Hang the theory

Certainly, the Bearbull Income Portfolio defies conventional wisdom. Its returns have regularly beaten its benchmark, the FTSE All-Share index, yet without showing the volatility that is consistent with portfolio theory. In other words, the income fund has delivered the rewards without being lumbered with the supposed risks.

The table, Big reward, small risk tells the story. It is based on lots of data - monthly returns for the period 2000-10 - so it should be statistically significant. During these 11 years the income fund produced an average monthly return of 0.68 per cent. That might not sound a lot, but it is worth having. Put another way, the compound annual growth rate in the portfolio's value is almost 9 per cent. In contrast, over the same period the average monthly return from the All-Share index barely registers at just 0.06 per cent - the equivalent of a compound annual growth rate of 0.3 per cent.

Big reward, small risk

Theory tells us that the income fund's excess returns should be accompanied by excess risk; that the portfolio's returns should bounce around, being lovely in some months but horrible in others. If that were the case, then the portfolio's standard deviation would be much higher than it is. Standard deviation is a measure of how far a series of data deviates from its average. It is, if you like, the average distance of a series of figures from their average value. For the Bearbull income fund, the standard deviation is 3.16 per cent, which indicates that two thirds of the time each monthly return will be within the band of plus or minus one standard deviation of the average (ie, between 3.84 per cent and minus 2.48 per cent). That indicates a fair bit of bounciness, but nothing compared with the volatility of the All-Share's returns over the same period, which was 4.5 per cent, or anything between 4.56 per cent and minus 4.44 per cent.

So there you have it - the performance of the Bearbull income fund defies the theory. It offers the rewards without the concomitant risk. Conversely, for each unit of risk, it offers disproportionate rewards. What's going on?

I might want to persuade you that this is something to do with Bearbull's enviable stock-picking skills. When I add that the now-defunct Bearbull growth and speculative funds displayed the same characteristic, I might even start to believe that. However, for long periods those two portfolios kept much of their capital in cash, which tended to dampen volatility, while a large part of their returns depended on a few years' especially good returns. In contrast, the income fund has generally been pretty fully invested and so exposed to the vagaries of the stock market.

The best explanation is that this is to do with the nature of high-yield shares. Their prices are inherently more stable than shares in growth or recovery situations, where investment success is likely to depend on hard-to-predict events. Meanwhile, for high yielders, future dividends comprise a bigger proportion of the share price than in growth and speculative situations and the reliability of their dividends is pretty good. That limits the scope for how much share prices can bobble around.

That's fine, but it says little about why investment returns are so good. In Bearbull's case, this really could be something to do with stock picking. More generally, we can see why high-yielders are in demand in today's investment climate and we can add the familiar though slightly inadequate point that somehow investors serially under price high-yield shares. So, when their dividends continue to stream through, their share prices jump.

Whatever, it certainly does not do to underestimate the significance of dividends. Of the £226,000 of value added to the Bearbull Income Portfolio over its 12 years, 38 per cent has been via dividends distributed. Almost £11,000 of that came in 2010, the best year so far; though, assuming the portfolio's holdings stay as they are, something comfortably clear of £12,000 will be distributed in 2011. And - God willing - by mid 2012, the fund will have paid back its start-up capital in dividends. In these difficult times, that generates a warm feeling inside and prompts the thought that every investor should carve a decent chunk of his or her capital into an income fund. Then let portfolio theory go hang.

Dividend distribution from the income fund