’s say we are in the beginning of the roaring 1990s and we decide (by running asset allocation software, going with a gut feeling or looking at a crystal ball, whichever works) that the asset mix of 60 S&P 500 and 40 bonds is right for us. Being disciplined investors and knowing about the benefits of rebalancing, we religiously rebalance to this fixed mix to ensure that the portfolio remains within our risk tolerance. Eight years later we end up with a perfectly rebalanced portfolio of 60/40. The portfolio still has the same amount of risk as it had in the beginning of the 90s, right?

Wrong.  Looking at the sector composition of the S&P 500 Index, we see that, as of December 31, 1990, the technology sector weight was 8.9%. Ten years later the technology weight was a whopping 28.2%. Given how risky the sector is, intuitively we feel that this changes the overall risk level of the S&P, significantly increasing it. In other words, despite all the rebalancing, we now have a significantly more risky portfolio than the one into which we initially invested.

click to enlarge images

Risk changes over time - but is more persistent than returns

This intuitive approach is confirmed by calculating the actual risk of the S&P 500 (as measured by the 252-day rolling standard deviation). At the beginning of 1990, the volatility was approximately 15%. As the technology weight ballooned, the overall S&P 500 volatility increased to 20%.

This simple example illustrates one important fact – risk changes over time, and so should your asset mix (if you want to control downside and sleep well at night). Notice that we are not suggesting chasing performance or timing the markets. But we do recommend watching the market’s pulse and adjusting the proportion of asset classes downwards that are becoming more volatile, whether in bull or bear markets. Similarly you can increase the equity weight during quiet markets. Simply, we suggest timing the risk, rather than return.

The reason you can do this is that the risk is persistent, which means that if markets were volatile in the previous month, they will likely be volatile in the following month and vice versa. One measure of persistence is autocorrelation. The autocorrelation for monthly volatility of the S&P 500 is around 60%; the autocorrelation for monthly returns is close to 0%. Translation: risk is persistent, return is not. The persistence of volatility is the raison d'être for the whole risk modeling industry, an increasingly important part of professional investment management.

Ideally, investors should employ asset allocation with the help of a regularly updated risk model, putting overall portfolio risk in the context of each individual investor’s risk tolerance. For do-it-yourself investors, access to a risk model and the expertise necessary to use it, is often not an option. Alternatively, as a rule of thumb, one could look at the CBOE Volatility Index [VIX] which measures the implied volatility of S&P 500 index options. Persistently higher levels for this index would suggest rebalancing into a slightly more conservative asset mix, perhaps a 5% equity weight reduction. Persistently low levels might indicate that a slight increase in equity weight is sensible.

Worth the effort

In our experience, rebalancing to a constant volatility, as suggested above, yielded 3-4% per annum higher returns than rebalancing to a fixed asset mix (using back-tested data over the last ten years ending December 2007). While actual returns may differ, this is a meaningful difference worthy of every investor’s consideration.

If in the long term risk equals return, focusing on risk management today will pay off in the form of robust returns in the future.

This article has 7 comments! Add yours below...

Ioulia Tretiakova

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This article has 7 comments:

  •  
    nickgogerty
    Jun 16 10:55 AM
    My Website
    by using a metric "monthly" that is smaller than your period of auto-correlation moment 252 days aren't you building in the autocorrelation tautologically.

    vol by definition is mean reverting (due to its constraints of 0 in teminus for the referent) and thus has auto-correlation, but I think it is important to perhaps calculate your vol on a 30 day rolling metric and then look for monthly auto-correlations. Perhaps you used a 30 day vol., but the chart indicates 252 (annualized) vol and then refers to monthly correlations.

    The serial auto-correlation in returns is close to zero as stated, but present and positive with a historically positive skew, hence stock market growth over time.

    A regularly updated traditional risk model using Monte carlo or mean variance allocation is a form of trend following in its own right. Not that, there is anything wrong with that, but it should be acknowledged for what it is.
  •  
    granger
    Jun 16 01:08 PM
    Good stuff, thank you. I have never considered rebalancing in this manner. Gave me a lot to think about.
  •  
    Ioulia
    Tretiakova
    Jun 16 01:52 PM
    My Website
    Thank you for your comments, Nick.

    You are absolutely right, one cannot use overlapping intervals to calculate autocorrelation because the metric will be naturally upward biased. The 252-day chart is there for illustration only, as you correctly observed. In autocorrelation calculation for observations to be IID, I used non-overlapping intervals, 21-day to be exact. In addition, to account for kurtosis, 3sd and higher events, such a few trading days in October 1987 were taken out since tail events are not persistent. An alternative, of course, is to use rank correlation.

    I also appreciate your observation on the degree of equivalence of trend-following and risk-based investing. We have stared at risk for a long time and at some point I investigated the source of good backtested returns we were observing. A natural hypothesis, as you stated, would be to assume that a significant portion of it comes from trending. However, there are several aspects that make risk-based approach quite different from trend-following.
    - Firstly, the turnover is very low (typically we observe 2-3 trades a year in the core portion of our portfolios with about 5-7 ETFs).
    - Secondly, correlation to managed futures is in the low 20's (part of it is of course comes from not using short ETFs in the core portion).
    - Finally, but most importantly, is that as a return estimation input of our portfolio construction engine we use equilibrium returns, or as a rough approximation, returns that are proportionate to risk. Magnitude of historical returns don't even enter the equation, only return volatility. We thus avoid chasing past returns, something a traditional mean variance allocation tool might do if it uses historical returns.
  •  
    Ioulia
    Tretiakova
    Jun 16 01:54 PM
    My Website
    User 209335 is me!
  •  
    Indexor
    Jun 16 07:53 PM
    Investors, both individual and institutional, do not care about risk or standard deviations or volatility. Most do not understand terminolgy such as "autocorrelation tautologically," "rolling metric" or "kurtosis." At the end of every quarter, year or whatever time frame is being measured, what matters most is the gross return.

    Investors may buy into a "lower risk portfolio" for a few of those time periods, possibly even relative returns to risk-adjusted indices for a while longer. But most will gravitate toward higher returns, regardless of whether they are obtained by "chasing returns," using inverse ETFs or risk-focused asset allocation.
  •  
    Ioulia
    Tretiakova
    Jun 23 06:09 PM
    My Website
    Indexor,

    As you say, most individual investors do not care about standard deviation or volatility. I wouldn’t say the same for institutional investors, however. But most investors certainly do care about risk: they hate loosing money. Professional money managers, from a business continuity standpoint and because of their responsibility to manage clients’ money in a manner that would allow them both to sleep well at night, must try to control portfolio downside. Risk-based asset allocation does just that.

    The risk budgeting approach does not necessarily produce lower risk portfolios: in quiet markets one would in fact increase the aggressive holdings weight, which would actually produce a portfolio that does better than its static asset mix counterpart.

    As we know, positive and negative returns are asymmetrical in dollar terms and to recoup a 25% loss we need 30% gain, a phenomenon also known as volatility drag. Clients do not need to understand all the terminology, but their portfolio manager must. A risk-efficient downside-managed portfolio will generate better returns in the long term.
  •  
    winyaz
    Jul 15 11:00 AM
    Very good article. For my stock portfolio I account for the volatility of each stock when determining position size. It makes sense to do something similar for an allocation of funds, however if I were to base the position size strictly off volatility, the bond funds would get a very large position size. Could you provide an example of how one might apply this, say to a basic portfolio of US stocks, Int'l stocks, and bonds?

    Don
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