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The alpha to beta of it

Here’s something that, despite more years in the investment game than I care to contemplate, I’ve never done before. Perhaps I should have. The results reveal interesting findings about the Bearbull Income Portfolio. You should try it for yourselves with your own portfolio.

The exercise comes under the heading, ‘Assessing a portfolio’s performance’; specifically, via those ubiquitous measures, alpha and beta. These two are thrown around indiscriminately in the investment scene. In crude terms, beta indicates the extent to which a portfolio relies on background forces for its performance; alpha measures how much performance might derive from an investor’s ability. As such, beta is borderline bad because it provides a free ride if the background forces happen to be going the right way or a costly detour if they’re moving the wrong way. Alpha is good because it quantifies how well an investor can find a smooth path through the investment jungle.

So is it a concern that the Bearbull portfolio used to be powered by lots of alpha but has seen that factor fade these past few years? Meanwhile, beta, whose chief function for years was to exert a calming effect on the portfolio’s otherwise good returns, now seems to power it (see the chart). Of course, it’s not that simple and, for starters, let’s strip away the mystery that comes from using Greek letters to describe a bit of investment maths.

Basically, alpha and beta derive from the simplest charting equation known to man, thought up just as soon as René Descartes first linked geometry and algebra in the early 17th century. The equation in question is the so-called ‘slope-intercept form’ of a two-dimension chart where the algebra reads as y = mx + b. So, draw a straight line within a system of x (horizontal) and y (vertical) coordinates and the equation will say whether the line slopes up or down (reading left to right), how steeply it slopes (its rise over run) and where it crosses the vertical axis.

To confuse matters – and for reasons I can’t begin to explain – finance theory takes this simple slope-intercept equation and substitutes beta for ‘m’ and – most confusing of all – alpha for ‘b’. Thus it ends up with finance theory’s so-called ‘single-index model’, for which two economists won the Nobel Prize, and says the expected return on a stock or a portfolio is bx + alpha, where ‘x’ is that background force or, in practical terms, the market to which a security or a portfolio is most exposed. Roughly translated, the equation says investment returns will be driven by the market’s returns multiplied by beta (that’s ‘bx’), plus alpha.

However, investment analysis needs data to draw this all-important line that finds the values for alpha and beta that shed light on past returns and – hopefully – predict future ones. The data are the periodical returns from the variables under observation; in Bearbull’s case, the monthly returns of the income portfolio and its so-called independent variable, the FTSE All-Share index. The average chart position of all those monthly returns becomes the sloping line. Put another way, the line is the average position of a scattergram of dots showing the simultaneous monthly returns of the Bearbull portfolio (y axis) and the All-Share index (x axis).

The slope line for the Bearbull portfolio shows that over its 23-year life it generates lots of alpha and has low dependence on the All-Share’s movements for its returns. The slope-intercept equation for monthly returns equals 0.53 times beta plus 0.37 per cent alpha. Given average monthly returns of 0.28 per cent for the All-Share index over the whole period, that means the equation becomes 0.53 times 0.28 per cent plus 0.37 per cent, or 0.52 per cent. Annualise that figure and, with a bit of rounding error, it comes to 6.2 per cent. Give or take, that coincides with the Bearbull portfolio’s average annual returns before dividends received and, by implication, it is a prediction of a typical month’s future returns.

All that alpha should be encouraging. But the concern is that a different picture emerges when alpha and beta are calculated over shorter periods. Hence the chart below, which shows those markers based on the portfolio’s five-year rolling-average monthly returns. In other words, each month’s data point is the average value for the preceding 60 months, which should be long enough to provide sensible figures.

The results show that the Bearbull portfolio used to generate lots of alpha, but has produced less and less to the extent that since late 2018 it has produced none at all (see the chart, which plots alpha against the right-hand axis). Simultaneously, the fund’s beta, which was drifting downwards for the 10 years 2004-14, has reversed and leapt upwards from the start of 2020 since when it has averaged the same as the market.



The jump in beta is less of a concern. It owes much to the first half of 2020 when – uncertain how to respond to Covid-19 – the All-Share index was all over the place and the income portfolio’s value stocks even more so. The portfolio’s 25 per cent drop in March 2020, while the market fell 15 per cent, was alone sufficient to tilt the five-year beta up by about a fifth from 0.8 to 1.0. Besides, I can live happily with a beta of 1.0 or so; to the extent that the fund has a long-term investment perspective and that the equity market on average rises more than it falls, it should be fine.

Not so, however, the steady evaporation of alpha. Absolute peak alpha was way back in 2005 when the fund was generating annualised alpha rates of over 14 per cent – an amount always unlikely to persist. Even in mid-2014, when the current seven-year decline began, alpha was running at 8.4 per cent annualised. Its erosion coincided with relatively poor performance. In the seven years to 2014, the fund’s total return beat the market five times; for the seven starting in 2015, the opposite was the case – five times the fund underperformed the market. The fact that only two of those years were lossmaking tended to obscure the deterioration.

As to remedies, they might be tougher to find. It’s not that the chief criteria for stock selection can change. The aim remains to buy shares in what appear to be good companies selling at reasonable prices; ‘good’ being defined by reference to conventional financial analysis with emphasis on free cash generation and ‘reasonable prices’ assessed by a stab at valuation driven by what seem like sustainable profits capitalised at appropriate target rates of return.

However, the chief point is to encourage readers to calculate alpha and beta for their own portfolios. All that’s needed is a decent slug of performance data for the portfolio and for a benchmark that reflects the portfolio’s characteristics. Using the ‘Linest’ and ‘Intercept’ functions of Excel, the rest is child’s play. The results will be thought-provoking. Get cracking.


Shares boughtDate dealt Price (p)  Cost (£) Price now (p) Value (£) Change (%)v All-Share (%)IndustryWeight (%)
1,665GlaxoSmithKlineFeb-001,28221,4821,44624,069 13-19Pharmaceuticals9
13,150NatWest 9% PrefsNov-12121 16,016177 23,210 467Fixed interest8
14,000Real Estate Credit InvJan-13110 15,432156 21,840 4211Speciality finance8
40,000RecordSep-1436.5 14,69879.6 31,840 11895Financials11
29,250Air PartnerSep-1484 24,71587 25,331 3-4Travel & leisure9
4,550VesuviusAug-15392 17,827555 25,253 4228Industrials9
12,806Randall & QuilterMar-1815119,354164 21,002 96Aim:insurance8
850The Williams Co'sAug-18$29.8720,136$24.6015,115 -18-17Utilities5
8,000Henry BootJul-1924419,60227522,000 1314Real Estate Inv't8
575Anglo AmericanAug-201,94411,2573,06217,607 5832Basic materials6
240Berkeley GroupAug-204,65711,2584,58210,997 -2-18Housebuilder4
4,775Stock SpiritsAug-2023111,08639118,670 7042Drinks 7
8,000Carr's GroupAug-2013811,08016112,880 17-2Foods5
3,650Moneysupermarket.comAug-2030211,0962509,118 -17-31Technology3
     Interest accrued    
Starting capital (Sept 1998)  £ 100,000Total283,892 184   
FTSE All-Share index  2,384  4,081 71   
Retail Price Index  164 30686   
Income distributed:  £ 223,865      
As at 8 Sept 2021. Source: FactSet, Investors' Chronicle