Modelling stock market returns
For me, investment management represents an attempt to select those risks which are balanced with commensurate returns (emphasis on the ‘commensurate’) and discard those risks which are not. And to that end, I, like every other asset allocator, trust in all kinds of models; derivatives of the famous Capital Asset Pricing Model, for example, and various Mean-Variance Optimisation models too.
Such models are certainly useful. But my faith in the validity of their output has its limits.
I’m not the only sceptic in the congregation. Those in my field often sound a maxim borrowed from computer scientists, warning of the peril associated with the many inputs. ‘Garbage in, garbage out’ they quip.
Being a deeper doubter, I have to confess that even that maxim troubles me. I don’t doubt its veracity in the physical sciences, but I notice that it gives rise to a belief among investment managers that higher-quality assumptions yield higher-quality outcomes. The danger is that increasingly intricate inputs generate increasing confidence in modeled outputs. I consider that to be a mistake.
I mention all of this because I want to present a simplified model to inform some sort of answer to the following questions…
What kind of returns might we see from investment in the British stock market over the next 10 years or so? (Spoiler: around 8.8% annualised, perhaps).
How attractive are British stock prices in the aggregate, is the market overpriced, underpriced, or fairly priced? (Spoiler: the market is likely moderately underpriced).
… and before I do, I want you to regard that model with an appropriate level of scepticism.
Having said that, it is a model that assists me in forming a suite of Capital Market Assumptions (CMAs, target risk and return rates for various classes of equity and bond investments) which, in turn, have all kinds of valuable practical applications both internally and externally. If you’re one of those wealth managers providing a cash flow planning service, for instance, you are – knowingly or unknowingly – reliant on a series of CMAs.
Looking back and looking forward
The simplest forecast I can make is to assume that the next 10 years will mirror the prior 10 years. It’s an approach that has its merits, prime among them is that it requires just one readily-available input set. It’s easily adapted too, if I suspect that the next 10 years will be a little better I can add, say, 1% or subtract 1% for the reverse.
For reference, investment in the UK stock market returned around 6.0% annualised over the most recent decade.
The fatal flaw in this approach is that the worse my reference market has performed, the less I expect of it in the future, and vice versa. That doesn’t sit right with me. Contrast, for example, the -1.5% annualised return between March 1999 and March 2009, and the +11.3% return between March 2009 and March 2019.
That’s why my preference is for a model that leaves room for greater future returns when past returns have been low and lower future returns when past returns have been high.
As luck would have it, there is another simple model that fulfills that obligation. It is based on Professor Jeremy Siegal’s observation that the ‘earnings yield is a good predictor of long-term real returns.’ I take the ‘good predictor’ part with a pinch of salt, but, that being the case, all I need to do to form a target for the long-term real return is to divide 1 by the reference market’s P/E ratio. (Prof. Siegel has a much more sophisticated view on the ‘earnings’ part than do I, but the principle is the same).
Taking a P/E ratio of 12.1 for the UK market, I get a ‘real return’ of 8.3% (1 divided by 12.1). To convert the ‘real return’ into a ‘nominal return,’ it is necessary to add a little extra for inflation; adding 2% gives me a 10.3% annualised target rate. Again, this is an approach that has its merits.
The flaw is that it lacks a reference timeframe, limiting its application for my purposes – I want to target a specific investment horizon, equal in this instance to ten years.
Imperfect as both models are, they do provide valuable context, something with which to compare my own modelled results.
Long run ‘expectations’
There is a popular model among asset managers often described as the ‘building block’ approach. The design, sophistication, and application of that model vary greatly among practitioners but the ‘blocks’ almost always number three, comprising ‘valuation change’, ‘growth’, and ‘income’. (Sidenote: I’m not sure where this approach has its genesis but Sebastian Page, in his excellent book ‘Beyond Diversification,’ tips a nod in the direction of a 1984 paper by Jarrod Wilcox titled ‘The P/B-ROE Valuation Model’. Having reviewed that paper, I can certainly see the resemblance).
It’s a model I like; it’s simple, easily adapted, and well-suited to my application requirements. Let me see if I can bring it to life…
Supposing you instructed me to ignore any effect from income payments (dividends for example) and estimate at what level the UK stock market might be in 10 years. There is an uncomplicated way to form a guessed answer. I mentioned earlier that the P/E ratio for the UK market currently stands at 12.1, meaning that the current level is 12.1 times the market’s aggregate earnings.
It follows then, that all I have to do is guess what level earnings will be at in 10 years and multiply it by what I believe the P/E ratio will be.
An example will help…
Assuming the aggregate price level for the UK stock market is 100 today, the underlying earnings will amount to 8.3 (100 divided by 12.1). If I grow those earnings at, say, 4.3% for each of the next 10 years, I get an earnings target of 12.6. I’ll further assume that the P/E ratio will rise from 12.1 today to 14.0 by then. Our future market level is 12.6 (future earnings) x 14.0 (future P/E ratio) = 177.
That is equivalent to an increase in the current level of 5.9% annualised.
Needless to say, I have no way of knowing what the P/E ratio will be in 10 years, nor do I know at what rate earnings will grow, but I can begin with reasonable estimates to form a ‘central’ forecast and work out from there.
Thus far, I have ignored the income building block in our three-block approach. This is the trickiest feature in my view. Over the years, I have adopted several different modes for estimating its impact on returns. I’ve settled on simply assuming that the current dividend yield remains constant and that those dividends are re-invested at the end of each year. Assuming a yield of 3.8%, the effect is to increase my 5.9% ‘capital return’ to an 8.8% annualised ‘total return.’
(Sidenote: I’ve included a brief description for each of those inputs at the end of this article).
Overpriced, underpriced or ‘fairly’ priced?
8.8% sounds attractive to me. But is it?
And if it is, how attractive is it?
Investment in stocks (also known as equities) is a very risky enterprise. Investment in UK government bonds (known as gilts) is less risky. (There are those that will dispute this, but they are wrong for all kinds of reasons). To entice investment, stocks need to offer a return greater than that offered by less risky investments. That extra bit of return is known as the ‘equity risk premium’.
If I purchase a gilt today which is due to mature in 10 years, I can expect to get an annualised return somewhere in the region of 3.7%, that being the current ‘redemption yield’. The difference between that yield (3.7%) and our expected stock market return (8.8%) describes a positive equity risk premium of 5.1%. The equity risk premium is an important consideration in my approach to investment.
I have what I describe as a ‘minimum required equity risk premium’. Markets that are ‘underpriced’ will offer a higher premium than my minimum and markets that are ‘overpriced’ will promise a lower premium.
Currently, my minimum for the UK is set at 3.6%.
That being the case, my model suggests that the British stock market is underpriced.
Conclusion
I’m inclined to accept that modeled outcome, I think it reasonable. The conditions under which I would expect to see significant discounting are undoubtedly present – there has been a long run of unwelcome news associated with the United Kingdom (witness, for example, four Prime Ministers in seven years), and that is something that very often fosters low prices.
Of course, even if my model correctly characterises the UK stock market as underpriced, there is no way of knowing when it will revert to a more neutral price level. The model I have described is not a trading tool, it has no application in the short run. Indeed, it may well be that British stocks trend toward a wider underpriced state in the months ahead; there is certainly plenty to be cautious about both at home and abroad.
In the long run, though, I think there is a good case to be made for owning British stocks.
A note on the input estimates I have used
P/E rising from 12.1 to 14.0: I assume that today’s P/E reverts to the mean.
4.3% growth: I assume that earnings rise in line with the OECD’s 10-year forecast for nominal GDP.
3.8% income: I take the current dividend yield and assume that the implied payout ratio remains static throughout.
3.6% UK equity risk premium: I use Professor Aswath Damodaran’s approximation for the historic equity risk premium in the US markets over the last 50 years (4.4%) and adjust it for the 0.8 relative standard deviation of the UK market (standard deviation of UK market divided by standard deviation of US market).