# The risk of passive portfolios

The risk of a passively managed portfolio is the risk of asset classes. Unlike actively managed portfolios where there are additional layers of risk such as manager risks, uncompensated risks are practically absent. Passive portfolios are, by definition, diversified so much that the only remaining risks are the ones which markets as a whole possess, and these tend to be the “compensated” risks for which investors tend to get paid. So… how risky are asset classes?

The most common risk measure of portfolios is the standard deviation of returns. Standard deviation is a statistical measure of the dispersion of returns relative to an average. To oversimplify, for normal distributions, one standard deviation is the distance from average that the thing being measured gets, about two thirds of the time. For example, if the average annual return of an index is said to be 10%, with a 20% standard deviation, that means that in only one third of years will there be a return outside of the range -10% and +30%.

Most statistical distributions follow the “bell curve” (called that because it looks like a bell), also known as the “normal distribution ” or “Gaussian”, and for these types of distributions one standard deviation either side of mean (average) covers about 68% of data points, two standard deviations cover about 95% and three standard deviations about 99.7%. This 68-95-99.7 rule is called the “three sigma rule”. There is a good web page at Stanford University which has some java based charts, explaining this principle graphically. See http://www-stat.stanford.edu/~naras/jsm/NormalDensity/NormalDensity.html

The nice thing about standard deviations is that they are easy to calculate with a spreadsheet, and easier to quote. It takes no time at all to say “this portfolio has a standard deviation of 10%”, which is fortunate because quoting standard deviations to a retail investor is usually nothing but a waste of time, for the simple reason that most lay people don’t understand it!

Even someone that understands what a standard deviation actually means can not immediately deduce the answers to such questions as “how much can I expect this asset to fall during bear markets?” and “how long do these bear markets last?”

It is true that a statistician could reconstruct some of that data using statistical formulas, but only after making a number of assumptions about the distribution of the data such as whether or not it is really normally distributed, an assumption which in fact we know not to be entirely true.

Being aware of the main fault with standard deviations, that nobody really understands what they mean, and their secondary fault that people who do know what they are know that they don’t really work all that well, we wanted another way of showing the risk of a portfolio.

There are plenty of methods of risk measurement out there, many of them souped up variations on standard deviation which supposedly improve technically on standard deviation in one way or another, but we feel they all share the same basic problem as standard deviation: it is really hard for a lay person to visualise the level of risk they are taking on. Thus, while many advisers may be fulfilling their legal obligations to disclose risks by including a lot of quoted standard deviations in their financial plans, their clients just aren’t getting it. That perhaps is why fights sometimes break out between clients and their advisers when the portfolio gets hit by an entirely routine and common bear market.

Our solution is a graphical representation of risk. Borrowing from the techniques of trading, we display risk in terms of a portfolio’s “drawdown”. Drawdown is the amount that a portfolio has fallen below its previous highest high. We use the measure in a slightly different way to that employed by traders, but the method does translate quite well into a form suitable for portfolio constructors.

Drawdown in the way we use it is simply how far below a previous maximum the market is trading at any given time. The best way to explain it is just by showing some pictures. This first chart shows the All Ordinaries ASX200 Accumulation index, a common performance benchmark of Australian shares, plotted on a logarithmic axis against the highest highs it had achieved prior to that time. The shaded area is the amount the portfolio has fallen at any given moment. (Data period plotted is January 1980 to April 2008)

This next chart shows, as a percentage, how great those falls were:

The answers to the questions which a lay investor might ask are very clear from such a chart. How often does the market go backwards? How big are the big falls and how frequent are they? Is the latest drop unusual in size compared with history?

The method is equally applicable to portfolios, in fact that is where the method particularly shines because it provides a very easy way to explain the benefits of diversification.

The following chart has the drawdowns of the ASX200 (in blue) and the MSCI World Index (in red), representing international developed market shares over the same 1980-2008 time period. The green series is a simple 50/50 combination of the two of these.

What should be immediately obvious from the above chart is the way that the combination of domestic and international shares never had drawdowns as great as the largest drawdown suffered by either asset class. It shouldn’t be too difficult to see why either, this chart making the concept of blending portfolios a lot easier to understand than if we were to quote more traditional measures of risk such as the standard deviation of each asset class and their covariance.

In fact, if you look really closely you’ll see that at some points, most notably right at the end of the chart, the green line actually had a lower drawdown than either asset class individually. This was not a miscalculation, that is the result of portfolio rebalancing, moving money from the overweight asset into the underweight one. That kind of contrarian discipline often results in a slightly higher return, though not always.

Adding additional asset classes tends to make the portfolio behave even more benignly. Listed property and international emerging market stocks are also available, blunting the sharp edges from the maximum drawdown charts still further.

If an even lower level of risk is desired, one can start adding “conservative” asset classes like bonds and cash. A portfolio can be diluted down to have basically zero drawdown by adding a sufficient mixture of conservative assets.

So how risky are multiple asset class portfolios?

We’ve prepared a lot of different drawdown charts over time and have even developed software for exploring the effect on drawdown charts of changes in things such as the amount of a tilt toward small companies and value, emerging markets, different international vs. domestic ratios etc. It is our conclusion from these calculations that tilts of this kind make little difference in the long term to maximum drawdowns. In the above charts the Australian market tended to have greater falls than international markets in the earlier period, but more recently has been much more benign.

That sort of behaviour is to be expected. Different asset classes go through their cycles at different times, and it is not unusual for some parts of a portfolio to do well at some times while others do poorly. If it were possible to predict which parts would do well, in advance, then we could tilt the portfolio toward these favourably positioned asset classes. Unfortunately, the track records of market forecasters of all sorts, from newsletter gurus to tactical asset allocation using managed funds, indicate that this skill is not widely possessed.

This chart illustrates one of the principles which we have noticed. The three portfolios here are all “growth” portfolios with an 85% allocation to shares and property, and 15% to cash and bonds. They have fairly similar drawdowns in absolute terms, with none of these portfolios seeming to consistently be superior to the others in terms of average drawdowns reached during bear markets. The three portfolios are:

- in blue, a traditional portfolio made up only of the commonly used market indexes, property, bonds and cash;
- in orange, as per the traditional portfolio, but half of the international shares have been allocated to emerging markets; and
- in green, a portfolio where all the shares allocation is in “Fama French” value and small cap indices.

This is a fairly common pattern which we have observed. The “tilted” portfolios tend not to be all that different in terms of drawdowns achieved. In the previous chart we see that in 1994 the emerging markets portfolio had a bigger drop than the conventional or Value and Small portfolios, but in 2002 the conventional portfolio lost more. The Value and Small portfolio during this period generally lost a little less, but in other periods similar portfolios have had bigger drops than conventional.

In order to have a meaningful impact on portfolio drawdown, the only reliable “tilt” you can make is toward the conservative asset classes, bonds and cash. The different risks of different styles of equity investing do not tend to manifest themselves as volatility.

The main difference between the portfolios is one of “tracking error”, a form of risk which is mainly psychological in nature. If you want a portfolio that will be “vanilla”, i.e. one which will only underperform when everyone else’s portfolio is underperforming, then the conventional portfolio is appropriate. An unconventional portfolio introduces the risk of your portfolio falling at a time when everyone else’s portfolios are doing just fine. For some people, that is a very bad thing, and hence conventionality is a factor that needs to be taken into account.

Incidentally, in the period of these portfolios’ tests although the downside was roughly the same for the three growth portfolios the returns were different. The emerging markets tilted portfolio outperformed the conventional portfolio by nearly 1.5%pa, and the value and small cap tilted portfolio outperformed by just over 1%pa. (Return is on the vertical axis, monthly standard deviation is on the horizontal axis, as is traditional in these charts, so an asset in the upper right is a high risk/high return asset class, lower left is low risk and low return, upper left is low risk and high return, and lower right is high risk and low return.)

The most (only?) effective way to change a portfolio’s downside risk is to vary the allocation between growth assets and conservative assets like cash and bonds. The chart below shows six different portfolios which are identical in every sense except that the allocation to bonds and cash is increased by 20% for each portfolio. An even more conservative portfolio could have been devised by shifting money from the bond component to the cash component, if required.

The drawdown chart makes the difference in risk quite obvious, something which can’t necessarily be said of a more conventional return vs. standard deviation chart for the same portfolios. As before, annual average return is on the vertical axis, monthly standard deviations are on the horizontal axis:

**Just how risky then are asset class portfolios?**

Using longer term data (which unfortunately we don’t have for some asset classes, like emerging markets), the conventional (ordinary market index) portfolios with 100% shares and real estate tend to have a downside risk in the largest market drops of the last 40 years of about 30%. We round this up a little to 35%, just to add a safety margin into our assumptions.

Given our shorter term analysis with emerging markets, value and small companies, we make an assumption which we consider to be reasonable, though we are not certain of it, that portfolios with some of the large company stocks substituted by emerging markets and small companies and value companies will have roughly the same drawdown, though there will be fluctuations in the shorter term.

By diluting portfolios’ risk down with cash and bonds, drawdown can be reduced to very near zero. (A 100% cash portfolio would have zero drawdown risk, assuming it is invested with a good quality bank or in quality government treasury notes and bank bills).

So there is the answer: investors in highly diversified passive portfolios risk between 35% and 0% of their capital, depending on the asset allocation. To experience these losses, you would need to invest just before a major fall, and then pull out again at the bottom. Not necessarily a likely outcome, but possible. Risk management is about dealing with probabilities, so for our current purposes we think this is the best answer we can give.