Risk matters

Conventional finance theory typically describes investor preferences in the two dimensions of expected return and risk, where risk is measured in terms of the standard deviation of returns.

In most circumstances this two-dimensional description of investor preferences fits well with the concept of diminishing marginal utility of wealth. Essentially the idea is that as your wealth piles up, each incremental dollar is going to make less difference to your quality of life than the one that came before it.

For example, consider the following two hypothetical alternatives for determining how much investible funds you may have accumulated when you retire:

(A)   the certainty of retiring with a $1.85 million retirement fund; or

(B)    the uncertainty of having to toss a coin to find out whether your retirement fund contains $0.85 million (heads) or $2.85 million (tails).

Pretty much everyone will prefer option (A). In both scenarios they have an “expected return” of $1.85 million, but in option (A) the standard deviation (risk) of the return is zero, whereas in the option (B) the standard deviation (risk) of their potential return is $1.0 million.

The choice between those two options was easy. But different people can have different preferences if you require them to make a sacrifice to reduce risk.

For example, think about which option you would choose if you had to choose between the following two alternatives:

(C)   the certainty of retiring with a $1.35 million retirement fund; or

(D)   (the same as (B)), the uncertainty of having to toss a coin to find out whether your retirement fund contains $0.85 million (heads) or $2.85 million (tails).

Some readers may prefer option (C), because they prefer the certainty of knowing that they definitely have $1.35 million to fund their retirement. But many other readers may favour option (D), because they can see that the expected value of the coin toss (i.e. the average of $0.85 million and $2.85 million) is significantly greater than the certainty of $1.35 million.

People who prefer (C) over (D) are implicitly taking the view that having their retirement fund boosted from $0.85 million to $1.35 million would make more difference to their quality of life than the bonus of having their retirement fund further enhanced from $1.35 million to $2.85 million.

These two options very roughly reflect two distribution of possibilities that an affluent saver with 10 to 15 years before retirement might be faced with if they’re choosing between a very conservative investment strategy and a very aggressive investment strategy. Option (C) can be thought of as representing the likely outcome if they invested everything in government bonds, while option (D) represents two reasonably likely (~ one standard deviation) outcomes that they could experience if they invested all their savings in a relatively aggressive equity fund.

Of course, most investors choose something that sits between these two extremes, investing their money in funds that contain a mix of fixed interest and equities, or in funds that favour lower-risk equities. The range of possibilities associated with such funds could be roughly represented as alternative (E) below:

(E)    The uncertainty of having to toss a coin to find out whether your retirement fund contains $1.1 million (heads) or $2.1 million (tails).

It may be interesting to reflect on whether you prefer this alternative (E) to both (C) and (D) above. If you do, then (like most investors), you would probably prefer a fund that has risk characteristics that fall somewhere between those for (C) and (D). Using the FMA’s risk indicator guide, funds that are invested entirely in government bonds (suiting investors who prefer option (C)) are likely to have a risk indicator of between 1 and 3, and aggressive equity funds (suiting investors who prefer option (D)) are likely to have risk indicators of 6 or 7. Investors who prefer alternative (E) are likely to better meet their risk preferences with funds that show a risk indicator of 4 or 5.   

 Indifferent to risk?

While most people putting aside money for the future are prepared to make a sacrifice to limit downside risk, I occasionally hear investors declaring that they are almost indifferent to risk, and only care about expected return. Why do they take this view?

Famously, Sam Bankman-Fried (the person behind the rise and fall of crypto-currency exchange FTX, now serving time in a US prison) claimed to be virtually indifferent to risk, always choosing to prefer the highest return regardless of risk. As I understand it, his logic was that he expected to end up as a big-time philanthropist, giving away all his money, and the world had so many problems that you could do as much good with your second billion and third billion as you could with the first billion, so he figured that there was no diminishing marginal utility for wealth ear-marked for philanthropy, and he should therefore focus on maximising return regardless of risk.  

To a certain extent this sort of logic might make sense for people who were confident that they had more than enough money to meet their and their family’s future needs, who believe they can make the world a better place by giving away everything else they might accumulate. Such investors could take a conservative approach with the funds they earmarked for their personal & family needs, but be prepared to take a lot of risk to maximise return for the surplus money that they intended to give away. (But they shouldn’t go as far as Bankman-Fried and take risks that could put them in jail!).

Common fallacies

However, in many other cases, I think that people who claim to be indifferent to risk are misunderstanding the distribution of future returns that they’re exposing themselves to. Some common fallacies that I believe sometimes effect investors’ thinking on these issues include the following:

• A belief that markets inherently reward all forms of risk.
• A mistaken belief that historical equity risk returns are a good guide to the “equity risk premium” that investors may earn in the future.
• A mistaken belief that the “expected return” represents the median possible return over a period of several years.
• A strong attachment to the “Gambler’s fallacy”, whereby they believe that bad years are significantly more likely to be followed by good years, such that volatility in investment returns is seen as mere noise around a pre-ordained upward trend.

I will discuss each of these fallacies in turn:

 The belief that markets inherently reward all forms of risk

It is a truism in investment markets that you must take on some risk in orders to achieve better returns than the “risk-free returns” that you could achieve by investing entirely in treasury bills or inflation-linked government bonds.

It also generally true that when you look at different funds with different asset allocations, the funds with the highest allocations to equities will have generally achieved better returns over the long term than funds that had more conservative allocations. (Although Accident Compensation Corporation stands out as an exception to this rule, having achieved better long-run returns than most other funds despite a markedly lower average allocation to equity markets).     

Most investors understand that returns can be correlated to risk and are used to reading the legally-mandated risk disclosures which indicate that higher risk is associated with “potentially higher returns”.

The problem can be that they will often take this observation too far and assume that investment markets automatically reward all forms of risk-taking. They therefore assume that investing in riskier funds or riskier stocks is likely to produce better long-term rewards than investing in lower risk alternatives.

However, the empirical evidence to support the notion that “higher risk means higher reward” is far more limited. If you carefully study historical data you can really only find strong evidence for one singular aspect of “higher risk means higher reward”, which is that equity markets have beaten fixed interest markets by a significantly greater margin over time than could be explained by chance alone.

In fact, when you look at how different stocks perform within the equity market, the evidence actually points in the opposite direction. Over the long term, more volatile stocks have tended to deliver worse returns than more stable stocks, as shown by the following data from a 2006 paper by Ang, Hodrick, Xing, & Zhang:

Source: Ang, Hodrick, Xing, & Zhang (2006); https://ssrn.com/abstract=681343

The data for this study ended in 2000. But we have performed comparable back-testing for the period since 2000, and find that the highest risk stocks have continued to deliver the worst returns over the period from 2000 to 2023, as shown in the graph below:

Source: Back-testing performed on Bloomberg, using MSCI & Bloomberg data.

The preceding two graphs under-state how truly terrible returns from volatile (risky) stocks have been, because these graphs are presented in terms of average monthly returns. Average returns tend to be artificially higher than compound returns when returns are particularly volatile. Think of a stock that rises 11% then falls 10% with each alternating month. On average, this stock is sliding backwards (an 11% rise is not quite enough to recover from a 10% fall), but the “average monthly return” it produces is +0.5% per month.

To correct for this distortion, the following graph shows the compound annual returns that investors would have achieved from baskets of stocks re-sorted monthly (since 2000) based on recent volatility. From this perspective, it should be very clear that rather there being a reward for risk within the equity market, there has actually been a penalty for tilting towards the most exciting (risky) stocks.

Source: Back-testing performed on Bloomberg, using MSCI & Bloomberg data.

Based on the long-term historical relationships between individual stock risk and subsequent return, it seems reasonable to expect that equity funds that skew towards higher risk will deliver worse returns over time. This is contrary to the misguided expectations of some investors, who seem to think that they should get better returns by investing in funds that skew towards the excitement of more volatile stocks.

A second aspect to consider when equating risk with return is that it is conceptually impossible that markets would reward a lack of diversification, which will sometimes be a major source of risk in many portfolios and funds. If you split the ownership of a diversified share market up between a bunch of undiversified funds, it is conceptually impossible that the average return of the funds investing in the share market would suddenly become better than the overall return of the share market.

Diversifying investment portfolios is a free lunch – it reduces risk, and on average it should not reduce return. However, this does not mean that an index fund investing in 2,000 different securities is automatically the best solution. A well-constructed fund or portfolio containing just 50 or 60 stocks can achieve over 95% of the potential benefits of diversification provided it contains a good mix of countries, sectors, and investment characteristics. And in any case, market capitalisation based indices are arguably failing the diversification test in today’s environment, with a heavy skew to US-based mega-tech companies, which potentially leaves a market-cap-weighted index fund vulnerable to some risks that could be diversified away in a more evenly weighted portfolio.

 Belief that historical returns over recent decades are a good indicator of future returns

Famously, equity markets have delivered significantly better returns than fixed interest markets over the 20^th and 21^st centuries. According to Dimson, Marsh & Staunton’s latest yearbook, US equities delivered nominal pre-tax returns of 9.6% per annum from 1900 to 2023, while US bonds delivered nominal pre-tax returns of just 4.6% per annum.

But is this a good guide to what may occur in the future?

In short, no. A key component of the return that equities have historically delivered to investors has been the cash that they were able to distribute to shareholders through dividends and buybacks.

Historically, US equities traded at much lower multiples to their underlying profitability and cash generation than is the case today. The high cash generation (~ dividend yields) due to these low valuations meant that investors were historically able to enjoy good returns despite the unfortunate reality that that the earnings power of existing listed companies inevitably tends to lag growth in the economy (due to new companies constantly emerging and taking a share of the “profit pool”). Today, the reality of existing companies ceding profit share to emerging new companies continues, but valuations are much richer. Accordingly, it is difficult to envisage US equities generating local currency nominal returns of much more than 7.5% per annum over the next 20 years.   

This is an issue that I have written about in past columns, so I won’t lengthen an already-long column by discussing this issue any further today.

 Belief that expected return = median possible return

Most people will be familiar with the bell curve of a normal distribution (pictured below). This is a perfectly symmetrical graph, where the area under the curve shows the relative probability of each value. For this distribution, the average value (the apex of the curve) exactly matches the median value, such that there it is equally probable that a value will be above or below the average.  

 

When people hear investment advisors telling them to expect an equity risk premium of (say) 4% per annum, they will often imagine that the range of possibilities will follow a normal distribution, and that there should therefore be a 50% chance that equities will outperform fixed interest by at least 4% per annum over the long term.

But does this graph above truly reflect the distribution of probabilities for investment returns?

If you look at share market returns over short periods of time (e.g. a month), the bell curve of the normal distribution seems to be a reasonably good proxy for how returns are distributed, as we can see in the graph below. This graph plots monthly returns in the US share market (for the last 50 years) against the theoretical curve implied by the normal distribution. If anything, this shows a slight positive skew, whereby returns are better than average slightly more than half of the time.

 However, when you combine normally-distributed short-term returns with the power of compounding, the distribution of possible outcomes becomes very positively skewed over longer periods of time, and should in theory get close to lognormally distributed, if the distribution of returns from one year to the next is truly random.

The graph below shows a lognormal return distribution that you might expect from a share market over a period of a decade. A high expected return (measured as a weighted average of all possibilities) is reflected in a small probability of truly spectacular returns combined with a much greater likelihood of fairly ordinary returns. If the potential distribution of 10-year return is distributed in a lognormal distribution as shown in the graph below, there would be a 59% probability that actual returns would be lower than the expected average return.

In this graph above, the expected average return is +8.25% per annum, but the most likely return is just +4.34% per annum, and the median return is +6.96% per annum. If the investor had been told to expect a return of +8.25% per annum, it is highly likely that they will end up a little disappointed.    

If we look at actual returns from history (see graph below), there have not really been enough decades of good data to definitively conclude whether long-term returns do in fact fall in a lognormal distribution, a normal distribution, or something completely different:

Source: Robert Shiller’s online data, http://www.econ.yale.edu/~shiller/data.htm

For what it’s worth, US share market data from the past 140 years does show that only 5 of the last 14 decades have delivered above-average returns. (Of course, average returns from the US share market have been particularly good over the past 145 years. But note that this is almost certainly an upwardly-biased sample, as I have selected one of the best performing share markets over a period of unprecedented growth in the world economy, which included with a significant upward re-pricing of equity markets towards the end of the period).  

In summary, even if it is rational to expect that investment returns will be good on average over the next decade, this doesn’t mean that they inevitably will be, and the most likely outcome is that returns will be lower than we expect, because an expectation of good average returns is skewed upwards by the small chance of particularly remarkable returns counter-balancing a greater probability of unremarkable returns.

Venture Capital

The difference between expected returns and most-likely returns can be particularly harsh when investors invest in early-stage venture capital in the hope of increasing their expected returns. This is because returns from venture capital tend to be very positively skewed (i.e. most VC investments disappoint, but the occasional VC investment performs spectacularly well).

To the extent that there is any evidence for a risk premium for venture capital investing, it seems that it is only achieved by a small percentage of specialist investors, and that small percentage of investors achieve most of their good returns on a small percentage of their investments. While individuals or funds dabbling in the occasional venture capital investment may believe that they’re enhancing their expected return, they’re almost always handicapping their most-likely return. Anecdotally, I’m aware of several people who have at some stage in their life sunk a significant portion of their net worth into some early-stage venture capital investment that caught their imagination. In the vast majority of cases, they’re significantly worse off as a result. While angel investors may make a valuable contribution to economic growth, it seems rare for them to achieve better returns than they could achieve from more conventional investing.

Belief in the gambler’s fallacy

Simply speaking, the gambler’s fallacy is essentially a gambler’s belief that the “law of averages” means that after a run of bad luck, they’re due for a bit of good luck. This is a clear fallacy at a roulette table, but belief in a similar phenomenon in listed equity investing can also contribute to investors under-appreciating the extent to which they’re putting their future wealth at risk when they move up the risk spectrum.

My impression is that when many investors anticipate an average return of (say) 9% per annum from their equity investments over the next decade, they understand that some of the annual returns will be a lot worse than this (say, -10%) and some of the annual returns will be much better than this (say, +28%), but they believe that the “law of averages” somehow pre-ordains that there will be as many good years as bad years, and they therefore think that there is a strong likelihood that their average return will be close to their expectation of 9% per annum after 10 or so years.

The reality is that the actual distribution of equity returns is much closer to a random walk than this. Although there has been a modest historical tendency for equity returns to reverse direction from one year to the next, it is only a very weak tendency. Further, if we try to deconstruct why equity returns have been slightly better on average in the year after a decline, the biggest explanation seems to be that dividend yields have been higher after share prices have declined, and higher dividend yields historically contributed to stronger returns in the following year. This would not be a significant saviour for investors if the US share market fell (say) 20% from current levels, as the dividend yield is already so low that boosting it wouldn’t make much of a difference for the return we could anticipate over the following year.

Different types of investments have different likelihoods of reverting from one year to the next. Generally, the pattern is that lower-risk more yield-based investments (e.g. government bonds) have the strongest tendency to reverse direction, while riskier more speculative investments (e.g. crypto-currencies or venture capital) are probably the least likely to reverse direction.

Hence, while the “gambler’s fallacy” may not entirely be a fallacy when applied to lower risk investments, it is a dangerous form of thinking when applied to riskier investments where future cashflow generation is inherently uncertain.  

Conclusions

Risk is real in investing.

If you choose to take more risk in your investment portfolio, this will most likely increase the probability of poor outcomes, even for time horizons more than a decade into the future.

Of course, adding risk can also significantly increase the likelihood of particularly favourable returns, provided that you add risk sensibly, by choosing to favour risk exposures that tend to be rewarded by investment markets. There is strong evidence that markets have historically rewarded investors who shift funds from fixed interest to equities, but there has been no reward for investors who tilt their equity portfolios towards higher risk stocks, or who add to their risk exposures by neglecting to diversify their risks.

Nicholas Bagnall is chief investment officer of Te Ahumairangi Investment Management

Disclaimer: This article is for informational purposes only and is not, nor should be construed as, investment advice for any person. The writer is a director and shareholder of Te Ahumairangi Investment Management Limited, and an investor in the Te Ahumairangi Global Equity Fund. Te Ahumairangi manages client portfolios (including the Te Ahumairangi Global Equity Fund) that invest in global equity markets. Te Ahumairangi manages client portfolios that tilt away from higher-risk equities, which means that the writer is biased towards one of the conclusions reached in this column. Te Ahumairangi also manages funds for Accident Compensation Corporation, which was mentioned favourable in the column.