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A scatter gram approach

In my last few articles, I have discussed how standard deviations can be used to measure the volatility of asset classes, sectors and funds, so providing a key tool in portfolio planning.

By way of a quick reminder, the higher the standard deviation, the higher the historic volatility of an asset. Thus, the relative volatilities of hundreds of funds can be quickly determined by scanning through their standard deviations.

I would now like to look at three further useful tools in measuring volatility. The latter two are useful in that they also bring into the equation the relationship between risk and reward – that is, historical standard deviations considered alongside historical past performance.

The first of these measurements is the beta and compares the standard deviation of a fund against the standard deviation of the sector average. If the average standard deviation of an investment sector over a period is four, the following betas would be noted for each fund.

It can be seen that the beta does nothing more than illustrate relationships between the volatility of different funds. Yet when assessing the merits and drawbacks of any fund, the beta provides a straightforward assessment of its volatility relative to the sector average without having to spend extra time looking at the whole sector.

Regarding the use of the beta, a couple of examples should assist. If a client wants to invest in the above sector but seeks a more volatile fund, his adviser might seek a fund with a high beta. For a different client seeking to reduce risk, the adviser might seek a low beta. Betas above one represent funds with above-average volatility while those below one represent lower-volatility funds.

Finally, it is usual although by no means invariable to find funds with high betas in the top or bottom quartiles in the past-performance tables as they generally enjoy higher highs and lower lows than funds with low betas. To make sense of this, it is important to consider the second measure – the alpha.

A semi-technical definition of the alpha is “the excess return per unit of risk”. Put more simply, the alpha assesses the past performance which could have been expected of a fund for a given level of historic risk. It achieves this by comparing the relationship between risk and reward of all the funds in a sector and determining the average of these funds.

I have always found it easier to understand alphas by relating them to scatter grams (the third measure I noted at the start of this article). With a scatter gram, the diagonal line represents the average rate of return for each level of risk and you can see that – as almost invariably happens in scatter grams – most funds have a risk/return relationship (or alpha) very close to the average.

Note that whereas the sector average for betas is denoted as one, the sector average for alphas is nil. A positive alpha means a fund has produced a higher rate of return than the sector average for that level of risk while a negative alpha indicates a lower rate of return than the sector average relative to the volatility of the fund.

You can see from the scatter gram (below) that Fund A has had high volatility, as evidenced graphically by its position along the risk axis. You should also note that its past performance has been significantly better than other funds with similar volatility. This fund will have a high positive alpha. Other funds of similar volatility with performance just above the average will have a low positive alpha.

By contrast, Fund B, while also having a high standard deviation relative to the sector, has produced poor past performance figures relative to that volatility. It is therefore below the average line on the scatter gram and will have quite a high negative alpha. Funds with similar volatility with performance just below the average line will have a low negative alpha.

Bringing these issues into focus, a summary of the above funds is instructive (below). At a glance, we can see Fund A has had much higher volatility than the sector average (high beta) but performed much better than could have been expected against its sector peers. By comparison, Fund B, while being less volatile, has performed much worse than funds with similar volatility. The rest of the data in the chart should now be fairly self-explanatory. An ability to read and understand these measurements is surely a great benefit to advisers in ongoing fund selection.

It is important to note that these are historic measurements. We are always told past performance is not necessarily a guide to the future but funds with historic high volatility tend to remain volatile.

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