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Diversification: Do you really understand it? (Part 2 of 3)

They say that there is no such thing as a free lunch in investments.  I’m not sure who ‘they’ are, but they’re wrong.  Diversification is a prime example of a free lunch that pension fund trustees should be looking for.

Part 2: Beware “diworsification”

In Part 1, we argued that it is more useful to think in terms of diversifying risks rather than assets.  In this part, we are going to look at how the risk reduction benefits from diversification can quickly be eroded if each risk you take is a little less well rewarded than the one before it.

The best way of illustrating this is graphically.  However before we do so, we need to explain what the charts mean and this involves maths.  Apologies to those for whom the following seems condescending, but it’s tricky to cater for a diverse audience.

We’ll start with straightforward diversification as per the theoretical textbook.

Imagine that we have found a number of assets that offer rewarded risk, and that the risk from each asset is completely unconnected to the risks from the other assets.  So if one asset were to fall in value, then it would give you no clues as to whether any of the other assets would do badly or well.  We call this being ‘uncorrelated’.

Let’s also imagine that each of these assets offers exactly the same level of expected reward per unit of risk.

So let’s suppose:

  • That each asset has a long-term return of 2% pa above the return on cash.
  • The ‘volatility’ of each asset is 4% pa. 

‘Volatility’ is a measure of risk.  The difference between the actual return and the expected return should be less than the ‘volatility’ in two years out of three.  So in this example, we expect the return to be in the range of 2% (=2-4) worse than cash up to 6% (=2+4) better than cash with a two-thirds probability.  So there is a 1-in-3 chance that the return in any given year will be outside of this range.  (For the mathematically inclined, it is a standard deviation).  An asset with a volatility of 2% would be half as risky.

  • Each asset is uncorrelated to all of the other assets.

Investing 100% of your portfolio in one of these assets would give you an expected return of 2%pa above cash with a volatility of 4%pa.

In our imaginary world, all of these assets have the same long-term return, so splitting your portfolio 50:50 between two of the assets would not affect your expected returns.  However, there is a chance that if one of them did badly, this might be offset by the other doing well.  So the risk decreases.  In this case, the volatility  would reduce to 2.8%pa. 

Splitting your portfolio between more assets would further reduce your risk without harming your expected returns, as can be seen in the chart below.  This is the free lunch.

The ‘information ratio’ is the return divided by the risk, and is a good measure of how effectively your risk budget is being spent.

Unfortunately, we cannot invest in this imaginary world.  There are two problems we face in the real world.


We appreciate that “diworsification” is a corny pun.  Sorry!  As actuaries, we are not permitted to dabble in real humour.

One of our assumptions was that all of these assets yielded the same expected return.  This is a heroic assumption and unlikely to be borne out in practice.  It is likely that our second best idea for an investment will not be quite as good as the best one.  And the third best will be slightly weaker that that, and so on…

If that is the case then moving away from being 100% invested in our favourite asset will dilute our returns (as well as reducing our risk.) 

For example we have reworked the chart above assuming that each ‘bet’ had only 90% of the excess return of the previous.  So the annual expected returns above cash would be 2% for Asset 1, 1.8% for Asset 2, 1.62% for Asset 3. 

We also look at the results of assuming a 20% reduction in returns for each successive asset.

So if each idea is only 90% as good as the previous one, then diversification starts to work against you (in terms of return per unit of risk) after you have added your 12th best idea.  Up until then it would have been beneficial.  If each idea is only 80% as good as the last, then this point is reached after adding only six assets.

The practical implication is to take care when adding more and more to your portfolio or strategy.  If your new ‘bets’ or sources of return are not as good as your existing ‘bets’ then you are likely to erode the advantage of diversification very quickly.

However, we have still been assuming that the risks from each asset are completely unrelated to the others.  This is unrealistic, and brings us to our second problem.  We’ll deal with “correlation” in the third and final part of this series.

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