How best to balance your portfolio

"Don't put all your eggs in one basket" sounds like sensible advice. Almost all investment guides extol the benefits of diversification, which has been called "the last free lunch in finance". However, you can take diversification too far.

There is evidence that beyond a certain point the benefits of spreading your bets start to diminish sharply, while the industrialist Andrew Carnegie famously advised his friends that "the way to become rich is to put all your eggs in one basket and then watch that basket". So which side should you take in the battle between diversification and concentration?

How much is too much?

At its most basic level, diversification means spreading your portfolio between investments that are less than perfectly correlated with one another (in other words, they don't all move in the same direction, by the same amount, at the same time). This should theoretically reduce your investment risk, without hitting returns commensurately in other words, it potentially improves the risk/reward trade-off.

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This makes sense for example, having some exposure to gold, bonds and cash, as well as equities, in your portfolio, can reduce the volatility of your returns, simply because each of these asset classes tends to behave differently under different economic circumstances.

But what about diversification at the level of a portfolio of stocks? A famous 1977 study by EJ Elton and MJ Gruber, published in The Journal of Business, found that the average standard deviation of a US share was 49.3%. In other words, nearly a third of the time, its value would go up or down by more than half.

However, if you bought another share, the combined standard deviation fell to 37.4% the portfolio became less volatile. And increasing the portfolio to ten shares cut this further to 24%.

To an extent, this is all common sense of course it's going to be less risky to hold two shares in a portfolio, rather than just one. However, there is a point at which you can over-diversify and it comes a lot sooner than perhaps you might think. Most studies show that having anything more than 15-20 shares in a portfolio has little impact on the amount of risk (as measured by the volatility of your returns, at least) you're taking.

For example, Elton and Gruber found that moving from a 20 to a 20,000-stock portfolio would only cut risk from 21.7% to 19.2% and 90% of the risk reduction resulting from this strategy came from the first 15 shares.

You then have to take into account the fact that, as well as providing little benefit, buying more shares increases your trading costs. Even in the age of online trading, most brokers charge a fixed fee per trade, and possibly a percentage commission as well. So having an overstuffed portfolio can significantly bump up your costs and therefore hammer your returns.

The ideal balance

So what is the ideal balance between concentration and diversification?It depends on your objectives. If you just want a portfolio that hugs the market, requires little work and doesn't attempt to beat the market, then spreading your portfolio makes sense. Of course, if you are going to go down this path then you should do so via low-cost passive funds, since there is little point in paying extra fees for "closet trackers" that just end up hugging the market.

You also need to make sure that the holdings in question are genuinely different a portfolio of 40 tech companies (as you might get from a tech index tracker) isless diversified than holding justa handful of firms acrossdifferent industries.

But if you want actively to manage your share portfolio on your own behalf, then having between 15 and 20 investments seems to be the best balance between diversification and concentration. And this matters just as much for professional investors, who also have to research and keep track of each stock in their portfolio.

I remember attending a presentation by an investment trust that had more than a hundred stocks in the fund's portfolio. I asked the investment team which ones they liked the best. They replied that they "loved each stock in their portfolio equally". The fund later, unsurprisingly, underwent a major reorganisation that involved cutting back on many of those "equally loved" positions in its overcrowded portfolio.

Finding high-conviction managers

Indeed, a study from 2012 by Danny Yeung and others looked at more than 4,700 US fund managers' portfolios and concluded that managers should have more faith in their own convictions.

The authors found that theoretical portfolios that only held each manager's top 20 stocks, rather than every stock in their fund, beat the market by an annual average of 4% a year between 1999 and 2009, while only taking a small amount of extra risk. (The top five choices did even better, but were significantly more risky.) The conclusion is that there's a very significant trade-off between diversification and conviction.

There are two ways to spot whether a fund manager or investment trust is concentrated or overly diversified. The first is to look at the percentage of the portfolio taken up by the top ten holdings. Another is to look at the "active share", which compares the difference between a stock's weight in a portfolio and its weight in its index.

While it's possible to have a high active share (generally seen as a figure above 60) and still be lightly concentrated (and vice versa), funds with high active scores tend to take big bets and, according to a 2013 paper byAntti Petajisto, also tend to outperform.